Eur. Phys. J. C (2013) 73:2373DOI 10.1140/epjc/s10052-013-2373-2
Special Article - Tools for Experiment and Theory
Implications of LHCb measurements and future prospects
The LHCb Collaboration1,
andA. Bharucha2, I.I. Bigi3, C. Bobeth4, M. Bobrowski5, J. Brod6, A.J. Buras7, C.T.H. Davies8, A. Datta9,C. Delaunay10, S. Descotes-Genon11, J. Ellis10,12, T. Feldmann13, R. Fleischer14,15, O. Gedalia16, J. Girrbach7,D. Guadagnoli17, G. Hiller18, Y. Hochberg16, T. Hurth19, G. Isidori10,20, S. Jger21, M. Jung18, A. Kagan6, J.F. Kamenik22,23, A. Lenz10,24, Z. Ligeti25, D. London26, F. Mahmoudi10,27, J. Matias28, S. Nandi13, Y. Nir16,P. Paradisi10, G. Perez10,16, A.A. Petrov29,30, R. Rattazzi31, S.R. Sharpe32, L. Silvestrini33, A. Soni34, D.M. Straub35,D. van Dyk18, J. Virto28, Y.-M. Wang13, A. Weiler36, J. Zupan6
1CERN, 1211 Geneva 23, Switzerland
2Institut fr Theoretische Physik, University of Hamburg, Hamburg, Germany
3Department of Physics, University of Notre Dame du Lac, Notre Dame, USA
4Technical University Munich, Excellence Cluster Universe, Garching, Germany
5Karlsruhe Institute of Technology, Institut fr Theoretische Teilchenphysik, Karlsruhe, Germany
6Department of Physics, University of Cincinnati, Cincinnati, USA
7TUM-Institute for Advanced Study, Garching, Germany
8School of Physics and Astronomy, University of Glasgow, Glasgow, UK
9Department of Physics and Astronomy, University of Mississippi, Oxford, USA
10European Organization for Nuclear Research (CERN), Geneva, Switzerland
11Laboratoire de Physique Thorique, CNRS/Univ. Paris-Sud 11, Orsay, France
12Physics Department, Kings College London, London, UK
13Theoretische Elementarteilchenphysik, Naturwissenschaftlich Techn. Fakultt, Universitt Siegen, Siegen, Germany
14Nikhef, Amsterdam, The Netherlands
15Department of Physics and Astronomy, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
16Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel
17LAPTh, Universit de Savoie, CNRS/IN2P3, Annecy-le-Vieux, France
18Institut fr Physik, Technische Universitt Dortmund, Dortmund, Germany
19Institute for Physics, Johannes Gutenberg University, Mainz, Germany
20Laboratori Nazionali dellINFN di Frascati, Frascati, Italy
21Department of Physics & Astronomy, University of Sussex, Brighton, UK
22J. Stefan Institute, Ljubljana, Slovenia
23Department of Physics, University of Ljubljana, Ljubljana, Slovenia
24Institute for Particle Physics Phenomenology, Durham University, Durham, UK
25Ernest Orlando Lawrence Berkeley National Laboratory, University of California, Berkeley, USA
26Physique des Particules, Universit de Montral, Montral, Canada
27Clermont Universit, Universit Blaise Pascal, CNRS/IN2P3, Clermont-Ferrand, France
28Universitat Autonoma de Barcelona, Barcelona, Spain
29Department of Physics and Astronomy, Wayne State University, Detroit, USA
30Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, USA
31Institut de Thorie des Phnomnes Physiques, EPFL, Lausanne, Switzerland
32Physics Department, University of Washington, Seattle, USA
33INFN, Sezione di Roma, Roma, Italy
34Department of Physics, Brookhaven National Laboratory, Upton, USA
35Scuola Normale Superiore and INFN, Pisa, Italy
36DESY, Hamburg, Germany
Received: 28 November 2012 / Revised: 22 February 2013 / Published online: 26 April 2013 CERN for the benet of the LHCb collaboration 2013. This article is published with open access at Springerlink.com
Abstract During 2011 the LHCb experiment at CERN collected 1.0 fb1 of s = 7 TeV pp collisions. Due to the
e-mail: [email protected]
large heavy quark production cross-sections, these data provide unprecedented samples of heavy avoured hadrons. The rst results from LHCb have made a signicant impact on the avour physics landscape and have denitively proved the concept of a dedicated experiment in the forward
Page 2 of 92 Eur. Phys. J. C (2013) 73:2373
region at a hadron collider. This document discusses the implications of these rst measurements on classes of extensions to the Standard Model, bearing in mind the interplay with the results of searches for on-shell production of new particles at ATLAS and CMS. The physics potential of an upgrade to the LHCb detector, which would allow an order of magnitude more data to be collected, is emphasised.
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . 21.1 Current LHCb detector and performance . . 31.2 Assumptions for LHCb upgrade performance 4
2 Rare decays . . . . . . . . . . . . . . . . . . . . . 42.1 Introduction . . . . . . . . . . . . . . . . . . 42.2 Model-independent analysis of new physics contributions to leptonic, semileptonic and radiative decays . . . . . . . . . . . . . . . . 4
2.3 Rare semileptonic B decays . . . . . . . . . 52.4 Radiative B decays . . . . . . . . . . . . . . 102.5 Leptonic B decays . . . . . . . . . . . . . . 112.6 Model-independent constraints . . . . . . . . 132.7 Interplay with direct searches and model-dependent constraints . . . . . . . . . 14
2.8 Rare charm decays . . . . . . . . . . . . . . 172.9 Rare kaon decays . . . . . . . . . . . . . . . 182.10 Lepton avour and lepton number violation . 182.11 Search for NP in other rare decays . . . . . . 19
3 CP violation in the B system . . . . . . . . . . . . 203.1 Introduction . . . . . . . . . . . . . . . . . . 203.2 B0(s) mixing measurements . . . . . . . . . . 203.3 CP violation measurements with hadronicb s penguins . . . . . . . . . . . . . . . . 30
3.4 Measurements of the CKM angle gamma . . 32
4 Mixing and CP violation in the charm sector . . . 434.1 Introduction . . . . . . . . . . . . . . . . . . 434.2 Theory status of mixing and indirect CPviolation . . . . . . . . . . . . . . . . . . . . 48
4.3 The status of calculations of ACP in the
Standard Model . . . . . . . . . . . . . . . . 514.4 ACP in the light of physics beyond the
Standard Model . . . . . . . . . . . . . . . . 534.5 Potential for lattice computations of directCP violation and mixing in the D0D0 system 57
4.6 Interplay of ACP with non-avour
observables . . . . . . . . . . . . . . . . . . 574.7 Future potential of LHCb measurements . . 604.8 Conclusion . . . . . . . . . . . . . . . . . . . 625 The LHCb upgrade as a general purpose detector in the forward region . . . . . . . . . . . . . . . . 635.1 Quarkonia and multi-parton scattering . . . . 635.2 Exotic meson spectroscopy . . . . . . . . . . 65
5.3 Precision measurements of b- and c-hadron properties . . . . . . . . . . . . . . . . . . . 65
5.4 Measurements with electroweak gauge bosons 675.5 Searches for exotic particles with displaced vertices . . . . . . . . . . . . . . . . . . . . . 69
5.6 Central exclusive production . . . . . . . . . 70
6 Summary . . . . . . . . . . . . . . . . . . . . . . . 716.1 Highlights of LHCb measurements and their implications . . . . . . . . . . . . . . . . . . 71
6.2 Sensitivity of the upgraded LHCbexperiment to key observables . . . . . . . . 73
6.3 Importance of the LHCb upgrade . . . . . . 75Acknowledgements . . . . . . . . . . . . . . . . . . 75References . . . . . . . . . . . . . . . . . . . . . . . 75The LHCb Collaboration . . . . . . . . . . . . . . . 89
1 Introduction
During 2011 the LHCb experiment [1] at CERN collected 1.0 fb1 of s = 7 TeV pp collisions. Due to the large
production cross-section, (pp b bX) = (89.6 6.4
15.5) b in the LHCb acceptance [2], with the comparable number for charm production about 20 times larger [3, 4], these data provide unprecedented samples of heavy avoured hadrons. The rst results from LHCb have made a signicant impact on the avour physics landscape and have denitively proved the concept of a avour physics experiment in the forward region at a hadron collider.
The physics objectives of the rst phase of LHCb were set out prior to the commencement of data taking in the roadmap document [5]. They centred on six main areas, in all of which LHCb has by now published its rst results:(i) the tree-level determination of [6, 7], (ii) charmless two-body B decays [8, 9], (iii) the measurement of mixing-induced CP violation in B0s J/ [10], (iv) analysis of
the decay B0s + [1114], (v) analysis of the decay
B0 K0+ [15], (vi) analysis of B0s and other
radiative B decays [16, 17].1 In addition, the search for CP violation in the charm sector was established as a priority, and interesting results in this area have also been published [18, 19].
The results demonstrate the capability of LHCb to test the Standard Model (SM) and, potentially, to reveal new physics (NP) effects in the avour sector. This approach to search for NP is complementary to that used by the ATLAS and CMS experiments. While the high-pT experiments search for on-shell production of new particles, LHCb can look for their effects in processes that are precisely predicted in the SM. In particular, the SM has a highly distinctive
1Throughout the document, the inclusion of charge conjugated modes is implied unless explicitly stated.
Eur. Phys. J. C (2013) 73:2373 Page 3 of 92
avour structure, with no tree-level avour-changing neutral currents, and quark mixing described by the CabibboKobayashiMaskawa (CKM) matrix [20, 21] which has a single source of CP violation. This structure is not necessarily replicated in extended models. Historically, new particles have rst been seen through their virtual effects since this approach allows one to probe mass scales beyond the energy frontier. For example, the observation of CP violation in the kaon system [22] was, in hindsight, the discovery of the third family of quarks, well before the observations of the bottom and top quarks. Crucially, measurements of both high-pT and avour observables are necessary in order to decipher the nature of NP.
The early data also illustrated the potential for LHCb to expand its physics programme beyond these core measurements. In particular, the development of trigger algorithms that select events inclusively based on properties of b-hadron decays [23, 24] facilitates a much broader output than previously foreseen. On the other hand, limitations imposed by the hardware trigger lead to a maximum instantaneous luminosity at which data can most effectively be collected (higher luminosity requires tighter trigger thresholds, so that there is no gain in yields, at least for channels that do not involve muons). To overcome this limitation, an upgrade of the LHCb experiment has been proposed to be installed during the long shutdown of the LHC planned for 2018. The upgraded detector will be read out at the maximum LHC bunch-crossing frequency of 40 MHz so that the trigger can be fully implemented in software. With such a exible trigger strategy, the upgraded LHCb experiment can be considered as a general purpose detector in the forward region.
The Letter of Intent for the LHCb upgrade [25], containing a detailed physics case, was submitted to the LHCC in March 2011 and was subsequently endorsed. Indeed, the LHCC viewed the physics case as compelling. Nevertheless, the LHCb Collaboration continues to consider further possibilities to enhance the physics reach. Moreover, given the strong motivation to exploit fully the avour physics potential of the LHC, it is timely to update the estimated sensitivities for various key observables based on the latest available data. These studies are described in this paper, and summarised in the framework technical design report for the LHCb upgrade [26], submitted to the LHCC in June 2012 and endorsed in September 2012.
In the remainder of this introduction, a brief summary of the current LHCb detector is given, together with the common assumptions made to estimate the sensitivity achievable by the upgraded experiment. Thereafter, the sections of the paper discuss rare charm and beauty decays in Sect. 2, CP violation in the B system in Sect. 3 and mixing and CP violation in the charm sector in Sect. 4. There are several other important topics, not covered in any of these sections, that
can be studied at LHCb and its upgrade, and these are discussed in Sect. 5. A summary is given in Sect. 6.
1.1 Current LHCb detector and performance
The LHCb detector [1] is a single-arm forward spectrometer covering the pseudorapidity range 2 < < 5, designed for the study of particles containing b or c quarks. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream. The combined tracking system has a momentum resolution p/p that varies from0.4 % at 5 GeV/c to 0.6 % at 100 GeV/c, and an impact parameter resolution of 20 m for tracks with high transverse momentum. Charged hadrons are identied using two ring-imaging Cherenkov detectors. Photon, electron and hadron candidates are identied by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identied by a system composed of alternating layers of iron and multiwire proportional chambers. The trigger consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage which applies a full event reconstruction.
During 2011, the LHCb experiment collected 1.0 fb1 of integrated luminosity during the LHC pp run at a centreof-mass energy s = 7 TeV. The majority of the data was
recorded at an instantaneous luminosity of Linst = 3.5
1032 cm2 s1, nearly a factor of two above the LHCb design value, and with a pile-up rate (average number of visible interactions per crossing) of 1.5 (four times the
nominal value, but below the rates of up to 2.5 seen in
2010). A luminosity levelling procedure, where the beams are displaced at the LHCb interaction region, allows LHCb to maintain an approximately constant luminosity throughout each LHC ll. This procedure permitted reliable operation of the experiment and a stable trigger conguration throughout 2011. The hardware stage of the trigger produced output at around 800 kHz, close to the nominal 1 MHz, while the output of the software stage was around 3 kHz, above the nominal 2 kHz, divided roughly equally between channels with muons, b decays to hadrons and charm decays. During data taking, the magnet polarity was ipped at a frequency of about one cycle per month in order to collect equal sized data samples of both polarities for periods of stable running conditions. Thanks to the excellent performance of the LHCb detector, the overall data taking efciency exceeded 90 %.
Page 4 of 92 Eur. Phys. J. C (2013) 73:2373
1.2 Assumptions for LHCb upgrade performance
In the upgrade era, several important improvements compared to the current detector performance can be expected, as detailed in the framework TDR. However, to be conservative, the sensitivity studies reported in this paper all assume detector performance as achieved during 2011 data taking.The exception is in the trigger efciency, where channels selected at hardware level by hadron, photon or electron triggers are expected to have their efciencies double (channels selected by muon triggers are expected to have marginal gains, that have not been included in the extrapolations).Several other assumptions are made:
LHC collisions will be at s = 14 TeV, with heavy
avour production cross-sections scaling linearly with s;
the instantaneous luminosity2 in LHCb will be Linst =
1033 cm2 s1: this will be achieved with 25 ns bunch crossings (compared to 50 ns in 2011) and = 2;
LHCb will change the polarity of its dipole magnet with
similar frequency as in 2011/12 data taking, to approximately equalise the amount of data taken with each polarity for better control of certain potential systematic biases;
the integrated luminosity will be Lint = 5 fb1 per year,
and the experiment will run for 10 years to give a total sample of 50 fb1.
2 Rare decays
2.1 Introduction
The term rare decay is used within this document to refer loosely to two classes of decays:
avour-changing neutral current (FCNC) processes that
are mediated by electroweak box and penguin type diagrams in the SM;
more exotic decays, including searches for lepton avour
or number violating decays of B or D mesons and for light scalar particles.
The rst broad class of decays includes the rare radiative process B0s and rare leptonic and semileptonic decays
B0(s) + and B0 K0+. These were listed as
priorities for the rst phase of the LHCb experiment in the roadmap document [5]. In many well motivated new physics models, new particles at the TeV scale can enter in diagrams
2It is anticipated that any detectors that need replacement for the LHCb upgrade will be designed such that they can sustain a luminosity of
Linst= 2 1033 cm2 s1 [26]. Operation at instantaneous luminosi-
ties higher than the nominal value assumed for the estimations will allow the total data set to be accumulated in a shorter time.
that compete with the SM processes, leading to modications of branching fractions or angular distributions of the daughter particles in these decays.
For the second class of decay, there is either no SM contribution or the SM contribution is vanishingly small and any signal would indicate evidence for physics beyond the SM. Grouped in this class of decay are searches for GeV scale new particles that might be directly produced in B or D meson decays. This includes searches for light scalar particles and for B meson decays to pairs of same-charge leptons that can arise, for example, in models containing Majorana neutrinos [2729].
The focus of this section is on rare decays involving leptons or photons in the nal states. There are also several interesting rare decays involving hadronic nal states that can be pursued at LHCb, such as B+ K++,
B+ K+K+ [30, 31], B0s 0 and B0s 0 [32];
however, these are not discussed in this document.
Section 2.2 introduces the theoretical framework (the operator product expansion) that is used when discussing rare electroweak penguin processes. The observables and experimental constraints coming from rare semileptonic, radiative and leptonic B decays are then discussed in Sects. 2.3, 2.4 and 2.5 respectively. The implications of these experimental constraints for NP contributions are discussed in Sects. 2.6 and 2.7. Possibilities with rare charm decays are then discussed in Sect. 2.8, and the potential of LHCb to search for rare kaon decays, lepton number and avour violating decays, and for new light scalar particles is summarised in Sects. 2.9, 2.10 and 2.11 respectively.
2.2 Model-independent analysis of new physics contributions to leptonic, semileptonic and radiative decays
Contributions from physics beyond the SM to the observables in rare radiative, semileptonic and leptonic B decays can be described by the modication of Wilson coefcients C( )i of local operators in an effective Hamiltonian of the form
Heff =
4GF
2 VtbV tq
CiOi + C iO i[parenrightbig] + h.c., (1)
where q = d, s, and where the primed operators indicate
right-handed couplings. This framework is known as the operator product expansion, and is described in more detail in, e.g., Refs. [33, 34]. In many concrete models, the operators
e2 162 [summationdisplay]
i
Eur. Phys. J. C (2013) 73:2373 Page 5 of 92
that are most sensitive to NP are a subset of
O( )7 =
In spite of the larger theory uncertainties on the branching fractions as compared to inclusive decays, the attainable experimental precision can lead to stringent constraints on the Wilson coefcients. Moreover, beyond simple branching fraction measurements, exclusive decays offer powerful probes of C( )7, C( )9 and C( )10 through angular and CP-violating observables. The exclusive decays most sensitive to NP in b s transitions are B K , B0s +,
B K+ and B K+. These decays are dis
cussed in more detail below.
2.3 Rare semileptonic B decays
The richest set of observables sensitive to NP are accessible through rare semileptonic decays of B mesons to a vector or pseudoscalar meson and a pair of leptons. In particular the angular distribution of B K+ decays, discussed
in Sect. 2.3.2, provides strong constraints on C( )7, C( )9 and C( )10.
2.3.1 Theoretical treatment of rare semileptonic B M + decays
The theoretical treatment of exclusive rare semileptonic decays of the type B M + is possible in two kinematic
regimes for the meson M: large recoil (corresponding to low dilepton invariant mass squared, q2) and small recoil (high q2). Calculations are difcult outside these regimes, in particular in the q2 region close to the narrow cc resonances (the J/ and (2S) states).
In the low q2 region, these decays can be described by QCD-improved factorisation (QCDF) [46, 47] and the eld theory formulation of soft-collinear effective theory (SCET) [48, 49]. The combined limit of a heavy b-quark and an energetic meson M, leads to the schematic form of the decay amplitude [50, 51]:
T = C + B T M + O(QCD/mb). (3)
which is accurate to leading order in QCD/mb and to all orders in S. It factorises the calculation into process-independent non-perturbative quantities, B M form fac
tors, , and light cone distribution amplitudes (LCDAs), B(M), of the heavy (light) mesons, and perturbatively calculable quantities, C and T which are known to O(1S)
[50, 51]. Further, in the case that M is a vector V (pseudoscalar P ), the seven (three) a priori independent B V
(B P ) form factors reduce to two (one) universal soft
form factors , (P ) in QCDF/SCET [52]. The factorisa
tion formula Eq. (3) applies well in the dilepton mass range, 1 < q2 < 6 GeV2.5
5Light resonances at q2 below 1 GeV2 cannot be treated within QCDF, and their effects have to be estimated using other approaches. In addi-
mbe ( qPR(L)b)F ,
[parenrightbig],
O( )10 = ( qPL(R)b)[parenleftbig]
gmbe2 [parenleftbig] qT aPR(L)b[parenrightbig]Ga,
O( )9 = ( qPL(R)b)[parenleftbig]
O( )8 =
5 [parenrightbig],
(2)
O( )S =
mbmBq ( qPR(L)b)(
),
O( )P =
mbmBq ( qPR(L)b)(
5 ),
which are customarily denoted as magnetic (O( )7), chromo-magnetic (O( )8), semileptonic (O( )9 and O( )10), pseudoscalar (O( )P) and scalar (O( )S) operators.3 While the radiative b
q decays are sensitive only to the magnetic and chromo-magnetic operators, semileptonic b q + decays are, in
principle, sensitive to all these operators.4
In the SM, models with minimal avour violation (MFV) [35, 36] and models with a avour symmetry relating the rst two generations [37], the Wilson coefcients appearing in Eq. (1) are equal for q = d or s and the ratio of
amplitudes for b d relative to b s transitions is sup
pressed by |Vtd/Vts|. Due to this suppression, at the current
level of experimental precision, constraints on decays with a b d transition are much weaker than those on decays with
a b s transition for constraining C( )i. In the future, pre
cise measurements of b d transitions will allow powerful
tests to be made of this universality which could be violated by NP.
The dependence on the Wilson coefcients, and the set of operators that can contribute, is different for different rare B decays. In order to put the strongest constraints on the Wilson coefcients and to determine the room left for NP, it is therefore desirable to perform a combined analysis of all the available data on rare leptonic, semileptonic and radiative B decays. A number of such analyses have recently been carried out for subsets of the Wilson coefcients [3843].
The theoretically cleanest branching ratios probing the b s transition are the inclusive decays B Xs and
B Xs + . In the former case, both the experimental
measurement of the branching ratio and the SM expectation have uncertainties of about 7 % [44, 45]. In the latter case, semi-inclusive measurements at the B factories still have errors at the 30 % level [44]. At hadron colliders, the most promising modes to constrain NP are exclusive decays.
3In principle there are also tensor operators, OT (5) =
( qb)(
(5) ), which are relevant for some observables.
4In radiative and semileptonic decays, the chromomagnetic operator O8 enters at higher order in the strong coupling S.
Page 6 of 92 Eur. Phys. J. C (2013) 73:2373
For B K + , the three K spin amplitudes, corre
sponding to longitudinal and transverse polarisations of the K, are linear in the soft form factors , ,
AL,R, CL,R, AL,R0 CL,R , (4)
at leading order in QCD/mb and S. The CL,R, are com
binations of the Wilson coefcients C7,9,10 and the L and R
indices refer to the chirality of the leptonic current. Symmetry breaking corrections to these relationships of order S are known [50, 51]. This simplication of the amplitudes as linear combinations of CL,R, and form factors, makes it pos
sible to design a set of optimised observables in which any soft form factor dependence cancels out for all low dilepton masses q2 at leading order in S and QCD/mb [5355], as discussed below in Sect. 2.3.2.
Within the QCDF/SCET approach, a general, quantitative method to estimate the important QCD/mb corrections to the heavy quark limit is missing. In semileptonic decays, a simple dimensional estimate of 10 % is often used, largely from matching of the soft form factors to the full-QCD form factors (see also Ref. [56]).
The high q2 (low hadronic recoil) region, corresponds to dilepton invariant masses above the two narrow resonances of J/ and (2S), with q2 [greaterorsimilar] (1415) GeV2. In this region, broad cc-resonances are treated using a local operator product expansion [57, 58]. The operator product expansion (OPE) predicts small sub-leading corrections which are suppressed by either (QCD/mb)2 [58] or SQCD/mb [57]
(depending on whether full QCD or subsequent matching on heavy quark effective theory in combination with form factor symmetries [59] is adopted). The sub-leading corrections to the amplitude have been estimated to be below 2 % [58] and those due to form factor relations are suppressed numerically by C7/C9 O(0.1). Moreover, duality violating
effects have been estimated within a model of resonances and found to be at the level of 2 % of the rate, if sufciently large bins in q2 are chosen [58]. Consequently, like the low q2 region, this region is theoretically well under control.
At high q2 the heavy-to-light form factors are known only as extrapolations from light cone sum rules (LCSR) calculations at low q2. Results based on lattice calculations are being derived [60], and may play an important role in the near future in reducing the form factor uncertainties.
2.3.2 Angular distributionof B0 K0+ and B0s + decays
The physics opportunities of B V + ( = e, , V =
K, , ) can be maximised through measurements of the
tion, the longitudinal amplitude in the QCDF/SCET approach generates a logarithmic divergence in the limit q2 0, indicating problems
in the description below 1 GeV2 [50].
angular distribution of the decay. Using the decay B
K( K) + , with K on the mass shell, as an exam
ple, the angular distribution has the differential form [61, 62]
d4 [B K( K) + ]
dq2 d cos l d cos K d
=
932 [summationdisplay]
i
Ji[parenleftbig]q2[parenrightbig]gi(l, K, ), (5)
with respect to q2 and three decay angles l, K, and . For the B0 (B0), l is the angle between the + () and the opposite of the B0 (B0) direction in the dimuon rest frame, K is the angle between the kaon and the direction opposite to the B meson in the K0 rest frame, and is the angle between the + and K+ decay planes in the B rest frame. There are twelve angular terms appearing in the distribution and it is a long-term experimental goal to measure the coefcient functions Ji(q2) associated with these twelve terms, from which all other B K() + observables can
be derived.
In the SM, with massless leptons, the Ji depend on bilinear products of six complex K spin amplitudes AL,R, ,0,6
such as
J1s =
3
4
[bracketleftbig][vextendsingle][vextendsingle]AL[vextendsingle][vextendsingle]2 + [vextendsingle][vextendsingle]AL [vextendsingle][vextendsingle]2 + [vextendsingle][vextendsingle]AR[vextendsingle][vextendsingle]2 + [vextendsingle][vextendsingle]AR [vextendsingle][vextendsingle]2[bracketrightbig].
(6)
The expressions for the eleven other Ji terms are given for example in Refs. [54, 63]. Depending on the number of operators that are taken into account in the analysis, it is possible to relate some of the Ji terms. The full derivation of these symmetries can be found in Ref. [54].
When combining B and B decays, it is possible to form both CP-averaged and CP-asymmetric quantities: Si =
(Ji + Ji)/[d( +
)/dq2] and Ai = (Ji Ji)/[d( + )/dq2], from the Ji [53, 54, 6266]. The terms J5,6,8,9 in
the angular distribution are CP-odd and, consequently, the associated CP-asymmetry, A5,6,8,9 can be extracted from an untagged analysis (making it possible for example to measure A5,6,8,9 in B0s + decays). Moreover, the
terms J7,8,9 are T -odd and avoid the usual suppression of the corresponding CP-asymmetries by small strong phases [64]. The decay B0 K0+, where the K0 decays to
K+, is self-tagging (the avour of the initial B meson is determined from the decay products) and it is therefore possible to measure both the Ai and Si for the twelve angular terms.
In addition, a measurement of the T -odd CP asymme-tries, A7, A8 and A9, which are zero in the SM and are not suppressed by small strong phases in the presence of
6Further amplitudes contribute in principle, but they are either suppressed by small lepton masses or originate from non-standard scalar/tensor operators.
Eur. Phys. J. C (2013) 73:2373 Page 7 of 92
NP, would be useful to constrain non-standard CP violation.
This is particularly true since the direct CP asymmetry in the inclusive B Xs decay is plagued by sizeable long-
distance contributions and is therefore not very useful as a constraint on NP [67].
2.3.3 Strategies for analysis of B0 K0 + decays
In 1.0 fb1 of integrated luminosity, LHCb has collected the worlds largest samples of B0 K0+ (with K0
K+) and B0s + decays, with around 900 and 80
signal candidates respectively reported in preliminary analyses [68, 69]. These candidates are however sub-divided into six q2 bins, following the binning scheme used in previous experiments [70]. With the present statistics, the most populated q2 bin contains 300B0 K0+ candidates
which is not sufcient to perform a full angular analysis.
The analyses are instead simplied by integrating over two of the three angles or by applying a folding technique to the angle, + for < 0, to cancel terms in the angular
distribution.In the case of massless leptons, one nds:
d d =
2 (1 + S3 cos 2 + A9 sin 2), (7)
d dK =
3
4 sin K[parenleftbig]2FL cos2 K + (1 FL) sin2 K[parenrightbig], (8)
(10)
where the rst value is in good agreement with the recent preliminary result from LHCb of q20 = 4.9 +1.31.1 GeV2/c4
[68] for the B0 K0+ decay.
It is possible to access information from other terms in the angular distribution by integrating over one of the angles and making an appropriate folding of the remaining two angles. From and K only [73] it is possible to extract:
S5 =
4 3
d d =
38(1 FL)[parenleftbig]1 + cos2 [parenrightbig]
+AFB cos [parenrightbigg] sin , (9)
where = +
3 4FL sin2 +
[bracketleftbigg][integraldisplay]
3/2
/2
[integraldisplay]
2
3/2
/2
[integraldisplay] [bracketrightbigg] d[bracketleftbigg][integraldisplay]
1
[integraldisplay]
0
1
[bracketrightbigg]
0
0
d cos K d3(
) dq2 d cos Kd [slashBig]
d( +
. The observables appear linearly in the expressions. Experimentally, the ts are performed in bins of q2 and the measured observables are rate averaged over the q2 bin. The observables appearing in the angular projections are the fraction of longitudinal polarisation of the K, FL, the lepton system forwardbackward asymmetry, AFB, S3 and A9.
The differential branching ratio, AFB and FL have been measured by the B factories, CDF and LHCb [68, 70, 71]. The observable S3 is related to the asymmetry between the parallel and perpendicular K spin amplitudes7 is sensitive to right-handed operators (C 7) at low q2, and is negligibly small in the SM. In the future, the decay B0 K0e+e
7The quantity S3 = (1 FL)/2 A(2)T (in the massless case) allows
access to one of the theoretically clean quantities, namely A(2)T. The
observable A(2)T is a theoretically cleaner observable than S3 due to the cancellation of some of the form-factor dependence [72].
could play an important role in constraining C 7 through S3 since it allows one to probe to smaller values of q2 than the B0 K0+ decay. First measurements have been
performed by CDF and LHCb [68, 71].8 The current experimental status of these B0 K0+ angular observables
at LHCb, the B factories and CDF is shown in Fig. 1. Improved measurements of these quantities would be useful to constrain the chirality-ipped Wilson coefcients (C 7, C 9 and C 10).
Whilst AFB is not free from form-factor uncertainties at low q2, the value of the dilepton invariant mass q20, for which the differential forwardbackward asymmetry AFB vanishes, can be predicted in a clean way.9 The zero crossing-point is highly sensitive to the ratio of the two Wilson coefcients C7 and C9. In particular the model-independent upper bound on |C9| implies
q20 > 1.7 GeV2/c4, which improves to q20 > 2.6 GeV2/c4, assuming the sign of C7 to be SM-like [40]. At next-to-leading order one nds [51]:10
q20[bracketleftbig]K0 + [bracketrightbig] = 4.36 +0.330.31 GeV2/c4, q20[bracketleftbig]K+ + [bracketrightbig] = 4.15 +0.270.27 GeV2/c4,
)dq2 . (11)
Analogously to AFB, the zero-crossing point of S5 has been shown to be theoretically clean. This observable is sensitive to the ratio of Wilson coefcients, (C7 + C 7)/(C9 + mb(C7 + C 7)), and if measured would add complementary
information to AFB and S3 about new right-handed currents.
8Depending on the convention for the angle , d /d of Eq. (7) can also depend on S9, which is tiny in the SM and beyond. Note that, due to different angular conventions, the quantity AIm reported in Ref. [68] corresponds to S9, while AIm in Ref. [71] corresponds to A9.
9In the QCDF approach at leading order in QCD/mb, the value of q20 is free from hadronic uncertainties at order 0s. A dependence on the soft form factor and on the light-cone wave functions of the B and K mesons appears only at order 1s.
10A recent determination of q20 in B0 decays gives 4.0 0.3 GeV2/c4
[40]. The shift with respect to Ref. [51] is of parametric origin and is driven in part by the choice of the renormalisation scale ( = 4.2 GeV
instead of 4.8 GeV), but also due to differences in the implementation of higher O(S) short-distance contributions.
Page 8 of 92 Eur. Phys. J. C (2013) 73:2373
Fig. 1 Summary of recent measurements of the angular observables (a) FL, (b) AFB, (c) S3 and (d) S9 in B0 K0+ decays at
LHCb, CDF and the B factories [68]. Descriptions of these observables are provided in the text (see Eqs. (7), (8) and (9) and footnote 8).
The theory predictions at low- and high-dimuon invariant masses are indicated by the coloured bands and are also described in detail in the text
2.3.4 Theoretically clean observables in B0 K0 +
decays
By the time that 5 fb1 of integrated luminosity is available at LHCb, it will be possible to exploit the complete NP sensitivity of the B K + both in the low- and high-q2
regions, by performing a full angular analysis. The increasing size of the experimental samples makes it important to design optimised observables (by using specically chosen combinations of the Ji) to reduce theoretical uncertainties.
In the low q2 region, the linear dependence of the amplitudes on the soft form factors allows for a complete cancellation of the hadronic uncertainties due to the form factors at leading order. This consequently increases the sensitivity to the structure of NP models [53, 54].
In the low q2 region, the so-called transversity observables A(i)T, i = 2, 3, 4, 5 are an example set of observables
that are constructed such that the soft form factor dependence cancels out at leading order. They represent the complete set of angular observables and are chosen to be highly
sensitive to new right-handed currents via C 7 [53, 54]. A second, complete, set of optimised angular observables was constructed (also in the cases of non-vanishing lepton masses and in the presence of scalar operators) in Ref. [55]. Recently the effect of binning in q2 on these observables has been considered [72]. In these sets of observables, the unknown QCD/mb corrections are estimated to be of order 10 % on the level of the spin amplitudes and represent the dominant source of theory uncertainty.
In general, the angular observables are shown to offer high sensitivity to NP in the Wilson coefcients of the operators O7, O9, and O10 and of the chirally ipped operators [53, 54, 62, 64]. In particular, the observables S3,
A9 and the CP-asymmetries A7 and A8 vanish at leading order in QCD/mb and S in the SM operator basis [64]. Importantly, this suppression is absent in extensions with non-vanishing chirality-ipped C 7,9,10, giving rise to contributions proportional to Re(CiCj ) or Im(CiCj ) and making these terms ideal probes of right-handed currents [53, 54, 62, 64]. CP asymmetries are small in the SM, be-
Eur. Phys. J. C (2013) 73:2373 Page 9 of 92
cause the only CP-violating phase affecting the decay is doubly Cabibbo-suppressed, but can be signicantly enhanced by NP phases in C9,10 and C 9,10, which at present are poorly constrained. In a full angular analysis it can also be shown that CP-conserving observables provide indirect constraints on CP-violating NP contributions [54].
At large q2, the dependence on the magnetic Wilson coefcients C( )7 is suppressed, allowing, in turn, a cleaner extraction of semileptonic coefcients (C( )9 and C( )10). A set of transversity observables H(i)T, i = 1, 2, 3 have been designed
to exploit the features of this kinematic region in order to have small hadronic uncertainties [65]. As a consequence of symmetry relations of the OPE [40, 65, 66, 74], at high q2,
combinations of the angular observables Ji can be formed within the SM operator basis (i.e. with C i = 0), which de
pend:
only on short-distance quantities (e.g. H(2,3)T);
only on long-distance quantities (FL and low q2 opti
mised observables A(2,3)T).
Deviations from these relations are due to small sub-leading corrections at order (QCD/mb)2 from the OPE.
In the SM operator basis it is interesting to note that A(2,3)T, which are highly sensitive to short distance contributions (from C 7) at low q2, instead become sensitive to long-distance quantities (the ratio of form factors) at high q2. The extraction of form factor ratios is already possible with current data on S3 (A(2)T) and FL and leads to a consistent picture between LCSR calculations, lattice calculations and experimental data [41, 74]. In the presence of chiralityipped Wilson coefcients, these observables are no longer short-distance free, but are probes of right-handed currents [42]. At high q2, the OPE framework predicts H(2)T = H(3)T
and J7 = J8 = J9 = 0. Any deviation from these relation
ships, would indicate a problem with the OPE and the theoretical predictions in the high q2 region.
2.3.5 B+ K++ and B+ K+e+e
The branching fractions of B0(+) K0(+)+ have been
measured by BaBar, Belle and CDF [70, 75, 76]. In 1.0 fb1 LHCb observes 1250 B+ K++ decays [77], and in
the future will dominate measurements of these processes. Since the B K transition does not receive contribu
tions from an axial vector current, the primed Wilson coefcients enter the B0(+) K0(+)+ observables al
ways in conjunction with their unprimed counterparts as (Ci + C i). This is in contrast to the B K+ de
cay and therefore provides complementary constraints on the Wilson coefcients and their chirality-ipped counterparts.
An angular analysis of the + pair in the B0(+)
K0(+)+ decay would allow the measurement of two
further observables, the forwardbackward asymmetry AFB and the so-called at term FH [78]. The angular distribution of a B meson decaying to a pseudoscalar meson, P , and a pair of leptons involves just q2 and a single angle in the dilepton system, l [78]
1
d [B P + ]
d cos l
3
4(1 FH)[parenleftbig]1 cos2 l[parenrightbig] +
1
2FH + AFB cos l. (12)
In the SM, the forwardbackward asymmetry of the dilepton system is expected to be zero. Any non-zero forwardbackward asymmetry would point to a contribution from new particles that extend the SM operator basis. Allowing for generic (pseudo-)scalar and tensor couplings, there is sizeable room for NP contributions in the range
|AFB| [lessorsimilar] 15 %. The at term, FH/2, that appears with AFB in
the angular distribution, is non-zero, but small (for = e, )
in the SM. This term can also see large enhancements in models with (pseudo-)scalar and tensor couplings of up to FH 0.5. Recent SM predictions at low- and high-q2 can
be seen in Refs. [40, 56, 78, 79]. The current experimental limits on B(B0s +) now disfavour large CS and CP ,
and if NP is present only in tensor operators then NP contributions are expected to be in the range |AFB| [lessorsimilar] 5 % and
FH [lessorsimilar] 0.2.
In addition to AFB, FH and the differential branching fraction of the decays, it is possible to probe the universality of lepton interactions by comparing the branching fraction of decays B0(+) K0(+) + with two different lepton
avours (e.g. electrons versus muons):
RK = /e [parenleftbig]with the same q2 cuts[parenrightbig]. (13) Lepton universality may be violated in extensions to the
SM, such as R-parity-violating SUSY models.11 In the SM,
the ratio RSMK is expected to be close to unity, RSMK =
1 + O(m2/m2B) [83].
It is also interesting to note that at high q2 the differential decay rates and CP asymmetries of B0(+) K0(+) +
and B0(+) K0(+) + ( = e, ) are correlated [40] and
exhibit the same short-distance dependence (in the SM operator basis). Any deviation would point to a problem for the OPE used in the high q2 region.
2.3.6 Rare semileptonic b d + decays
Rare b d radiative decay processes, such as B ,
have been observed at the B factories [84, 85]. In the 2011
11There are hints of lepton universality violation in recent measurements of B D() by BaBar [80] and Belle [81, 82].
=
Page 10 of 92 Eur. Phys. J. C (2013) 73:2373
Fig. 2 Invariant mass of selected B+ ++ candidates in
1.0 fb1 of integrated luminosity [86]. In the legend, part. reco. and combinatorial refer to partially reconstructed and combinatorial backgrounds respectively
data sample, the very rare decay B+ ++ was ob-
served at the LHCb experiment (see Fig. 2). This is a rare b d + transition, which in the SM is suppressed by
loop and CKM factors proportional to |Vtd/Vts|. In the
1.0 fb1 data sample, LHCb observes 25.3 +6.76.4 signal can
didates corresponding to a branching fraction of B(B+
++) = (2.4 0.6 0.2) 108 [86]. This measure
ment is in good agreement with the SM prediction, i.e. consistent with no large NP contribution to b d + pro
cesses and with the MFV hypothesis.The b d transitions can show potentially larger CP-
and isospin-violating effects than their b s counterparts
due to the different CKM hierarchy [51]. These studies would need the large statistics provided by the future LHCb upgrade. A 50 fb1 data sample will also enable a precision measurement of the ratio of the branching fractions of B+ meson decays to ++ and K++. This ratio would enable a useful comparison of |Vtd/Vts| to be made using
penguin processes (with form factors from lattice QCD) and box processes (using ms/ md and bag-parameters from lattice QCD) and provide a powerful test of MFV.
2.3.7 Isospin asymmetry of B0(+) K0(+)+ and
B0(+) K0(+)+ decays
Analyses at hadron colliders (at LHCb and CDF) have mainly focused on decay modes with charged tracks in the nal state. B meson decays involving K0 mesons are experimentally much more challenging due to the long lifetimes of K0S and K0L mesons (the K0L is not reconstructable within LHCb). Nevertheless, LHCb has been able to select60 B0 K0+ decays, reconstructed as K0S +,
and 80 B+ K++, reconstructed as K+ K0S+,
which are comparable in size to the samples that are available for these modes in the full data sets of the B factories.
The isolation of these rare decay modes enables a measurement of the isospin asymmetry of B K()+ decays,
AI =
B(B0 K0+) ( B0B+ )B(B+ K++)
B(B0 K0+) + ( B0B+ )B(B+ K++)
.
(14)
At leading order, isospin asymmetries (which involve the spectator quark) are expected to be zero in the SM. Isospin-breaking effects are subleading in QCD/mb, and are dif-cult to estimate due to unknown power corrections. Nevertheless isospin-breaking effects are expected to be small and these observables may be useful in NP searches because they offer complementary information on specic Wilson coefcients [87].
The LHCb measurement of the K and K isospin asymmetries in bins of q2 are shown in Fig. 3. For the K modes
AI is compatible with the SM expectation that ASMI 0, but
for the K+/K0 modes, AI is seen to be negative at low- and high-q2 [77]. This is consistent with what has been seen at previous experiments, but is inconsistent with the nave expectation of ASMI 0 at the 4 level.12 Such a discrepancy
would be hard to explain in any model that is also consistent with other experimental results. Improved measurements are needed to clarify the situation.
2.4 Radiative B decays
While the theoretical prediction of the branching ratio of the B K decay is problematic due to large form factor
uncertainties, the mixing-induced asymmetry13 SK provides an important constraint due to its sensitivity to the chirality-ipped magnetic Wilson coefcient C 7. At leading order it vanishes for C 7 0, so the SM prediction is
tiny and experimental evidence for a large SK would be a clear indication of NP effects through right-handed currents [89, 90]. Unfortunately it is experimentally very challenging to measure SK in a hadronic environment, requiring both avour tagging and the ability to reconstruct the K0 in the decay mode K0 K00. However, the channel
B0s , which is much more attractive experimentally,
offers the same physics opportunities, with additional sensitivity due to the non-negligible width difference in the B0s system. Moreover, LHCb can study several other interesting radiative b-hadron decays.
12A calculation of ASMI(B K+) has recently become available
[88], giving values consistent with the nave expectation within 1 %.
13Note that the notation S used here and in the literature for mixing-induced asymmetries is not related to the use of the notation in Sect. 2.3 for CP-averaged properties of the angular distributions.
Eur. Phys. J. C (2013) 73:2373 Page 11 of 92
Fig. 3 (a) B K+ and (b) B K+ isospin asymmetries in 1.0 fb1 of data collected by the LHCb Collaboration in 2011 [77]
2.4.1 Experimental status and outlook for rare radiative decays
In 1.0 fb1 of integrated luminosity LHCb observes 5300 B0 K0 and 690 B0s [17] candidates. These
are the largest samples of rare radiative B0 and B0s decays collected by a single experiment. The large sample of
B0 K0 decays has enabled LHCb to make the worlds
most precise measurement of the direct CP-asymmetry
ACP(K ) = 0.8 1.7 0.9 %, compatible with zero as
expected in the SM [17].
With larger data samples, it will be possible to add additional constraints on the C7C 7 plane through measurements of b s processes. These include results from
time-dependent analysis of B0s [91], as described in
detail in the LHCb roadmap document [5]. Furthermore, the large 0b production cross-section will allow for measurements of the photon polarisation through the decays 0b () [92, 93]. In fact, the study of 0b tran
sitions is quite attractive from the theoretical point of view, since the hadronic uncertainties are under good control [94
96]. However, because the 0b has J P = 12+ and can be po
larised at production, it will be important to measure rst the 0b polarisation.
B V P decays with a photon, a vector and a pseu
doscalar particle in the nal state can also provide sensitivity to C 7 [97100]. The decays B K and B+
K1(1270)+ have been previously observed at the B factories [101, 102] and large samples will be available for the rst time at LHCb.
2.5 Leptonic B decays
2.5.1 B0s + and B0 +
The decays B0(s) + are a special case amongst
the electroweak penguin processes, as they are chirality-suppressed in the SM and are most sensitive to scalar and
pseudoscalar operators. The branching fraction of B0(s) + can be expressed as [103106]:
B[parenleftbig]B0q +[parenrightbig]
G2F 2
= 643 f 2Bq Bq m3Bq [vextendsingle][vextendsingle]V
tbV tq[vextendsingle][vextendsingle]2
[radicaltp]
[radicalvertex]
[radicalvertex]
1
4m2
m2Bq
[braceleftbigg][parenleftbigg]1
4m2
m2Bq
[parenrightbigg][vextendsingle][vextendsingle]CS
C S[vextendsingle][vextendsingle]2
+
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
CP C P [parenrightbig] + 2m
mBq [parenleftbig]C
10 C 10[parenrightbig]
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
2 [bracerightbigg], (15)
where q = s, d.
Within the SM, CS and CP are negligibly small and the dominant contribution of C10 is helicity suppressed. The coefcients Ci are the same for B0s and B0 in any scenario (SM or NP) that obeys MFV. The large suppression of
B(B0 +) with respect to B(B0s +) in MFV
scenarios means that B0s + is often of more inter
est than B0 + for NP searches. The ratio B(B0s
+)/B(B0 +) is however a very useful probe of
MFV.
The SM branching fraction depends on the exact values of the input parameters: fBq , Bq and |VtbV tq|2. The
B0s decay constant, fBs , constitutes the main source of uncertainty on B(B0s +). There has been signicant
progress in theoretical calculations of this quantity in recent years. As of the year 2009 there were two unquenched lattice QCD calculations of fBs , by the HPQCD [107]
and FNAL/MILC [108] Collaborations, which, when averaged, gave the value fBs = 238.8 9.5 MeV [109]. The
FNAL/MILC calculation was updated in 2010 [110], and again in 2011 to give fBs = 242 9.5 MeV [111, 112].
Also in 2011, the ETM Collaboration reported a value of
Page 12 of 92 Eur. Phys. J. C (2013) 73:2373
fBs = 23210 MeV [113]. The HPQCD Collaboration pre
sented in 2011 a result, fBs = 227 10 MeV [114], which
has recently been improved upon with an independent calculation that gives fBs = 225 4 MeV [115].
A weighted average of FNAL/MILC11 [111], HPQCD11 [114] and HPQCD12 [115] was presented recently [109], giving fBs = 227.6 5.0 MeV. Using this
value, the SM prediction for the branching ratio is [116]:
B[parenleftbig]B0s +[parenrightbig]SM = (3.1 0.2) 109. (16)
This value is taken as the nominal B(B0s +)SM. Note
that, in addition to fBs , other sources of uncertainty are due to the B0s lifetime, the CKM matrix element |Vts|, the
top mass mt, the electroweak corrections and scale variations. For a more detailed discussion of the SM prediction, see Ref. [117]. It is also possible to obtain predictions for
B(B0s +)SM with reduced sensitivity to the value of
fBs using input from either ms [118] or from a full CKM t [119].
Likewise for fBd , using the average of ETMC-11 (fBd =
195 12 MeV) [113], FNAL/MILC-11 (fBd = 197
9 MeV) [111, 112] and HPQCD-12 (fBd = 191 9 MeV)
[115] results, which gives fBd = 194 10 MeV [120], the
branching ratio of B0 + is:
B[parenleftbig]B0 +[parenrightbig]SM = (1.1 0.1) 1010. (17)
NP models, especially those with an extended Higgs sector, can signicantly enhance the B0(s) + branching
fraction even in the presence of other existing constraints. In particular, it has been emphasised in many works [121128] that the decay B0s + is very sensitive to the presence
of SUSY particles. At large tan where tan is the ratio of vacuum expectation values of the Higgs doublets14the
SUSY contribution to this process is dominated by the exchange of neutral Higgs bosons, and both CS and CP can receive large contributions from scalar exchange.
In constrained SUSY models such as the CMSSM and NUHM1 (see Sect. 2.7), predictions can be made for
B(B0s +) that take into account the existing con
straints from the general purpose detectors. These models predict [129]:
1 < B(B0s +)CMSSM
B(B0s +)SM
< 2,
(18)
The LHCb [13] (and CMS [130]) measurements of B0s
+ have already excluded the upper range of these predictions.
14Note that elsewhere in this document the symbol is used to denote an angle of the unitarity triangle of the CKM matrix.
Other NP models such as composite models (e.g. Littlest Higgs model with T -parity or Topcolour-assisted Technicolor), models with extra dimensions (e.g. Randall Sundrum models) or models with fourth generation fermions can modify B(B0s +) [116, 131135]. The NP con
tributions from these models usually arise via (C10C 10), and they are therefore correlated with the constraints from other b s + processes, e.g. with B(B+ K++)
which depends on (C10 + C 10). The term (CP C P ) in
the branching fraction adds coherently with the SM contribution from (C10C 10), and therefore can also destructively interfere. In such cases, if (CSC S) remains small,
B(B0s +) could be smaller than the SM prediction.
A measurement of B(B0s +) well below the SM pre
diction would be a clear indication of NP and would be symptomatic of a model with a large non-degeneracy in the scalar sector (where C( )P is enhanced but C( )S is not).
If only C10 is modied, these constraints currently require the branching ratio to be above 1.1 1010 [42]. In the
presence of NP effects in both C10 and C 10, even stronger suppression is possible in principle.
At the beginning of 2012, the LHCb experiment set the world best limits on the B(B0(s) +) [13].15 At 95 %
C.L.
B[parenleftbig]B0s +[parenrightbig] < 4.5 109,
B[parenleftbig]B0 +[parenrightbig] < 1.0 109.
Experimentally the measured branching fraction is the time-averaged (TA) branching fraction, which differs from the theoretical value because of the sizeable width difference between the heavy and light B0s mesons [136, 137].16 In general,
B[parenleftbig]B0s +[parenrightbig]TH
= [bracketleftbig][parenleftbig]1 y2s[parenrightbig]/(1 + A ys)[bracketrightbig] B[parenleftbig]B0s +[parenrightbig]TA (19) where A = +1 in the SM and ys = s/(2s) =
0.088 0.014 [139]. Thus the experimental measurements
have to be compared to the following SM prediction for the time-averaged branching fraction:
B[parenleftbig]B0s +[parenrightbig]SM,TA
= B[parenleftbig]B0s +[parenrightbig]SM,TH/(1 ys)
= (3.5 0.2) 109. (20)
With 50 fb1 of integrated luminosity, taken with an upgraded LHCb experiment, a precision better than 10 % can
15Results on B(B0(s) +) presented at HCP2012 [14] are not in
cluded in this discussion.
16This was previously observed in a different context [138].
1 < B(B0s +)NUHM1
B(B0s +)SM
< 3.
Eur. Phys. J. C (2013) 73:2373 Page 13 of 92
be achieved in B(B0s +), and 35 % on the ratio B(B0s +)/B(B0 +). The dominant system
atic uncertainty is likely to come from knowledge of the ratio of fragmentation fractions, fd/fs, which is currently known to a precision of 8 % from two independent determinations.17 One method [140]18 is based on hadronic B decays [142, 143], and relies on knowledge of the B(s)
D(s) form factors from lattice QCD calculations [144]. The other [145] uses semileptonic decays, exploiting the expected equality of the semileptonic widths [146, 147]. However, the two methods have a common, and dominant, uncertainty which originates from the measurement of B(D+s
K+K+), which in the PDG is given to 4.9 % (coming from a single measurement from CLEO [148]). A new preliminary result from Belle has recently been presented [149]inclusion of this measurement in the world average will improve the uncertainty on B(D+s K+K++) to
3.5 %. With the samples available with the LHCb upgrade, it will be possible to go beyond branching fraction measurements and study the effective lifetime of B0s +, that
provides additional sensitivity to NP [136].
In Sect. 2.7, the NP implications of the current measurements of B(B0s +) and the interplay with other ob
servables, including results from direct searches, are discussed for a selection of specic NP models. In general, the strong experimental constraints on B(B0s +)
[13, 130, 150, 151] largely preclude any visible effects from scalar or pseudoscalar operators in other b s + de
cays.19
2.5.2 B0s +
The leptonic decay B0s + provides interesting infor
mation on the interaction of the third generation quarks and leptons. In many NP models, contributions to third generation quarks/leptons can be dramatically enhanced with respect to the rst and second generation. This is true in, for example, scalar and pseudoscalar interactions in super-symmetric scenarios, for large values of tan . Interestingly, there is also an interplay between b s+ processes
and the lifetime difference s12 in B0s mixing (see Sect. 3).
The correlation of both processes has been discussed model-independently [152, 153] and in specic scenarios, such as
17This value is valid for B mesons produced from s = 7 TeV pp
collisions within the LHCb acceptance. It will, in principle, need to be remeasured at each different LHC collision energy, and may depend on the kinematic acceptance of the detector (i.e. on the transverse momentum and pseudorapidity of the B mesons). However, once a suitable B0s branching fraction, such as that for B0s J/ or B0s K+K, is
known to good precision, normalisation can be carried out without direct need for an fd/fs value.
18The results from Ref. [140] were updated at HCP2012 [141].
19Barring a sizeable, fortuitous cancellation among CS,P and C S,P [79].
leptoquarks [154, 155] or Z models [156158]. There are presently no experimental limits on B0s +, however
the interplay with s12, and the latest LHCb-measurement of d/s would imply a limit of B(B0s +) < 3 % at
90 % C.L. Any improvement on this limit, which might be in reach with the existing LHCb data set, would yield strong constraints on models that couple strongly to third generation leptons. A large enhancement in b s+ could help
to understand the anomaly observed by the D0 experiment in their measurement of the inclusive dimuon asymmetry [159] and could also reduce the tension that exists with other mixing observables [152, 153].
The study of B0s + at LHCb presents signicant
challenges. The leptons must be reconstructed in decays that involve at least one missing neutrino. Although it has been demonstrated that the decay Z + can be sep
arated from background at LHCb, using both leptonic and hadronic decay modes [160], at lower energies the backgrounds from semileptonic heavy avour decays cause the use of the leptonic decay modes to be disfavoured. However, in the case that three-prong decays are used, the vertices can be reconstructed from the three hadron tracks. The analysis can then benet from the excellent vertexing capability of LHCb, and, due to the nite lifetime of the lepton, there are in principle sufcient kinematic constraints to reconstruct the decay. Work is in progress to understand how effectively the different potential background sources can be suppressed, and hence how sensitive LHCb can be in this channel.
2.6 Model-independent constraints
Figure 4, taken from Ref. [42], shows the current constraints on the NP contributions to the Wilson coefcients (dened in Eq. (1)) C( )7, C( )9 and C( )10, varying only one coefcient at a time. The experimental constraints included here are: the branching fractions of B Xs , B Xs + ,
B K+ and B0s +, the mixing-induced asym
metries in B K and b s and the branching fraction
and angular observables in B K+. One can make
the following observations:
At 95 % C.L., all Wilson coefcients are compatible with
their SM values.
For the coefcients present in the SM, i.e. C7, C9 and
C10, the constraints on the imaginary part are looser than on the real part.
For the Wilson coefcients C( )10, the constraint on B(B0s
+) is starting to become competitive with the constraints from the angular analysis of B K()+.
The constraints on C 9 and C 10 from B K+ and
B K+ are complementary and lead to a more
constrained region, and better agreement with the SM, than with B K+ alone.
Page 14 of 92 Eur. Phys. J. C (2013) 73:2373
Fig. 4 Individual 2 constraints in the complex planes of Wilson coefcients, coming from B Xs + (brown), B Xs (yellow),
ACP(b s ) (orange), B K (purple), B K+ (green),
B K+ (blue) and B0s + (grey), as well as combined 1
and 2 constraints (red) [42]
A second allowed region in the C7C 7 plane charac
terised by large positive contributions to both coefcients, which was found previously to be allowed e.g. in Refs. [38, 39], is now disfavoured at 95 % C.L. by the new B K+ data, in particular the measurements
of the forwardbackward asymmetry from LHCb.
The second point above can be understood from the fact that for the branching fractions and CP-averaged angular observables which give the strongest constraints, only NP contributions aligned in phase with the SM can interfere with the SM contributions. As a consequence, NP with non-standard CP violation is in fact constrained more weakly than NP where CP violation stems only from the CKM phase. This highlights the need for improved measurements of CP asymmetries directly sensitive to non-standard phases.20
Signicant improvements of these constraintsor rst hints for physics beyond the SMcan be obtained in the future by both improved measurements of the observables dis-
20LHCb has presented results on ACP(B0 K0+) at CKM
2012 [161].
cussed above and by improvements on the theoretical side. From the theory side, there is scope for improving the estimates of the hadronic form factors from lattice calculations, which will reduce the dominant source of uncertainty on the exclusive decays. On the experimental side there are a large number of theoretically clean observables that can be extracted with a full angular analysis of B0 K0+, as
discussed in Sect. 2.3.2.
2.7 Interplay with direct searches and model-dependent constraints
The search for SUSY is the main focus of NP searches in ATLAS and CMS. Although the results so far have not revealed a positive signal, they have put strong constraints on constrained SUSY scenarios. The understanding of the parameters of SUSY models also depends on other measurements, such as the anomalous dipole moment of the muon, limits from direct dark matter searches, measurements of the dark matter relic density and various B physics observables. As discussed in Sect. 2.5, the rare decay channels studied in LHCb, such as B0(s) +, provide stringent
Eur. Phys. J. C (2013) 73:2373 Page 15 of 92
tests of SUSY. In addition, the decays B K()+ pro
vide many complementary observables which are sensitive to different sectors of the theory. In this section, the implications of the current LHCb measurements in different SUSY models are explained, both in constrained scenarios and in a more general case.
First consider the constrained minimal supersymmetric standard model (CMSSM) and a model with non-universal Higgs masses (NUHM1). The CMSSM is characterised by the set of parameters {m0, m1/2, A0, tan , sgn()} and in
vokes unication boundary conditions at a very high scale mGUT where the universal mass parameters are specied.
Fig. 5 Constraints from avour observables in CMSSM in the plane (m1/2, m0) with A0 = 0, for tan = (left) 50 and (right)30 [162], us
ing SuperIso [106, 163]. The black line corresponds to the CMS
exclusion limit with 1.1 fb1 of data [164] and the red line to the CMS exclusion limit with 4.4 fb1 of data [165]
Fig. 6 SUSY spread of (top left) AFB(B K+) at low q2,
(top right) q20(B K+) and (bottom) FL(B K+) as
a function of the lightest stop mass, for A0 = 0 and tan = 50 [120],
using SuperIso [106, 163]. The solid red lines correspond to the
preliminary LHCb central value with 1.0 fb1 [68], while the dashed and dotted lines represent the 1 and 2 bounds respectively, including both theoretical and experimental errors
Page 16 of 92 Eur. Phys. J. C (2013) 73:2373
The NUHM1 relaxes the universality condition for the Higgs bosons which are decoupled from the other scalars, adding then one extra parameter compared to the CMSSM.
Figure 5 shows the plane (m1/2, m0) for large and moderate values of tan in the CMSSM where, for comparison, direct search limits from CMS are superimposed.It can be seen that, at large tan , the constraints from avour observablesin particular B(B0s +)are
more constraining than those from direct searches. As soon as one goes down to smaller values of tan , the avour observables start to lose importance compared to direct searches. On the other hand, B K+ related observ
ables, in particular the forwardbackward asymmetry, lose less sensitivity and play a complementary role. To see better the effect of AFB(B K+) at low q2,21 the AFB
zero-crossing point q20 and FL(B K+), in Fig. 6
their SUSY spread is shown as a function of the lightest stop mass for tan = 50 [120]. As can be seen from the
gure, small stop masses are excluded and in particular mt1 [lessorsimilar] 800 GeV is disfavoured by AFB at the 2 level.
The impact of the recent B K()l+l decay data on
SUSY models beyond MFV (NMFV) with moderate tan is shown in Fig. 7. The largest effect stems from left-right mixing between top and charm super-partners. Due to the Z-penguin dominance of the SUSY-avour contributions the constraints are most effective for the Wilson coefcient C10 (see Sect. 2.2). SUSY effects in C10 are reduced from about 50 % to 16 % (28 %) at 68 (95) % C.L. by the recent data on the rare decay B0 K0+ [167]. The constraints
are relevant to avour models based on radiative avour violation (see, e.g., Ref. [169]), and exclude solutions to the avour problem with avour generation in the up-sector and sub-TeV spectra. The avour constraints are stronger for lighter stops, hence there is an immediate interplay with direct searches.
Figure 8 shows the (MA, tan ) plane from ts of the CMSSM and NUHM1 parameter space to the current data from SUSY and Higgs searches in ATLAS and CMS, as well as dark matter relic density [129, 170]. The study in constrained MSSM scenarios is illustrative but not representative of the full MSSM. The strong constraints provided by the current data in the CMSSM are not necessarily reproduced in more general scenarios. To go beyond the constrained scenarios, consider the phenomenological MSSM (pMSSM) [171]. This model is the most general CP- and R-parity-conserving MSSM, assuming MFV at the weak scale and the absence of FCNCs at tree level. It contains 19 free parameters: 10 sfermion masses, 3 gaugino masses, 3 trilinear couplings and 3 Higgs masses.
21The effect of SUSY models on AFB(B K+) is discussed in
Ref. [166].
Fig. 7 SUSY spread in NMFV-models [167]. The light (dark) grey shaded areas are the 95 % (68 %) condence limit (C.L.) bounds from B K()l+l data [40]. The red dotted line denotes the
Z-penguin correlation CZp10/CZp9 = 1/(4 sin2 W 1). The SM point
(CSM9, CSM10) is marked by the red dot
To study the impact of the B0s + results on the
pMSSM, the parameter space is scanned and for each point in the space the consistency of the model with experimental bounds is tested [172]. The left panel of Fig. 9 shows the density of points as a function of MA before and after applying the combined 2010 LHCb and CMS B0s + limit
(1.1 108 at 95 % C.L. [173]), as well as the projection
for a SM-like measurement with an overall 20 % theoretical and experimental uncertainty. As can be seen the density of the allowed pMSSM points is reduced by a factor of 3, in the case of a SM-like measurement. The right panel shows the same distribution in the (MA, tan ) plane. Similar to the
CMSSM case, the region with large tan and small MA is most affected by the experimental constraints.
The interplay with Higgs boson searches can also be very illuminating as any viable model point has to be in agreement with all the direct and indirect limits. As an example, if a scalar Higgs boson is conrmed at 125 GeV,22
the MSSM scenarios in which the excess would correspond to the heaviest CP-even Higgs (as opposed to the lightest Higgs) are ruled out by the B0s + limit, since they
would lead to a too light pseudoscalar Higgs.
It is clear that with more precise measurements a large part of the supersymmetric parameter space could be disfavoured. In particular the large tan region is strongly af-
22At ICHEP 2012 the observation of a new particle consistent with the SM Higgs boson was reported by ATLAS and CMS [174, 175].
Eur. Phys. J. C (2013) 73:2373 Page 17 of 92
Fig. 8 Impact of the latest B0s + limits on the (MA, tan )
plane in the (left) CMSSM and (right) NUHM1 [168]. In each case, the full global t is represented by an open green star and dashed blue
and red lines for the 68 and 95 % C.L. contours, whilst the ts to the incomplete data sets are represented by closed stars and solid contours
Fig. 9 Distribution of pMSSM points after the B0s + con
straint projected on the MA (left) and (MA, tan ) plane (right) for all accepted pMSSM points (medium grey), points not excluded by the combination of the 2010 LHCb and CMS analyses (dark grey) and the
projection for the points compatible with the measurement of the SM expected branching fractions with a 20 % total uncertainty (light grey) [172]
fected by B0s + as can be seen in Fig. 5. Also, a mea
surement of B(B0s +) lower than the SM prediction
would rule out a large variety of supersymmetric models. In addition, B K+ observables play a complemen
tary role especially for smaller tan values. With reduced theoretical and experimental errors, the exclusion bounds in Figs. 6 and 7 for example would shrink leading to important consequences for SUSY parameters.
2.8 Rare charm decays
So far the focus of this chapter has been on rare B decays, but the charm sector also provides excellent probes for NP in the form of very rare decays. Unlike the B decays described in the previous sections, the smallness of the d, s and b quark masses makes the GlashowIliopoulosMaiani (GIM) cancellation in loop processes very effective. Branch-
ing ratios governed by FCNC are hence not expected to exceed O(1010) in the SM. These processes can then receive
contributions from NP scenarios which can be several orders of magnitude larger than the SM expectation.
2.8.1 Search for D0 +
The branching fraction of the D0 + decay is dom
inated in the SM by the long distance contributions due to the two photon intermediate state, D0 . The experi
mental upper limit on the two photon mode can be combined with theoretical predictions to constrain B(D0 +) in
the framework of the SM: B(D0 +) < 6 1011 at
90 % C.L. [176]. Particular NP models where this decay is enhanced include supersymmetric models with R-parity violation (RPV), which provides tree-level contributions that would enhance the branching fraction. In such models, the
Page 18 of 92 Eur. Phys. J. C (2013) 73:2373
branching fraction would be related to the D0D0 mixing parameters. Once the experimental constraints on the mixing parameters are taken into account, the corresponding tree-level couplings can still give rise to B(D0 +) of up
to O(109) [177].
Preliminary results from a search for these rare decays have been performed by the LHCb Collaboration [178]. The upper limit obtained with 0.9 fb1 of data taken in 2011 is:
B[parenleftbig]D0 +[parenrightbig]
1.3(1.1) 108 at 95 (90) % C.L. (21)
This upper limit on the branching fraction, already an improvement of an order of magnitude on previous results, is expected to improve down to 5 109 by the end of the rst
data-taking phase of the LHCb experiment.
2.8.2 Search for D+(s) h++ and D0 hh +
The D+(s) h++ decay rate is dominated by long dis
tance contributions from tree-level D+(s) h+V decays,
where V is a light resonance (V = , , ). The long-
distance contributions have an effective branching fraction (with V +) above 106 in the SM. Large devia
tions in the total decay rate due to NP are therefore unlikely.
However, the regions of the dimuon mass spectrum far from these resonances are interesting probes. Here, the SM contribution stems only from FCNC processes, that should yield no partial branching ratio above 1011 [179]. NP contributions could enhance the branching fraction away from the resonances by several orders of magnitude: e.g. in the RPV model mentioned above, or in models involving a fourth quark generation [179, 180].
The LHCb experiment is well-suited to search for D+(s) h+ decays. The long distance contributions can be used to normalise the decays searched for at high and low dimuon mass: their decay rate will be measured relative to that of D+(s) +(+). These resonant decays have a
clean experimental signature and their nal state only differs from the signal in the kinematic distributions, which helps to reduce the systematic uncertainties. The sensitivity of the LHCb experiment can be estimated by comparing the yields of D+(s) +(+) decays observed in
LHCb with those obtained by the D0 experiment, which established the best limit on these modes so far [181]. With an integrated luminosity corresponding to 1.0 fb1, upper limits on the D+ (D+s) modes are expected close to 108 (107) at 90 % C.L.
In analogy to the B sector, there is a wealth of observables potentially available in four-body rare decays of D mesons. In the decays D0 hh + (with h( ) = K or
), forwardbackward asymmetries or asymmetries based on T -odd quantities could reveal NP effects [179, 182, 183].
Clearly the rst challenge is to observe the decays which, depending on their branching fractions, may be possible with the 2011 data set. However, the 50 fb1 collected by the upgraded LHCb detector will be necessary to exploit the full set of observables in these modes.
2.9 Rare kaon decays
The cross-section for K0S production at the LHC is such that
1012K0S + would be reconstructed and selected in
LHCb with a fully efcient trigger. This provides a good opportunity to search for rare K0S decays in channels with high trigger efciency, in particular K0S +.
The decay K0S + is a avour-changing neutral
current that has not yet been observed. This decay is strongly suppressed in the SM, with an expected branching fraction of [184, 185]
B[parenleftbig]K0S +[parenrightbig] = (5.0 1.5) 1012, (22)
while the current experimental upper limit is 3.2 107 at
90 % C.L. [186]. The study of K0S + has been sug
gested as a possible way to look for new light scalars [184], and indeed NP contributions up to one order of magnitude above the SM expectation are allowed [185]. Enhancements above 1010 are less likely. Bounds on B(K0S +)
close to 1011 could be useful to discriminate among NP scenarios if other modes, such as K+ +
, indicated a non-standard enhancement of the s dl l transition. First
results from LHCb, B(K0S +) < 9 109 at 90 %
C.L. [187], have signicantly better sensitivity than the existing results. With improved triggers on low mass dimuons, LHCb could reach branching fractions of O(1011) or be
low with the luminosity of the upgrade. Decays of K0L mesons into charged tracks can also be reconstructed, but with much less (1 %) efciency compared to a similar de
cay coming from a K0S meson. This is due to the long distance of ight of the K0L state, which tends to decay outside the tracking system.
2.10 Lepton avour and lepton number violation
The experimental observation of neutrino oscillations provided the rst signature of lepton avour violation (LFV). The consequent addition of mass terms for the neutrinos in the SM implies LFV also in the charged sector, but with branching fractions smaller than 1040. NP could signicantly enhance the rates but, despite steadily improving experimental sensitivity, charged lepton avour violating (cLFV) processes like e , N eN,
e+ee, and + (with =
e, ) have not been observed. Numerous theories beyond the SM predict larger LFV effects in decays than decays, with branching fractions within experimental
Eur. Phys. J. C (2013) 73:2373 Page 19 of 92
reach [188]. An observation of cLFV would thus be a clear sign for NP, while lowering the experimental upper limit will help to further constrain theories [189].
Another approach to search for NP is via lepton number violation (LNV). Decays with LNV are sensitive to Majorana neutrino massestheir discovery would answer the long-standing question of whether neutrinos are Dirac or Majorana particles. The strongest constraints on minimal models that introduce neutrino masses come from neutrinoless double beta decay processes, but searches in heavy avour decays provide competitive and complementary limits in models with extended neutrino sectors.
In this section, LFV and LNV decays of leptons and B mesons with only charged tracks in the nal state are discussed.
2.10.1 Lepton avour violation
The neutrinoless decay + is a particularly
sensitive mode in which to search for LFV at LHCb as the inclusive production cross-section at the LHC is large (80 b, coming mainly from D+s decays23) and muon
nal states provide clean signatures in the detector. This decay is experimentally favoured with respect to the decays and e+ee due to the consid
erably better particle identication of the muons and better possibilities for background discrimination. LHCb has reported preliminary results from a search for the decay + using 1.0 fb1 of data [191]. The upper
limit on the branching fraction was found to be B(
+) < 7.8 (6.3) 108 at 95 % (90 %) C.L, to be
compared with the current best experimental upper limit from Belle: B( +) < 2.1 108 at 90 % C.L.
As the data sample increases this limit is expected to scale as the square root of the available statistics, with possible further reduction depending on improvements in the analysis.The large integrated luminosity that will be collected by the upgraded experiment will provide sensitivity corresponding to an upper limit of a few times 109. Searches will also be conducted in modes such as p+ or ,
where the existing limits are much weaker, and low background contamination is expected in the data sample.24
The pseudoscalar meson decays probe transitions of the type q q and hence are particularly sensitive to
leptoquark-models and thus provide complementarity to lep-tonic decay LFV processes [193, 194]. For the LHCb experiment, both decays from D and B mesons are accessible. Sensitivity studies for the decays B0(s) e+ and
23Calculated from the b b and c c cross-sections measured at the LHCb
experiment and the inclusive branching ratios b and c [190].
24Preliminary results on p+ and p were pre
sented at TAU 2012 [192].
D0 e+ are ongoing. Present estimates indicate that
LHCb will be able to match the sensitivity of the existing limits from the B factories and CDF in the near future.
2.10.2 Lepton number violation
In lepton number violating B and D meson decays a search can be made for Majorana neutrinos with a mass of O(1 GeV). These indirect searches are performed by
analysing the production of same sign charged leptons in D or B decays such as D+s ++ or B+ ++
[28, 195]. These same sign dileptonic decays can only occur via exchange of heavy Majorana neutrinos. Resonant production may be possible if the heavy neutrino is kinematically accessible, which could put the rates of these decays within reach of the future LHCb luminosity. Nonobservation of these LNV processes, together with low energy neutrino data, would lead to better constraints for neutrino masses and mixing parameters in models with extended neutrino sectors.
Using 0.4 fb1 of integrated luminosity from LHCb, limits have been set on the branching fraction of B+
D(s)++ decays at the level of a few times 107 and on B+ ++ at the level of 1 108 [196, 197].
These branching fraction limits imply a limit on, for example, the coupling |V4| between and a Majorana neu
trino with a mass in the range 1 < mN < 4 GeV/c2 of
|V4|2 < 5 105.
2.11 Search for NP in other rare decays
Many extensions of the SM predict weakly interacting particles with masses from a few MeV to a few GeV [198 202] and there are some experimental hints for these particles from astrophysical and collider experiments [203, 204]. For example, the HyperCP Collaboration has reported an excess of + p+ events with dimuon invariant
masses around 214 MeV/c2 [205]. These decays are consistent with the decay + pX with the subsequent de
cay X +. Phenomenologically, X can be interpreted
as a pseudoscalar or axial-vector particle with lifetimes for the pseudoscalar case estimated to be about 1014 s [206
208]. Such a particle could, for example, be interpreted as a pseudoscalar sgoldstino [207] or a light pseudoscalar Higgs boson [209].
The LHCb experiment has recorded the worlds largest data sample of B and D mesons which provides a unique opportunity to search for these light particles. Preliminary results from a search for decays of B0(s) ++
have been reported [210]. Such decays could be mediated by sgoldstino pair production [211]. No excess has been found and limits of 1.3 and 0.5 108 at 95 % C.L. have been set
for the B0s and B0 modes respectively. The analysis can naturally be extended to D0 ++ decays, as well as
Page 20 of 92 Eur. Phys. J. C (2013) 73:2373
B0(s) V 0+ (V 0 = K()0, 0, ), where the dimuon
mass spectrum can be searched for any resonant structure.
Such an analysis has been performed by the Belle Collaboration [212]. With the larger data sample and exible trigger of the LHCb upgrade, it will be possible to exploit several new approaches to search for exotic particles produced in decays of heavy avoured hadrons (see, e.g. Ref. [213]).
3 CP violation in the B system
3.1 Introduction
CP violation, i.e. violation of the combined symmetry of charge conjugation and parity, is one of three necessary conditions to generate a baryon asymmetry in the Universe [214]. Understanding the origin and mechanism of CP violation is a key question in physics. In the SM, CP violation is fully described by the CKM mechanism [20, 21]. While this paradigm has been successful in explaining the current experimental data, it is known to generate insufcient CP violation to explain the observed baryon asymmetry of the Universe. Therefore, additional sources of CP violation are required. Many extensions of the SM naturally contain new sources of CP violation.
The b hadron systems provide excellent laboratories to search for new sources of CP violation, since new particles beyond the SM may enter loop-mediated processes such as b q FCNC transitions with q = s or d, leading to discrep
ancies between measurements of CP asymmetries and their SM expectations. Two types of b q FCNC transitions are
of special interest: neutral B meson mixing ( B = 2) pro
cesses, and loop-mediated B decay ( B = 1) processes.
The LHCb experiment exploits the large number of b hadrons, including the particularly interesting B0s mesons, produced in protonproton collisions at the LHC to search for CP-violating NP effects. Section 3.2 provides a review of the status and prospects in the area of searches for NP in B0(s)
mixing, in particular through measurements of the mixing phases d(s) and the semileptonic asymmetries ad(s)sl. The
LHCb efforts to search for NP in hadronic b s penguin
decays, such as B0s , are discussed in Sect. 3.3. Sec
tion 3.4 describes the LHCb programme to measure the angle of the CKM unitarity triangle (UT) in decay processes described only by tree amplitudes, such as B DK,
B0 DK0 and B0s DsK. These measurements al
low precise tests of the SM description of quark-mixing via global ts to the parameters of the CKM matrix, as well as direct comparisons with alternative determinations of in decay processes involving loop diagrams, such as B0s
K+K. At the end of each section, a brief summary of the most promising measurements with the upgraded LHCb detector and their expected/projected sensitivities is provided.
3.2 B0(s) mixing measurements
3.2.1 B0(s)B0(s) mixing observables
The effective Hamiltonian of the B0qB0q (q = d, s) system
can be written as
Hq =
[parenrightBigg] , (23)
where Mq11 = Mq22 and q11 = q22 hold under the assumption
of CPT invariance. The off-diagonal elements Mq12 and q12 are responsible for B0qB0q mixing phenomena. The dispersive part Mq12 corresponds to virtual B = 2 transitions
dominated by heavy internal particles (top quarks in the SM) while the absorptive part q12 arises from on-shell transitions due to decay modes common to B0q and B0q mesons.
Diagonalising the Hamiltonian matrix leads to the two mass eigenstates BqH,L (H and L denote heavy and light, respectively), with mass MqH,L and decay width qH,L, being linear combinations of avour eigenstates with complex coefcients25 p and q that satisfy |p|2 + |q|2 = 1,
[vextendsingle][vextendsingle]BqL,H[angbracketrightbig] =
[parenleftBigg] Mq11 Mq12
Mq12 Mq22
[parenrightBigg]
i 2
[parenleftBigg] q11 q12
q12 q22
p[vextendsingle][vextendsingle]B0
q
[angbracketrightbig] q[vextendsingle][vextendsingle]B0
. (24)
The magnitudes of Mq12 and q12 and their phase difference are physical observables and can be determined from measurements of the following quantities (for more details see, e.g., Refs. [215, 216]):
the mass difference between the heavy and light mass
eigenstates
mq MqH MqL 2[vextendsingle][vextendsingle]Mq12[vextendsingle][vextendsingle]
q
[parenleftbigg]1 |
q12|2 8|Mq12|2
sin2 q12[parenrightbigg];
(25)
where q12 = arg(Mq12/ q12) is convention-independent; the decay width difference between the light and heavy
mass eigenstates
q qL qH
2[vextendsingle][vextendsingle]
q 12
sin2 q12[parenrightbigg]; (26)
25Strictly, the coefcients p and q should also have subscripts q to indicate that they can be different for B0 and B0s, but these are omitted to simplify the notation.
[vextendsingle][vextendsingle]
cos q12[parenleftbigg]1 + |
q12|2 8|Mq12|2
Eur. Phys. J. C (2013) 73:2373 Page 21 of 92
the avour-specic asymmetry26
aqsl |
p/q|2 |q/p|2 |p/q|2 + |q/p|2
| q12|
|Mq12|
sin q12
q mq tan q12. (27)
The correction terms in Eqs. (25) and (26) proportional to sin2 q12 are tiny. In addition, the ratio of q and p can be written
q p
[parenrightbigg]
=
mq + i2 q 2(Mq12 i2 q12)
, (28)
and hence in both B0 and B0s systems one obtains, to a good approximation, a convention-dependent expression (for an unobservable quantity) arg(q/p) arg(Mq12).
Since BB mixing is dominated by the box diagram with internal top quarks, this leads to an expression in terms of CKM matrix elements arg(q/p) = 2 arg(V tbVtq).
Further information can be obtained by measuring the phase difference between the amplitude for a direct decay to a nal state f and the amplitude for decay after oscillation. In the case that the decay is dominated by b c cs tree
amplitudes, and where f is a CP eigenstate f with eigenvalue f ,27 this phase difference is denoted as
q arg
[parenrightbigg], (29)
where Af andf are the decay amplitudes of B f and
B f , respectively. In the absence of direct CP violation Af /Af = f . With these approximations, the CP-violating
phases in B mixing give the unitarity triangle angles, d
2 and s 2s,28 where the angles are dened as [44]
arg
[parenleftbigg]f qpf
Af
[parenleftbigg]
VcdV cb
VtdV tb
[parenrightbigg], s arg
[parenleftbigg]
[parenrightbigg]. (30)
Clearly, if there is NP in Mq12 or in the decay amplitudes, the measured value of q can differ from the true value of ()2(s). Similarly, NP in either Mq12 or q12 can make the
observed value of aqsl differ from its SM prediction. Note, however, that even within the SM, there is a difference between q and q12 [217]. Nonetheless, the notations d(s)
and (s) are usually used interchangeably.
26The notation aqsl is used to denote avour-specic asymmetries, reecting the fact that the measurements of these quantities use semilep-tonic decays.
27The cases for more generic nal-states can be found in the literature, e.g. Ref. [44].
28Note the conventional sign-ip between and s ensures that both are positive in the SM.
The s notation has been used in the LHCb measurements of the CP-violating phase in B0s mixing, using J/
[10, 139] and J/f0(980) [218, 219] nal states. By using the same notation for different decays, an assumption that arg(f /Af ) is common for different nal states is being
made. This corresponds to an assumption that the penguin contributions to these decays are negligible. Although this is reasonable with the current precision, as the measurements improve it will be necessary to remove such assumptions several methods to test the contributions of penguin amplitudes are discussed below. These include measuring q with different decay processes governed by different quark-level transitions. Previous experiments have used the notation 2eff in particular for measurements based on b q qs
(q = u, d, s) transitions; for symmetry the notation 2effs is
used in corresponding cases in the B0s system, although the cancellation of the mixing and decay phases in B0s decays governed by b q qs amplitudes is expected to lead to a
vanishing CP violation effect (within small theoretical uncertainties).
In the SM, the mixing observables can be predicted using CKM parameters from a global t to other observables and hadronic parameters (decay constants and bag parameters) from lattice QCD calculation. These predictions can be compared to their direct measurements to test the SM and search for NP in neutral B mixing.
3.2.2 Current experimental status and outlook
The current measurements and SM predictions for the mixing observables are summarised in Table 1.
The HFAG average of the B0s mass difference ms in Table 1 is based on measurements performed at CDF [228]
and LHCb [226, 229]. It is dominated by the preliminary LHCb result obtained using 0.34 fb1 of data [226], which is also given in Table 1. These are all consistent with the SM prediction. Improving the precision of the SM prediction is desirable to further constrain NP in Ms12, and requires improving the accuracy of lattice QCD evaluations of the decay constant and bag parameter (see Ref. [216] and references therein).
The observables s and s have been determined simultaneously from B0s J/ decays using time-
dependent avour tagged angular analyses [230, 231]. The rst LHCb tagged analysis using 0.34 fb1 of data [10] already provided a signicant constraint on s and led to the rst direct evidence for a non-zero value of s. LHCb has also determined the sign of s to be positive at 4.7 condence level [232] by exploiting the interference between the K+K S-wave and P-wave amplitudes in the (1020)
mass region [233]. This resolved the two-fold ambiguity in the value of s for the rst time. LHCb has made a preliminary update of the B0s J/ analysis using the full data
VtsV tb VcsV cb
Page 22 of 92 Eur. Phys. J. C (2013) 73:2373
Table 1 Status of B mixing measurements and corresponding SM predictions. New results presented at ICHEP 2012 and later are not included. The inclusive same-sign dimuon asymmetry AbSL is dened below and in Ref. [159]
Observable Measurement Source SM prediction References
B0s system ms (ps1) 17.719 0.043 HFAG 2012 [44] 17.3 2.6 [220225]
17.725 0.041 0.026 LHCb (0.34 fb1) [226]
s (ps1) 0.105 0.015 HFAG 2012 [44] 0.087 0.021 [220225]
0.116 0.018 0.006 LHCb (1.0 fb1) [139]
s (rad) 0.044 +0.0900.085 HFAG 2012 [44] 0.036 0.002 [119, 221225]0.002 0.083 0.027 LHCb (1.0 fb1) [139]
assl (104) 17 91 +1415 D0 (no AbSL) [227] 0.29 +0.090.08 [119, 221225]105 64 HFAG 2012 (including AbSL ) [44]
Admixture of B0 and B0s systemsAbSL (104) 78.7 17.1 9.3 D0 [159] 2.0 0.3 [220225]
B0 system
md (ps1) 0.507 0.004 HFAG 2012 [44] 0.543 0.091 [216, 221225]
d/d 0.015 0.018 HFAG 2012 [44] 0.0042 0.0008 [220225]
sin 2 0.679 0.020 HFAG 2012 [44] 0.832 +0.0130.033 [119, 221225]
adsl (104) 5 56 HFAG 2012 [44] 6.5 +1.91.7 [119, 221225]
Fig. 10 (Left) Preliminary LHCb measurement of s and s from B0s J/ decays using 1.0 fb1 [139]. (Right) HFAG 2012 combination
of s and s results, where the 1 condence region is shown for each experiment and the combined result [44]. Note the different scales
sample of 1.0 fb1 collected in 2011 [139]. The results from
this analysis,
s = 0.001 0.101 0.027 rad, s = 0.116 0.018 0.006 ps1,
(31)
are shown in Fig. 10 (left), and are in good agreement with the SM expectations.
LHCb has also studied the decay B0s J/+.
This decay process is expected to proceed dominantly via b ccs (the s s produced in the decay rescatters to +
through either a resonance such as f0(980) or a nonresonant process). Therefore, these events can be used to measure s. The + mass range 7751550 MeV shown in
Fig. 11 (left) is used for the measurement. In contrast to
B0s J/, no angular analysis is needed to disentan
gle the CP eigenstates, since the nal state is determined to be dominantly CP-odd in this mass range [234]. On the other hand, s cannot be determined in this decay channel alone.29 Using as input the value of s obtained from B0s J/, the measurement from the analysis of
B0s J/+ with 1.0 fb1 is [219]s = 0.019 +0.1730.174 +0.0040.003 rad. (32)
Figure 11 (right) shows the log-likelihood scan for the s parameter for the B0s J/+ analysis. The latest
29The effective lifetime of B0s J/f0(980) is sensitive to s and
CP violation parameters [235] and has been measured by LHCb [236].
Eur. Phys. J. C (2013) 73:2373 Page 23 of 92
Fig. 11 (Left) + mass distribution of selected B0s J/+ candidates and range used for the s measurement. (Right) log-likelihood
difference as a function s [219]
HFAG average in Table 1 combines the LHCb results with the B0s J/ analysis results from CDF using 9.6 fb1
[237] and D0 using 8.0 fb1 [238]. The LHCb result dominates the combination, which is in good agreement with the
SM predictions, as seen in Fig. 10 (right).30
The LHCb B0s J/ and B0s J/+ analy
ses discussed above only used opposite side avour tagging [239, 240]. Future updates of these analyses will gain in sensitivity by also using the same side kaon tagging information, which so far has been used in a preliminary determination of ms [226, 241]. Currently, the systematic uncertainty on s is dominated by imperfect knowledge of the background, angular acceptance effects and by neglecting potential contributions of direct CP violation. All of these uncertainties are expected to be reduced with more detailed understanding and some improvements in the analysis. Therefore it is expected that the determination of s will remain limited by statistical uncertainties, even with the data samples available after the upgrade of the LHCb detector. In addition to B0s J/ and B0s J/+, other
b ccs decay modes of B0s mesons, such as J/, J/
[242] and D+sDs [243] will be investigated. These decays have been measured at LHCb [244, 245].
The SM prediction s = 0.036 0.002 rad could re
ceive a small correction from doubly CKM-suppressed penguin contributions in the decay. The value of this correction is not precisely known, and may depend on the decay mode. Moreover, NP in the b ccs decay may also affect
the results. Although such effects are already constrained by results from B+ and B0 decays, NP in the decay amplitudes can lead to polarisation-dependent mixing-induced CP asymmetries and triple product asymmetries in B0s J/
[246]. Such effects will be searched for in future analyses.
30Results from ATLAS and CMS, presented at ICHEP2012 or later, are not included in this compilation.
The avour-specic asymmetries provide important complementary constraints on B = 2 processes. The D0
collaboration has performed a direct measurement of assl in semileptonic B0s decays [227], which is only weakly constraining.31 However, a measurement of the inclusive same-sign dimuon asymmetry provides better precision, and shows evidence of a large deviation from its SM prediction [159]. The inclusive measurement is sensitive to a linear combination of the avour-specic asymmetries, AbSL = Cdadsl + Csassl, where Cq depend on the production
fractions and mixing probabilities, and are determined to be Cd = 0.594 0.022, Cs = 0.406 0.022 [159].32 As dis
cussed in Sect. 3.2.3, the D0 AbSL result is in tension with other B = 2 observables. Improved measurements of assl
and adsl from LHCb are needed to solve this puzzle.
In LHCb, assl can be determined from the asymmetry between the time-integrated untagged decay rates of B0s decays to D+sX and Ds+X, with Ds , K+K
(or with the full Ds K+K Dalitz plot). Detector-
and trigger-induced asymmetries can be calibrated in control channels, and the fact that data is taken with both magnet dipole polarities can be used as a handle to reduce systematic uncertainties. The effect of B0s production asymmetry is cancelled due to the fast oscillation, so the asymmetry in the yields of D+sX and Ds+X decays is trivially related to assl. A rst preliminary LHCb result on assl, based on 1.0 fb1, has been reported at ICHEP 2012, and is the most precise measurement of this quantity to date [248],
assl = (0.24 0.54 0.33) %. (33)
31An updated measurement has been presented by D0 at ICHEP 2012 [247].
32The factors Cd and Cs depend in principle on the collision environment and the kinematic acceptance, though the dependence appears to be weak. Trigger requirements can also affect the values of these parameters.
Page 24 of 92 Eur. Phys. J. C (2013) 73:2373
Fig. 12 Comparison of direct and indirect determinations of sin d sin 2 vs. B(B+ +), from Ref. [252]
It will also be possible to measure adsl using D+X nal states with D+ K++. In this case extra care must
be taken to calibrate the difference between K+ and K detection efciencies and an independent measurement of the
B0 production asymmetry is needed as input. Moreover, the CP-symmetric background from charged B decays is significant and must be accurately subtracted.
In the B0 system, md and sin d (i.e. sin 2) have been measured precisely by the B factories [44]. The measurements of d and adsl are consistent with their SM predictions, but their uncertainties are at least an order of magnitude larger than those of the predictions. Hence a large improvement in precision is needed to test the SM using these observables. In the B0 sector there has been for some time a tension between the measurements of sin 2 [44] and the branching ratio B(B+ +) [249, 250], as shown in
Fig. 12,33 and discussed in Sect. 3.2.4. This motivates improved measurements of sin 2 and improved understanding of the possible effects of penguin contributions to this observable.
LHCb has already presented rst results on md [229, 253] and sin 2 [254]. The md result is the worlds most precise single measurement of this quantity, while the sensitivity on sin 2 will be competitive with the B factory results using the data sample that will be collected by the end of 2012. LHCb can also search for enhancements in the value of d above the tiny value expected in the SM, e.g. by comparing the effective lifetimes of B0 J/K0S
33An updated measurement of B(B+ +) using the hadronic tag
method was presented by Belle at ICHEP 2012 [251]: this new result reduces, but does not completely remove, the tension in the ts. The analyses discussed here do not include this new result.
and B0 J/K0 [255]. Signicantly improving the pre
cisions of the B0 mixing observables is an important goal of the LHCb upgrade, as will be discussed in Sect. 3.2.6.
The SM predictions of b-hadron lifetimes and q are all obtained within the framework of the heavy quark expansion. LHCb is actively working on measurements of bhadron lifetimes and lifetime ratios, which will be used to test these predictions. The knowledge obtained from this work will allow to improve the SM predictions of q for the purpose of searching for NP. Furthermore, a more precise measurement of the ratio of B0s to B0 lifetimes could either support or strongly constrain the existence of NP in s12 [152, 153, 216, 220, 256].
3.2.3 Model independent constraints on new physics in B mixing
Neutral Bq meson mixing is described in terms of the three parameters |Mq12|, | q12| and q = arg(Mq12/ q12)
for each of the two systems q = d, s. In the context of
model-independent analyses, the NP contributions can be parametrised in the form of two complex quantities q and q [153, 257]
Mq12 = Mq,SM12| q|ei
q , q12 = q,SM12|q|ei
q , (34)
i.e., 4 real degrees of freedom. The observables which depend on these parameters are the mass and decay width differences and avour-specic CP-asymmetries. They can be expressed in terms of the SM predictions and NP parameters as
mq = ( mq)SM| q|,
q = ( q)SM|q|
cos(q,SM12 + q q) cos q,SM12
(35)
,
aqsl = [parenleftbig]aqsl[parenrightbig]SM |
q|
| q|
sin(q,SM12 + q q) sin q,SM12
, (36)
up to corrections suppressed by tiny ( q12/Mq12)2. Note that the expressions of Eqs. (35) and (36) depend only on the difference ( q q). The SM predictions of mq, q
and aqsl can be found in Table 1 and for q12 [220]
d,SM12 = (0.075 0.024) rad,
s,SM12 = (0.0038 0.0010) rad.
(37)
The values of mq have been precisely measured, giving rather strong constraints on | q| which are limited by
the knowledge of hadronic matrix elements. The new s measurement of LHCb starts to provide useful constraints.
Eur. Phys. J. C (2013) 73:2373 Page 25 of 92
Fig. 13 Model-independent t [256] in the scenario that NP affects Mq12 separately. The coloured areas represent regions with C.L. < 68.3 % for the individual constraints. The red area shows the region
with C.L. < 68.3 % for the combined t, with the two additional contours delimiting the regions with C.L. < 95.45 % and C.L. < 99.73 %
As discussed above, the CP-asymmetries aqsl are currently rather weakly constrained.
Further information can be extracted from the mixing-induced CP-asymmetries in B0 J/K0S and B0s
J/ decays
d = 2 + d d, s = 2s + s s, (38) where d and s denote shifts of d and s induced by either SM penguin diagrams or NP contributions in the decay process. In the SM d and s are related to the angles and s of the according unitarity triangles. When short-distance NP contributions are introduced, q depends on the phase q of Mq12, whereas the phase q of q12 does not enter.
The SM penguin pollution to q is expected to be negligible for the current precision of q, and is discussed in detail in Sect. 3.2.5. Beyond the SM, NP can contribute to q in principle in both the tree b ccs decay and the penguin pro
cess. However, in the model-independent analysis described here, NP contributions in the b ccs decay are neglected
and any observed deviation from the SM will be interpreted as effects of NP in neutral B meson mixing. When q is neglected, Eqs. (35), (36) and (38) allow to determine the NP parameters | q|, q, |q| and q.
The assumption of NP in Mq12 only, or equivalently in B = 2 processes only, implies that there is no NP
in B = 1 processes which contribute to the absorptive
part q12. Consequently, NP can only decrease q (since cos(q,SM12) is maximal, see Eq. (35)) with respect to the SM [231, 258]. This scenario has been studied in extensions of the CKM t of the SM which includes B = 2 measure
ments to constrain the CKM elements Vtq [256, 259], in
combination with many other avour-changing processes. Including LHCb measurements [139, 229]34 the SM point d = s = 1 is disfavoured by 2.4 [256] (prior to the
LHCb results being available, a similar analysis gave a discrepancy of 3.6 driven mainly by the anomalous dimuon asymmetry [259]). The analysis gives s consistent with the SM, within large uncertainties, whereas the more precise data in the B0 system hint at a deviation in d (see Fig. 13).
Moreover, NP effects up to 3040 % are still allowed in both systems at the 3 level. It should be noted, that the large deviations in the B0 sector are not only due to AbSL, but also due to the tension between sin d and B(B+ +).
NP contributions to the absorptive part q12 of B mixing can enter through B = 1 decays b qX with light
degrees of freedom X of total mass below mB. In some particular models such contributions can arise [154, 260] and interfere constructively or destructively with the SM contribution. The recent measurements of q and of AbSL revived interest in this possibility. Model-independent analyses have conrmed that the AbSL measurement cannot be accommodated within the SM [261, 262]. A model-independent t assuming NP in both Mq12 and q12 has been considered in the framework of an extended CKM t [256]. In this case, the experimental data can be accommodated, and the B0s system remains rather SM-like, but large NP contributions in the B0 system are required.
Model-independent analyses based on Eq. (34) are restricted to a particular set of observables, mainly those with B = 2, since correlations with B = 1 measurements are
34But not including results shown for the rst time at ICHEP 2012 or later.
Page 26 of 92 Eur. Phys. J. C (2013) 73:2373
difcult to quantify. Either additional assumptions on the nature of X in b qX or explicit NP models will per
mit better exploitation of the wealth of future experimental information. In fact, such analyses have found it difcult to accommodate the hypothesis of large NP in q12 with current B = 1 measurements, therefore NP in q12
seems unlikely to provide a full explanation of the measured value of AbSL. In the case of X = f f, the B = 1 oper
ators b (d, s)f f (f = q or ) are strongly constrained
[152], with the exception of b scc and b s+. Cur
rently, only a weak upper bound on B(B+ K++) [lessorsimilar]
3.3 103 at 90 % C.L. [263] exists whereas other de
cays B0s +, B Xs+ might be indirectly con
strained with additional assumptions (see also the discussion in Sect. 2.5.2). As an example, the improved LHCb measurement of B0
s /B0 allowed the derivation of a stronger bound on B(B0s +). Still, a model-independent anal
ysis of the complete set of b s+ operators does not
allow for deviations larger than 35 % from the SM in s12 [153], which is much too small to resolve the tension with
AbSL. For b d+ operators there exists a stronger con
straint B(B0 +) [lessorsimilar] 4 103 and even smaller NP
effects are expected in d12. Other proposed solutions such as the existence of new light spin-0 [264] or spin-1 [265] X states could be seriously challenged by improved measurements of quantities, such as ratios of lifetimes, which are theoretically under good control [220].
In summary, NP contributions to | q| are already quite
constrained due to mq measurements and theoretical progress is required in order to advance. Although the phases q are constrained by the recent LHCb measurement of s, and B factory measurements of d, there is a mild tension with the SM in model-independent ts of B = 2
measurements [153, 256, 261, 262], especially when allowing for NP in q12. On the other hand, NP effects in q12 are expected to be limited when constraints from B = 1
observables are taken into account. Independent improved measurements of aqsl are needed in order to resolve the nature of the current discrepancies between the B = 2 ob
servables with their SM expectations and other observables entering global CKM ts. Further, improved measurements of q and q, as well as of control channels, are needed to constrain NP in q12.
3.2.4 CKM unitarity ts in SM and beyond
This section presents the results of the unitarity triangle (UT) analysis performed by two groups: UTt [266] and CKMtter [252].35 The main aim of the UT analysis is the determination of the values of the CKM parameters, by
35Similar approaches have been developed in Refs. [267, 268].
comparing experimental measurements and theoretical predictions for several observables. The popular Wolfenstein parametrisation allows for a transparent expansion of the CKM matrix in terms of the sine of the small Cabibbo angle, , with the other three parameters being A,
and
.
Assuming the validity of the SM, one can perform a t to the available measurements. LHCb results already make important contributions to the constraints on and ms. With more statistics, LHCb results are expected to impact on other CKM t inputs, including and sin 2. It is important to note the crucial role of lattice QCD calculations as input to the CKM ts. For example, the parameters fBs [radicalbig]BBs and
enter the constraints on ms and md/ ms. At the end of 2011, the precision of the calculations was at the level of 5.4 % and 2.6 %, respectively [109]. The necessary further progress to obtain the full benet of the LHCb measurements appears to be in hand exploiting algorithmic advances as well as ever increasing computing power for the lattice calculations.
The overall quality of the t can be judged using the projection of the likelihoods on the { ,
} plane. This projection
is shown in Fig. 14. The t can also be made removing one of the inputs, giving a prediction for the removed parameter, which then can be compared to the experimental value. The results of this study are presented in Table 2. Both groups nd a tension between B(B ) and sin 2, as can be
seen in Fig. 12. (As discussed in Sect. 3.2.2 this tension will be reduced once the latest Belle result on B(B+ + )
[251] is included in the ts.) Improved measurements of sin 2 can shed further light on this problem.
In order to estimate the origin of the tensions, the UT-t and CKMtter groups have performed analyses including model-independent NP contributions to neutral meson mixing processes (see Refs. [256, 270] for details). The NP effects are introduced through the real valued C and parameters (ANP = CeiASM) in case of UTt and the complex
valued parameter (ANP = ASM) for CKMtter. The pa
rameters are added separately for the B0s and B0 sectors. In the absence of NP, the expected values are C = 1, = 0,
and = 1. For the B0 sector the ts return C = 0.94
0.14 and = (3.6 3.7), and = (0.823 +0.1430.095) +
i(0.199 +0.0620.048). The results for both groups show some
disagreement with the SM, driven by tensions in the input parameters mentioned above. In the B0s sector, on the other hand, the situation is much closer to the SM than before the
LHCb measurements were available: C = 1.02 0.10 and
= (1.1 2.2), and = (0.92 +0.130.08) + i(0.00 0.10).
The results of the studies by both groups point to the absence of big NP effects in B = 2 processes. Nevertheless
there is still signicant room for NP in mixing in both B0 and B0s systems. More precise results, in particular from
LHCb, can enable more careful studies. Besides providing null tests of the SM hypothesis, improved s and assl measurements are crucial to quantity effects of NP in mixing. In
Eur. Phys. J. C (2013) 73:2373 Page 27 of 92
Fig. 14 Result of the UT t within the SM: { ,
} plane obtained by (left) UTt [266] and (right) CKMtter [252]. The 95 % probability regions
selected by the single constraints are also shown with various colours for the different constraints
Table 2 Predictions for some parameters of the SM t and their measurements as combined by the UTt and CKMtter groups. Note that the two groups use different input values for some parameters. The
lines marked with (*) are not used in the full t. Details of the pull calculation can be found in Refs. [259, 269]. New results presented at ICHEP2012 and later are not included in these analyses
Parameter UTt CKMtter
Prediction Measurement Pull Prediction Measurement Pull
() 87.5 3.8 91.4 6.1 +0.5 95.9 +2.25.6 88.7 +2.25.9 1.0 sin 2 0.809 0.046 0.667 0.024 2.7 0.820 +0.0240.028 0.679 0.020 2.6
() 67.8 3.2 75.5 10.5 +0.7 67.2 +4.44.6 66 +1212 0.1 Vub(103) 3.62 0.14 3.82 0.56 +0.3 3.55 +0.150.14 3.92 0.09 0.45 0.0
Vcb(103) 42.26 0.89 41 1 0.9 41.3 +0.280.11 40.89 0.38 0.59 0.0 k(103) 1.96 0.20 2.229 0.010 +1.3 2.02 +0.530.52 2.229 0.010 0.0
ms (ps1) 18.0 1.3 17.69 0.08 0.2 17.0 +2.11.5 17.731 0.045 0.0
B(B )(104) 0.821 0.0077 1.67 0.34 +2.5 0.733 +0.1210.073 1.68 0.31 +2.8 s rad (*) 0.01876 0.0008 0.01822 +0.000820.00080
B(B0s )(109) (*) 3.47 0.27 3.64 +0.210.32 addition a precise determination is essential, not only fora SM global consistency test, but also to x the apex of theUT in the extended ts.
3.2.5 Penguin pollution in b ccs decays
In addition to the very clear experimental signature, precise determination of the B0 and B0s mixing phases is possible due to the fact that in the golden modes, B0
J/K0S and B0s J/, explicit calculation of the rele
vant matrix elements can be avoided, once subleading doubly Cabibbo-suppressed and loop-suppressed terms are assumed to vanish [271]. Estimates yield corrections of the
order O(103) only [272274]; it is however notoriously difcult to actually calculate the relevant matrix elements, and non-perturbative enhancements cannot be excluded. Given the future experimental precision for these and related modes, a critical reconsideration of this assumption is mandatory.
The main problem lies in the fact that once the assumption of negligible penguin contributions is dropped, the evaluation of hadronic matrix elements again becomes necessary, which still does not seem feasible to an acceptable precision for the decays in question. To avoid explicit calculation, symmetry relations can be used, exploiting either avour SU(3) or U-spin symmetry [275281]. Without tak-
Page 28 of 92 Eur. Phys. J. C (2013) 73:2373
ing into account any QCD evaluation and only using control channels to estimate the size of the penguin amplitude, the analyses in Refs. [278, 281] still allow a phase shift of up to a few degrees for d, which would correspond to a very large non-perturbative enhancement of the penguin size. In Ref. [278] a negative sign is preferred which (slightly) reduces the tension in the unitarity triangle t shown in Fig. 12.The reason for the large allowed range of the shift of d is due to the limited precision to which the corresponding control channels B0 J/0 and B0s J/K0, which
are Cabibbo-suppressed compared to the golden modes, are known. For s, an analogous analysis [277] cannot yet constrain the penguin contribution, due to the lack of a B
J/V control channel data for B0s J/. However, in
principle the effects in the B J/V modes are expected
to be of the same order of magnitude as in the B J/P
modes. The control channel B0s J/K0 has already
been observed at CDF [282] and LHCb [283], and work is ongoing to measure its decay rate, polarisations and direct CP asymmetries. This will enable the rst direct constraint on the shift of s due to penguin contributions in the decay B0s J/.36 For B0s J/f0(980) there is an ad
ditional complication due to the unknown hadronic structure of the f0(980) [235].
In addition to insufcient data, there are, at present, theoretical aspects limiting the precision of this method at present, the most important of which is the violation of SU(3) symmetry. Regarding the B0 mixing phase, a full SU(3) analysis can be performed [285] (instead of using only one control channel) to be able to model-independently include SU(3) breaking. The inclusion of SU(3)-breaking contributions is important: their neglect can lead to an overestimation of the subleading effects. Including recent data for two of the relevant modes [286, 287], the analysis shows that the data are at the moment actually compatible with vanishing penguin contributions, with SU(3)-breaking contributions of the order 20 %. Including the penguin contributions, an upper limit on the shift of the mixing-induced CP asymmetry S = sin d sin 2 is derived: | S| [lessorsimilar] 0.01,
with a negative sign for S slightly preferred.37 This is the most stringent limit available, despite the more general treatment of SU(3) breaking. In this analysis still some (conservatively chosen) theoretical inputs are needed to exclude ne-tuned solutions: SU(3)-breaking effects have been restricted to at most 40 % for a few parameters which are not well determined by the t and also have only small inuence on the CP violation observables, and the penguin matrix elements are constrained to be at most 50 % of the
36Other data-driven methods to control penguin contributions to B0s
J/ have been proposed [284].
37Note the denition of S here has a sign difference to that in Ref. [285].
leading contributions. Importantly, these theory inputs can be replaced by experimental measurements, namely of the CP asymmetries in the decay B0s J/K0S, the decay rate
of which has already been measured at LHCb [287] after its observation at CDF [282]. Furthermore, data from all the corresponding modes (i.e. Bd,u,s J/P , with
light pseudoscalar meson P = , ( ) or K) can be used
to determine the shift more precisely, i.e. the related uncertainty is not irreducible, but can be reduced with coming data.
Turning to the second golden mode, B0s J/, in
general, the absolute shift is not expected to be larger than in the B0 case. At the moment the data are not yet available to make a comparable analysis. While the penguin decay mode B0s is not related by symmetry with B0s J/,
comparing their decay rates indicates that the penguin contributions are small, and there are no huge enhancements to be expected for the penguin matrix elements in question.
Nonetheless, a quantitative analysis will ultimately be warranted here as well. In principle, these methods can be adapted to extract the B0s mixing phase including penguin contributions and model-independent SU(3) breaking, thereby improving the method proposed in Ref. [277]. The corresponding partners of the golden mode B0s J/ are
all the decays Bu,d,s J/V , with the light vector mesons
V = K, , or . However, the complete analysis requires
results on the polarisation fractions and CP asymmetries for each of these nal states, and for some of them the experimental signature is quite challenging. In addition, the meson is a superposition of octet and singlet, therefore the control channels involving K and are not as simply related as in the case with a pseudoscalar meson, but require the usage of nonet symmetry, whose precision has to be investigated in turn.
Nevertheless, signicant progress can be expected. Several B J/V modes, including B0(s) J/K0 [283],
are being studied at LHCb. While measurements of the modes involving b d transitions are expected to exhibit
rather large uncertainties at rst, the advantage of the proposed method is the long lever arm due to the relative enhancement 1/2 in the control channels, so that even
moderate precision will be very helpful.
3.2.6 Future prospects with LHCb upgrade
Current measurements of s carried out by LHCb in the J/ and J/+ nal states show no deviation from the SM prediction within uncertainties [139, 219], putting strong constraints on NP in B0s mixing, as discussed in
Sect. 3.2.3. Table 3 shows the current results with 1.0 fb1 and the projected precision for 50 fb1 with the upgraded detector. A precision of <10 mrad is expected for 50 fb1 with the upgraded detector. It is expected that even with
Eur. Phys. J. C (2013) 73:2373 Page 29 of 92
Table 3 LHCb measurements of s. The quoted uncertainties are statistical and systematic, respectively
Final state Current value (rad) with 1.0 fb1 Projected uncertainty (50 fb1)
J/ 0.001 0.101 0.027 0.008
J/+ 0.019 +0.1730.174 +0.0040.003 0.014
Both 0.002 0.083 0.027 0.007
this data sample, the main limitation will be statistical: the largest systematic uncertainties on the current measurement (background description, angular acceptance, effect of xed physics parameters) [139] are expected to be removed with more sophisticated analyses or to scale with statistics. Thus changes as small as a factor of two with respect to the SM should be observable with 3 signicance. This precision will make it possible either to measure a signicant deviation from the SM prediction or otherwise to place severe constraints on NP scenarios.
As discussed in Sect. 3.2.5, contributions from doubly CKM-suppressed SM penguin diagrams could have a nonnegligible effect on the mixing-induced CP asymmetry and bias the extracted value of s. Naive estimates of the bias are of the order O(103) only [272274], but this must be examined with experimental data using avour symmetries to exploit control channels. LHCb can perform an SU(3) analysis using measurements of the decays rates and CP asymmetries in B0s J/K0, B0 J/0 and B0 J/
as control channels for B0s J/. The necessary high
precision can only be reached using the large data sample that will be collected with the upgraded LHCb detector. The 50 fb1 data sample will also allow to measure s in the penguin-free (b cs/ucs) B0s D decay [288, 289].
Another important goal is a more precise determination of sin 2 in the B0 system, motivated by the tension between the direct and indirect determinations of sin 2 seen by both UTt and CKMtter groups, as shown in Table 2. With the upgraded detector, using the B0 J/K0S nal state alone,
a statistical precision of 0.006 is expected, to be com
pared to the current error from the B factories of 0.023
[190]. Given experience with the current detector it seems feasible to control the systematic uncertainties to a similar level. Such precision, together with better control of the penguin pollution, will allow us to pin down any NP effects in B0 mixing. In addition, the penguin-free (b cd/ucd)
B0 D0 channel can be used to get another handle on
sin 2 [290, 291].
The importance of improved measurements of q has been emphasised in Sects. 3.2.13.2.3. LHCb has made a preliminary measurement of s in B0s J/ using a
1.0 fb1 data sample [139]. The effective lifetime of B0s
J/f0(980) [292] has also been measured [236]. Based on this, the statistical precision on s with 50 fb1 is projected to be 0.003 ps1. It is hoped that the systematic un
certainty can be controlled to the same level.
A measurement of d is of interest as any result larger than the tiny value expected in the SM would clearly signal NP [154, 255, 293]. To determine this quantity, LHCb will compare the effective lifetimes of the two decay modes B0 J/K0S with B0 J/K0. The estimated preci
sion for 1.0 fb1 is 0.02 ps1. With the upgraded detec
tor and 50 fb1 a statistical precision of 0.002 ps1 on
d can be achieved. The systematic uncertainty is under study.
The LHCb upgrade will also have sufcient statistics to make novel tests of CPT symmetry. Any observation of CPT violation indicates physics beyond the SM. An example of a unique test in the B0 system uses B0 J/K0 and
its charge-conjugate decay, where the K0 decays semileptonically [294296]. This measurement involves looking at four separate decay paths that interfere. While several tests can be performed, one particular observable is the asymmetry Abk, that can be measured without the need of avour tagging, where
Abk = [parenleftbig] [parenleftbig]B0 + B0 J/[bracketleftbig]+[bracketrightbig][parenrightbig]
[parenleftbig]B0 + B0 J/[bracketleftbig]+[bracketrightbig][parenrightbig][parenrightbig]
[slashbig][parenleftbig] [parenleftbig]B0 + B0 J/[bracketleftbig]+[bracketrightbig][parenrightbig]
+ [parenleftbig]B0 + B0
J [bracketleftbig]+[bracketrightbig][parenrightbig][parenrightbig]. (39)
In terms of the CPT violation parameter , the kaon decay time tK, the B0 decay time tB, the B0 mass difference md and CP-violating phase 2, and kaon decay widths KS and KL, this can be expressed
Abk = Re[parenleftbig] [parenrightbig]
12 ( KS+ KL)tK sin 2(1 cos mdtB) e KS tK + e K
L tK .
2e
(40)
A signature of CPT violation would be a 1 cos mBtB
dependence of the decay rate after integrating over kaon decay times. Roughly 5000 such decays can be expected with the upgrade. It is possible to detect these decays with low background level, even with the missing neutrino, using the measured B0 direction, the detected J/ four-momentum, and the kaon decay vertex. Other methods to test CPT symmetry (e.g. Ref. [297]) are also under investigation.
Page 30 of 92 Eur. Phys. J. C (2013) 73:2373
3.3 CP violation measurements with hadronic b s
penguins
3.3.1 Probes for new physics in penguin-only b sq q
decays
The presence of physics beyond the SM can be detected by looking for its contribution to b sqq (q = s, d) decays,38
which in the SM can only proceed via FCNC loop diagrams that are dynamically suppressed. These decays provide a rich set of observables that are rather precisely known in the SM but could potentially receive sizeable corrections from new heavy particles appearing in the loop.
Direct CP asymmetries. In the SM b sqq decays are
dominated by the penguin diagram with an internal top quark. As a consequence, the direct CP asymmetry is expected to be small. If there is a NP amplitude with comparable size interfering with the SM amplitude, and it has different strong and weak phases than the SM amplitude, a much larger direct CP asymmetry can arise.
Polarisation and triple product asymmetries. For B de
cays into two vector mesons V1 and V2, followed by vector to two pseudoscalar decays V1 P1P 1 and V2
P2P 2, there are three transversity states, labelled longitudinal (0), perpendicular () and parallel ( ). Mea
surements of the fractions of the total decay rate in each of these states, which correspond to determinations of the polarisation in the nal state, provide useful information about the chiral structure of the electroweak currents, as well about non-perturbative effects such as rescattering and penguin annihilation. In the SM, the decay to each transversity state is dominated by a single amplitude with magnitude |Aj |, weak phase j and strong phase j . The
CP-violating observables Im(AAj j) are then
Im[parenleftbig]AAj j[parenrightbig]
= 2|A||Aj | cos( j ) sin( j ), j = 0, .
(41)
The values of these observables are tiny since in the SM the weak phases are the same to a very good approximation, but Im(AAj j) can signicantly differ from
zero if there is a sizeable CP-violating NP contribution in the loop.
These observables can be extracted from the differential distributions in terms of the angles 1, 2 and , where 1 (2) is the polar angle of P1 (P2) in the rest frame of V1 (V2) with respect to the opposite of the direction of motion of the B meson, and is the angle between the decay planes of V1 P1P 1 and V2 P2P 2 in the rest frame of
38Decays mediated primarily by b su transitions are discussed in
Sects. 3.4.4 and 3.4.5.
the B meson. The two observables can also be related to two triple product asymmetries for CP-averaged decays39
which are equal to asymmetries between the number of events with positive and negative values of U = sin 2
and V = sign(cos 1 cos 2) sin : Im[parenleftbig]AA [parenrightbig]
AU =
N(U > 0) N(U < 0)
N(U > 0) + N(U < 0)
, (42)
Im[parenleftbig]AA0 0[parenrightbig]
AV =
N(V > 0) N(V < 0)
N(V > 0) + N(V < 0)
. (43)
A review of this subject can be found in Ref. [298] and references therein.
Mixing-induced CP asymmetries. Mixing-induced CP
asymmetries in b sqq decays of neutral B to CP
eigenstates are precisely predicted. Due to the fact that the penguin diagram with an internal top quark is expected to dominate, the values of 2eff determined using B0 K0S, B0 K0S, B0 f0(980)K0S, etc.,
are all expected to give 2 (see, e.g. Refs. [299, 300]
and the discussion in Ref. [44]). Similarly, the values of 2effs determined from B0s , B0s K0K0, etc.,
are expected to vanish due to cancellation of weak phases between mixing (top box) and decay (top penguin) amplitudes. Higher order corrections from subleading diagrams are expected to be small compared to the precision that can be achieved in the near-term, but further theoretical studies will be needed as the upgrade era approaches. NP with a avour structure different from the SM will alter these CP asymmetries through the decay amplitudes, even if there is no NP in B mixing. A number of quasi-two-body or three-body decay modes can be studied.
Correlations between direct and mixing-induced asymme-
tries. Penguin-only decay modes are particularly interesting as the difference between formal tree and penguin contributions boils down to a difference in the quark-avour running in the loop of the penguins. This difference, dominated by short distances, can be assessed accurately using QCD factorisation, and it can be used to correlate the branching ratio and the CP asymme-tries of penguin-mediated modes. As discussed in Refs. [138, 301, 302], these observables can be correlated not only within the SM, but can also be used to extract the B0s mixing phase even in the presence of NP affecting only this phase.
39The triple product asymmetries in B0s and B0s K0K0 de
cay could in principle also receive contribution from non-zero mixing-induced CP asymmetries arising from NP in B0s mixing. However, this contribution is suppressed by s/s and is already highly constrained.
Eur. Phys. J. C (2013) 73:2373 Page 31 of 92
Fig. 15 (Left) t of the K+K+ mass distribution for B0s K0K0 candidates from 35 pb1 [303]; (right) t of the K+KKK+ mass
distribution for B0s candidates from 1.0 fb1 [304]
3.3.2 Current status and outlook of LHCb measurements
LHCb published the rst observation and measurement of the branching ratio and polarisation amplitudes in the B0s
K0K0 decay mode [303] using 35 pb1 of data collected in 2010. A clean mass peak corresponding to 50 8
B0s (K+)(K++) decays is seen (Fig. 15 (left)),
mostly from resonant B0s K0K0 decays. Using this
signal the longitudinal polarisation amplitude is measured
to be fL = 0.31 0.12(stat) 0.04(syst) and the branch
ing ratio to be B(B0s K0K0) = (2.81 0.46(stat)
0.45(syst)) 105.
LHCb also published the measurement of the polarisation amplitudes and triple product asymmetries in B0s
[304] using the 2011 data set of 1.0 fb1. In this data set 801 29 events are observed with excellent signal-to-
background ratio (see Fig. 15 (right)). The polarisation amplitudes are measured to be
|A0|2 = 0.365 0.022 (stat) 0.012 (syst),
|A|2 = 0.291 0.024 (stat) 0.010 (syst),
|A |2 = 0.344 0.024 (stat) 0.014 (syst),
(44)
qpj
Aj (46)
where j denotes one of the three transversity states, which are also CP eigenstates with eigenvalues j , and Aj (j )
is the decay amplitude of B0s (B0s) to the corresponding state. With this approximation it will be possible to determine the magnitude || and phase effs arg(). The
SM expectation is || 1 and effs 0 due to the dom
inance of the top-quark loop, and any observed deviation from these expectations would be a signature of NP. Since NP in B0s mixing is already constrained by measurement of s from B0s J/, the main interest in these b s
penguin modes is to look for NP in the decay processes. Based on simulation studies, a sensitivity on effs of 0.30.4 radians with 1.0 fb1 is expected for both B0s and
B0s K0K0.
3.3.3 Future prospects with LHCb upgrade
The latest results on mixing-induced CP violation in b s
transitions show no signicant deviation from the SM, as seen in Fig. 16, which compares the mixing-induced CP violation parameter sin 2eff measured in penguin-dominated b s decays with the value of sin 2 measured in the tree-
dominated b ccs decays. In the absence of NP these ob
servables should only differ by small amounts. Due to these results, large NP contributions in b sqq decays are un
likely but further tests with higher precision remain interesting. LHCb will be able to make competitive measurements of sin 2eff in B0 K0S and several other b
where the sum of the square of the amplitudes is constrained to unity. The triple product asymmetries in this mode are measured to be
AU = 0.055 0.036 (stat) 0.018 (syst), AV = 0.010 0.036 (stat) 0.018 (syst).
(45)
The results of this analysis are in agreement with, and more precise than, the previous measurement [305], and are also consistent with the SM.
First measurements of CP asymmetries in these modes from time-dependent avour-tagged angular analyses are expected to follow. With high statistics, it will be possible to
measure polarisation-dependent direct and mixing-induced CP asymmetries, but for the rst analysis it will be more convenient to determine a single complex observable common to all polarisations (as done for B0s J/)
= j
Page 32 of 92 Eur. Phys. J. C (2013) 73:2373
Table 4 Current and projected precisions of the key observables in b sqq decays
Observable Current LHCb upgrade (50 fb1) Theory uncertainty
AU,V (B0s ) 0.04 (LHCb 1.0 fb1) 0.004 0.02 [309]
effs(B0s ) 0.03 0.02 [306] effs(B0s K0K0) 0.03 0.02 [306]
sin 2eff(B0 K0S) 0.12 (B factories) 0.06 0.02 [179]
Fig. 16 HFAG compilation of results for sin 2eff in b sqq decays
[44]
sqq decays, but a signicant improvement in precision requires the 50 fb1 of the LHCb upgrade. The improved trigger efciency in the LHCb upgrade is particularly important for these decays, which have only hadrons in the nal state. With the upgrade data sample, the statistical error of sin 2eff(B0 K0S) is estimated to be roughly 0.06, which
is still above the SM uncertainty of 0.02 [306].
There are several more NP probes in b sqq decays that
can be exploited at LHCb and its upgrade, such as mixing-induced CP asymmetries and triple product asymmetries in both B0s and B0s K0K0 decays. The statistical
precision of effs with each channel is estimated to be 0.30.4 rad for 1.0 fb1. The projected precision for 50 fb1 is about 0.03 rad each. This can be compared with the uncertainties of their SM predictions of about 0.02 rad. It is also possible to perform a combined analysis of B0s K0K0
and its U-spin related channel B0 K0K0, which will
put strong constraint on the subleading penguin diagrams in B0s K0K0, thus further reducing the theoretical uncer
tainty in the measurement of effs [307, 308]. The statistical
precision of AU and AV is estimated to be about 0.004, compared with an upper bound of 0.02 on their possible sizes in the SM [298].
In summary, the LHCb upgrade will allow the exploitation of the full potential of the NP probes in b sqq de
cays. Table 4 compares the current and projected (LHCb upgrade, i.e. 50 fb1) precisions of the key observables with the theory uncertainties of their SM predictions.
3.4 Measurements of the CKM angle
3.4.1 Measurements of using tree-mediated decays
The CKM angle , dened as the phase = arg[VudV ub/
(VcdV cb)], is one of the angles of the unitarity triangle
formed from the hermitian product of the rst (d) and third (b) columns of the CKM matrix V . It is one of the least well known parameters of the quark mixing matrix. However, since it can be determined entirely through decays of the type B DK40 that involve only tree amplitudes
an unusual, even unique, property amongst all CP violation parametersit provides a benchmark measurement. The determination from tree level decays has essentially negligible theoretical uncertainty, at the level of / = O(106), as
will be shown in the next section. This makes a very appealing standard candle of the CKM sector. It serves as a reference point for comparison with values measured from loop decays (see Sect. 3.4.4).
Moreover, the determination of is crucial to improve the precision of the global CKM ts, and resulting limits on (or evidence for) NP contributions (see Sect. 3.2.4). In particular, the measurement of md and the oscillation phase sin 2 in B0B0 mixing can be converted to a measurement of (in the SM). This can be compared to the reference value from B DKtheir consistency veries that
the KobayashiMaskawa mechanism of CP violation is the dominant source in quark avour-changing processes. Existing measurements provide tests at the level of O(10 %),
but improving the precision to search for smaller effects of NP is well motivated.
40By B DK all related tree-dominated decay processes are im
plicitly included, including B+ DK+, B0 DK0, B0s D,
B0s DsK and B0 D(). In these specic decay processes,
the notation D refers to a neutral D meson that is an admixture of D0 and D0 states.
Eur. Phys. J. C (2013) 73:2373 Page 33 of 92
Several established methods to measure in tree decays exploit the B D()K() decays. They are based on the
interference between the b u and b c tree amplitudes,
which arises when the neutral D meson is reconstructed in a nal state accessible to both D0 and D0 decays. The interference between the amplitudes results in observables that depend on their relative weak phase . Besides they also depend on hadronic parameters, namely the ratio of magnitudes of amplitudes rB |A(b u)/A(b c)| and the
relative strong phase B between the two amplitudes. These hadronic parameters depend on the B decay under investigation. They can not be precisely calculated from theory (see, however, Ref. [310]), but can be extracted directly from data by simultaneously reconstructing several different D nal states.
The various methods differ by the D() nal state that is used. The three main categories of D decays considered so far by the B factories BaBar and Belle, and by CDF, are:
CP eigenstates (the GLW method [311, 312]), doubly Cabibbo-suppressed (DCS) decays (the ADS
method [313, 314]),
three-body, self-conjugate nal states (the GGSZ or
Dalitz method [315]).
An additional category has not been possible to pursue at previous experiments due to limited event sample sizes:
singly Cabibbo-suppressed (SCS) decays (the GLS meth
od [316]).
In practise, except for the case of two-body decays, there is often no clear distinction between the different methods.
The best sensitivity to obviously comes from combining the results of all different analyses. This not only improves the precision on , but provides additional constraints on the hadronic parameters. It also allows one to overcome the fact that CP-odd nal states such as K0S0 are not easily accessible in LHCbs hadronic environment.
A brief review of the main ideas of the different methods follows. The amplitudes of the B D0K and B
D0K processes are written as:
A[parenleftbig]B D0K[parenrightbig] = Aceic,
A[parenleftbig]D0 f [parenrightbig] = Af eif ,
A[parenleftbig]B D0K[parenrightbig] = Auei(u ),
A[parenleftbig]D0 f[parenrightbig] = A fei f,
(47)
2[ (B DCPK) + (B+ DCPK+)]
(B D0K) + (B+ D0K+)
,
(52)
ACP =
(B DCPK) (B+ DCPK+)
(B DCPK) + (B+ DCPK+)
.
(53)
where Ac, Au, Af and A f are real and positive (and CP vi
olation in D0 decays has been neglected). The subscripts c and u refer to the b c and b u transitions, respectively.
The amplitudes for the D0 decay can generally include the case where the D0 decays to a three-body nal state. In this
case, Af , A f, f and f are functions of the Dalitz plot co
ordinates. The amplitude of the process B D[ f ]K
can be written, neglecting D0D0 mixing, as
A[parenleftbig]B D[ f ]K[parenrightbig]
= AcAf ei(c+f ) + AuA fei(u+ f ), (48)
and the rate is given by
[parenleftbig]B D[ f ]K[parenrightbig]
A2cA2f + A2uA2f + 2AcAf AuA f Re[parenleftbig]ei(B+D )[parenrightbig]
A2c[parenleftbig]A2f + r2BA2f + 2rBAf A f Re[parenleftbig]ei(B+D )[parenrightbig][parenrightbig], (49)
where rB = Au/Ac, B = u c and D = f f . The
rate for the charge-conjugated mode (still neglecting CP violation in D0 decays) is obtained by exchanging .
Taking into account CKM factors and, in the case of charged B decays, colour suppression of the b u amplitude, rB is
expected to be around 0.1 for B decays and around 0.3 for B0 decays. From Eq. (49) all the relevant formulae of the
GLW, ADS and GGSZ methods can be derived.
In the GLW analysis, the neutral D mesons are selected in CP eigenstates fCP such as D KK+ (CP = +1) or
D K0S0 (CP = 1). Thus Af /A f = 1 and D = 0,
for CP = 1. Equation (49) becomes: [parenleftbig]B D[ fCP]K[parenrightbig]
A2c[parenleftbig]1 + r2B 2rB cos(B )[parenrightbig]. (50) The B DK decays, where the D decays to Cabibbo
favoured (CF) nal states (e.g. D0 K+) can be used
to normalise the rates in order to construct observables that minimise the systematic uncertainties. For those decays, to a good approximation,
[parenleftbig]B D[bracketleftbig] K+[bracketrightbig]K[parenrightbig]
= [parenleftbig]B+ D[bracketleftbig] K+[bracketrightbig]K+[parenrightbig] A2c. (51)
From Eqs. (50) and (51) and their CP conjugates the usual
GLW observables follow:
RCP =
Equations (52) and (53) provide a set of four observables that are connected to the three unknowns , rB and B through
RCP = 1 + r2B 2rB cos B cos , (54)
Page 34 of 92 Eur. Phys. J. C (2013) 73:2373
ACP =
2rB sin B sin RCP
. (55)
However, only three of these equations are independent since, from Eq. (55), RCP+ACP+ = RCPACP. Analo
gous relations hold for B DCPK and B DCPK de
cays, with different values of the hadronic parameters char-acterising the B decay. However, in the B DCPK case
one has to take into account a CP ip due to the different charge conjugation quantum numbers of the 0 and the photon from the D decay [317]: DCP DCP0, but
DCP DCP . For analysis of B DCPK the nite
width of the K resonance must be taken into account [318]. There are related important consequences for the ADS and
GGSZ analyses of B DK and B DK decays.
In the ADS analysis, the neutral D mesons are selected in CF and DCS decays, such as D0 K+ and D0
K+, respectively. The B decay rate is the result of the interference of the colour allowed B D0K decay fol
lowed by the DCS D0 K+ decay and the colour sup-
pressed B D0K decay followed by the CF D0
K+ decay. As a consequence, the interfering amplitudes are of similar magnitude and hence large interference effects can occur. From Eq. (49) one nds
[parenleftbig]B D[bracketleftbig] K[bracketrightbig]K[parenrightbig]
r2B + r2D 2rBrD cos(B + D ) (56) where both rD = Af /A f = |A(D0 K+)/A(D0
K+)| and the phase difference D are measured in charm
decays. The value of D can be determined directly using data collected from e+e collisions at the (3770) resonance, as has been done by CLEO [319, 320], but the most precise value comes from a global t including charm mixing parameters. The results provided by HFAG [44] from a combination with CP violation in charm allowed are rD = 0.0575 0.0007, D = (202+1011). Dening RADS and
AADS as
RADS =
(B D[ K+]K) + (B+ D[ +K]K+)
(B D[ K+]K) + (B+ D[ K+]K+)
, (57)
AADS =
(B D[ K+]K) (B+ D[ +K]K+)
(B D[ K+]K) + (B+ D[ +K]K+)
, (58)
and using Eqs. (51) and (56) gives
RADS = r2B + r2D + 2rBrD cos cos(B + D), (59) AADS = 2rBrD sin sin(B + D)/RADS. (60)
It has been noted that for the extraction of it can be more convenient to replace the pair of observables RADS, AADS with a second pair, R+, R, dened as:
R
(B [K]DK)
(B [K]DK)
= r2B + r2D + 2rBrD cos(B + D ). (61) Unlike RADS, AADS, the two quantities R+, R are sta
tistically independent. The ADS decay chain B
[K]DK has been observed for the rst time by
LHCb [6], conrming the evidence that had begun to accumulate in previous measurements [321323].
In the GGSZ analysis, the neutral D mesons are selected in three-body self-conjugate nal states. The channel that has been used most to date is D K0S+, though rst
results have also been presented with D K0SK+K and
other channels are under consideration. For concreteness, consider D K0S+, with Af eif = f (m2, m2+) and
A fei f = f (m2+, m2), where m2 and m2+ are the squared
masses of the K0S and K0S+ combinations. The rate in Eq. (49) can be re-written as:
[parenleftbig]B D[bracketleftbig] K0S+[bracketrightbig]K[parenrightbig]
[vextendsingle][vextendsingle]f [parenleftbig]m2
, m2[parenrightbig][vextendsingle][vextendsingle]2 +
r2B[vextendsingle][vextendsingle]f [parenleftbig]m2
, m2[parenrightbig][vextendsingle][vextendsingle]2
+ 2rB[vextendsingle][vextendsingle]f [parenleftbig]m2
, m2[parenrightbig][vextendsingle][vextendsingle][vextendsingle][vextendsingle]f [parenleftbig]m2
, m2[parenrightbig][vextendsingle][vextendsingle]
cos[parenleftbig]B + D[parenleftbig]m2, m2[parenrightbig] [parenrightbig], (62) where D(m2, m2) is the strong phase difference between
f (m2, m2) and f (m2, m2). Due to the fact that rB is re
quired to be positive, the direct extraction of rB, B and can be biased. To avoid these biases, the Cartesian coordinates have been introduced [324]
x = Re[bracketleftbig]rB ei(B )[bracketrightbig], y = Im[bracketleftbig]rB ei(B )[bracketrightbig], (63)
allowing Eq. (62) to be rewritten as
[parenleftbig]B D[bracketleftbig] K0S+[bracketrightbig]K[parenrightbig]
|f|2 + r2B|f|2 + 2[bracketleftbig]x Re[bracketleftbig]ff [bracketrightbig]
+ y Im[bracketleftbig]ff [bracketrightbig][bracketrightbig]. (64)
Eur. Phys. J. C (2013) 73:2373 Page 35 of 92
Here the notation has been simplied using f = f (m2,
m2). This Dalitz plot-based method can be implemented in
a model-dependent way by parametrising the amplitude as a function of the Dalitz plot of the three-body state, or in a model-independent way by dividing the Dalitz plot into bins and making use of external measurements of the D decay strong phase differences within these bins [315, 325, 326].41
Besides the established methods based on direct CP violation in B DK decays, it is also possible to measure
using time-dependent analyses of neutral B0 and B0s tree decays [328330]. The method still relies on the interference of b u and b c amplitudes, but interference is achieved
through B0 (B0s) mixing. Thus one measures the sum of and the mixing phase, namely + 2 and 2s in the B0
and B0s systems, respectively. Since both sin 2 and s are becoming increasingly well measured, these measurements provide sensitivity to .
Pioneering time-dependent measurements using the B0 D() decays have been performed by both
BaBar [331, 332] and Belle [333, 334]. In these decays the amplitude ratios rD = |A(B0 D()+)/A(B0
D()+)| are expected to be small, rD [lessorsimilar] 0.02, limit
ing the sensitivity. In the decays B0s DsK, however,
both b c and b u amplitudes are of same order in the
Wolfenstein parameter , O(3), so that the interference ef
fects are expected to be large. In addition, the decay width difference in the B0s system, s, is non-zero, which adds sensitivity to the weak phase through the hyperbolic terms in the time evolution (see also Ref. [335]). The time-dependent decay rates of the initially produced avour eigenstates are given by the decay equations
dB0s(B0s)f (t) dt es t
1
2|Af |2[parenleftbig]1 + |f |2[parenrightbig]
(q/p)(Af /Af ) where Af is the amplitude for a B0s to decay into f . Similar equations hold for the charge conjugate processes replacing Af by A f, f by f = (p/q)(A f/A f),
and with a separate set of coefcients C f, S f and D f. As
each decay is dominated by a single diagram, |f | = | f|.
The CP asymmetry observables are then given by
Cf = C f =
1 |f |2 1 + |f |2
, Sf =
2 Im(f )
1 + |f |2
,
Df =
2 Re(f )
1 + |f |2
,
(66)
S f =
2 Im( f) 1 + |
f|2
, D f =
2 Re( f) 1 + |
f|2
.
The equality Cf = C f results from |q/p| = 1 and |f | = | f|. The term f is connected to the weak phase by
f =
q p
Af =
V tbVts VtbV ts
[parenrightbigg][parenleftbigg]VubV cs V cbVus
[parenrightbigg][vextendsingle][vextendsingle][vextendsingle][vextendsingle]
A2 A1
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]e
Af
i
= [bracketleftbigg]cosh[parenleftbigg] st 2
[parenrightbigg]
st
[parenrightbigg]
= |f |ei( (2s)), (67)
where |A2/A1| is the ratio of the hadronic amplitudes
between B0s DsK+ and B0s D+sK, is their
strong phase difference, and 2s is the weak phase
difference. An analogous relation exists for f, f =
|f |ei( +(2s)). Thus one obtains ve observables from
Eq. (66) and solves for |f |, , and ( 2s).
The LHCb experiment has the necessary decay time resolution, tagging power and access to large enough signal yields to perform this time-dependent CP measurement.42
The signal yields can be seen from the measurement of
B(B0s DsK) [140] (see Sect. 3.4.3 below). The iden
tication of the initial avour of the signal B0s candidate can be done combining both the responses of opposite-side and same-side kaon tagging algorithms, as is planned for other measurements of mixing-induced CP-violation in B0s decays, and has already been implemented in the preliminary analysis of B0s Ds+ decays [226].
3.4.2 Theoretical cleanliness of from B DK decays The answer to the question of why it is interesting to measure precisely depends on the experimental precision that can be achieved. In the era of LHCb, the main motivation is the theoretically clean measurement of the SM CKM phase. The search for NP can thus be performed by comparing the extracted value of to other observables, for example in the CKM t (see Sect. 3.2.4). However, one can also cross-check for the presence of NP in B DK channels them
selves. One way is to test that the values of determined
42Preliminary results have been presented at CKM 2012 [336].
Df sinh
2 [bracketrightbigg], (65)
where s, s, ms are the usual mixing parameters of the B0s system and |q/p| = 1 has been assumed. The top (bot
tom) of the and signs is used when the initial particle is
tagged as a B0s (B0s) meson. In Eq. (65), Af is the decay amplitude for a B0s meson to decay to a nal state f , and f =
41As for D in the ADS method, the strong phase differences can be determined directly from (3770) DD data, which has been done
by CLEO [327]. In future, it is expected that the most precise value will come from a global t including results of time-dependent analyses of multibody charm decays.
Cf cos( mst) Sf sin( mst)
Page 36 of 92 Eur. Phys. J. C (2013) 73:2373
from the many different B DK type channels all coin
cide. Another is automatically built in to the method for extraction in the GGSZ analysis. Consider the case where the decay amplitudes get modied by an extra contribution with a new strong phase B and a weak phase . Then instead of the decay amplitudes in Eq. (48) one nds
A[parenleftbig]B fDK[parenrightbig]
1 + rDeiD[parenleftbig]rB ei(B ) + r Bei(
B
. (68)
This means that for B+ and B decays the rB ratios are different
rB+ [vextendsingle][vextendsingle]r
B ei(B+ ) + r Bei(
)
B
+ )
[vextendsingle][vextendsingle],
rB [vextendsingle][vextendsingle]r
(69)
Discovering that rB = rB+ would signal a CP-violating NP
contribution to the B DK amplitude. One signature of
NP would then be x2+ + y2+ = x2 + y2, though it is also pos
sible that the equality could be satised even in the presence of NP: in this case there can be a shift in the extracted value of .
Existing measurements place strong constraints on tree-level NP effects, yet the possibility of discoveries in this sector in the near term is not ruled out. In the far future, with much larger statistics, the measurement of is well suited to search for high scale NP since it is theoretically very clean. For example, NP with contributions of different chirality could give different shifts in , so the above test is meaningful.
A useful question to ask is, what is the energy scale that could be probed in principle? To answer this, the irreducible theoretical uncertainty in the determination of must be estimated. There are several sources that can induce a bias in the determination of from B DK decays. However,
most of these can be avoided, either (i) with more statistics (for example, the Dalitz plot model uncertainty where a switch to a model-independent method is possible), or (ii) by modifying the equations used to determine (an example is
to correct for effects of D0D0 mixing [337, 338]). The remaining, irreducible, theory uncertainties are then from the electroweak corrections.
The challenge to determine this uncertainty is that the hadronic elements can no longer be determined solely from the experiment. Not all electroweak corrections matter thoughthe important ones are the corrections that change the CKM structure. For instance, vertex corrections and Z exchanges do not affect , but corrections from box diagrams carry a different weak phase. The dominant contribution is effectively due to t and b running in the loop. For b us c transitions there is a tree level contribution
with VubV cs CKM structure, while the box diagram has (VtbV ts)(VubV cb). Since this has the same weak phase, it does not introduce a shift in . For b cs transitions, on
the other hand, the tree level is VcbV us, while the box dia
gram (VtbV ts)(VcbV ub), as illustrated in Fig. 17. The two
contributions have different weak phases, which means that the shift is non-zero.
The size of this effect is estimated by integrating over both t and b at the same time. The electroweak corrections in the effective theory are then described by a local operator whose matrix elements are easier to estimate. Although the Wilson coefcient of the operator contains large logarithms, log(mb/mW ), for O(1) estimates, the precision
obtained without resummation is sufcient. If one resums log(mb/mW ) then nonlocal contributions are also generated.
As a rough estimate only the local contributions need be kept. The irreducible theory error on is conservatively
)
B ei(B ) + r Bei(
B
[vextendsingle][vextendsingle].
Fig. 17 A B D0K box diagram electroweak correction (left)
with a different CKM structure than the leading weak decay amplitude (right)
Table 5 Ultimate NP scales that can be probed using different observables listed in the rst column. They are given by saturating the theoretical errors given respectively by (1) / = 106, (2) optimistically
assuming no error on fB, so that the ultimate theoretical error is only
from electroweak corrections, (3) using SM predictions in Ref. [31],(4) optimistically assuming perturbative error estimates / 0.1 % [339], and (5) from bounds for Re C1(Im C1) from UTtter [270]
Probe NP for (N)MFV NP NP for gen. FV NP
from B DK(1) O(102 TeV) O(103 TeV)
B (2) O(1 TeV) O(30 TeV)
b ss d(3) O(1 TeV) O(103 TeV)
from B J/K0S(4) O(50 TeV) O(200 TeV)
KK mixing(5) > 0.4 TeV (6 TeV) > 103(4) TeV
Eur. Phys. J. C (2013) 73:2373 Page 37 of 92
estimated to be / < O(106) (most likely it is even
/ [lessorsimilar] O(107)).
This limit is far beyond the achievable sensitivity of any foreseeable experiment. Nevertheless, it is interesting to consider what could be learnt in case such small deviations could be observed. Assuming MFV one can probe NP 102 TeV, while assuming general avour-violating
(FV) NP one can probe NP 103 TeV (where MFV and
general FV NP scales are dened as in Ref. [270]). This is by far the most precise potential probe of MFV, as shown in Table 5, due to the small theoretical uncertainty.
Since an experimental precision of / 106 is not
achievable in the near future, the NP scale reach must be adjusted for more realistic data sets. This is easily done, since the scale NP probed goes as the fourth root of the yield.
With the LHCb upgrade, an uncertainty of <1 on can be achieved (see Sect. 3.4.6), so that NP scales approaching NP 5(50) TeV can be probed for MFV (general FV) NP.
3.4.3 Current LHCb experimental situation
First results from LHCb in this area include a measurement using B DK with the GLW and ADS nal
states [6].43 A measurement of the branching ratio of B0s
DsK has also been performed [140]. Several other analyses, including studies of GGSZ-type nal states, are in progress.44
These measurements all share common selection strategies. They benet greatly from boosted decision tree algorithms, which combine up to 20 kinematic variables to effectively suppress combinatorial backgrounds. Charmless backgrounds are suppressed by exploiting the large forward boost of the D+(s) meson through a cut on its ight distance.
In the GLW/ADS analysis [6] of 1.0 fb1 of s = 7 TeV
data collected in 2011, the CP eigenstates D K+K,
+, and the quasi-avour-specic D K+ decay
are used. The CP asymmetries dened in Eq. (58), and the ratios R dened in Eq. (61), are measured for both the
B DK signal and the abundant B D control chan
nel. The latter has limited sensitivity to but provides a large control sample from which probability density functions are shaped, and can be used to help reduce certain systematic uncertainties. The control channel is also used to measure three ratios of partial widths
43Results from preliminary GLW-type analyses using B0 DK0
[340] and B DK+ [341] have been reported at ICHEP
2012.
44At CKM 2012, LHCb presented results of a model-independent GGSZ analysis of B DK with D K0S+ and D
K0SK+K [7], preliminary results from a ADS-type analysis of B
DK with D K3 [342], a preliminary determination of from
combined results using B DK and B D [343], and
preliminary results on the time-dependent CP violation parameters in B0s DsK [336].
RfK/ =
(B [f ]DK) + (B+ [f ]DK+)
(B [f ]D) + (B+ [f ]D+)
, (70)
where f represents KK, and the favoured K mode. The signal yields are estimated by a simultaneous t to 16 independent subsamples, dened by the charges (2), the
D nal states (4), and the DK or D nal state (2).
Figure 18 shows the projections of the suppressed K subsamples. It is crucial to control the cross feed of the abundant B D decays into the signal decays. This
is achieved using the two LHCb ring-imaging Cherenkov detectors [344]. The systematic uncertainties are dominated by knowledge of the intrinsic asymmetry of the detector in reconstruction of positive and negative B meson decays, and by the uncertainty on the particle identication requirements. The results are
RCP+ = 1.007 0.038 0.012, ACP+ = 0.145 0.032 0.010,
R = 0.0073 0.0023 0.0004,R+ = 0.0232 0.0034 0.0007,where the rst error is statistical and the second systematic;
RCP+ is computed from RCP+ RKKK/, RK/ /RKK/ with
an additional 1 % systematic uncertainty assigned to account for the approximation; ACP+ is computed as ACP+ =
AKKK, AK . From the R one can also compute RADS = 0.0152 0.0020 0.0004,
AADS = 0.52 0.15 0.02,
as RADS = (R + R+)/2 and AADS = (R R+)/(R +
R+). To summarise, the B DK ADS mode is ob-
served with 10 statistical signicance when comparing
the maximum likelihood to that of the null hypothesis. This mode displays evidence (4.0 ) of a large negative asymmetry, consistent with previous experiments [321323]. The combined asymmetry ACP+ is smaller than (but compatible
with) previous measurements [345, 346], and is 4.5 significant. The maximum likelihood is compared with that under the null hypothesis in all three DK nal states, diluted by the non-negligible correlated systematic uncertainties. From this, with a total signicance of 5.8 , direct CP violation is observed in B DK decays.
The analysis of the B0s DsK decay mode [140]
is based on a sample corresponding to an integrated luminosity of 0.37 fb1, collected in 2011 at a centre-of-mass energy of s = 7 TeV. This decay mode has been ob-
served by the CDF [347] and Belle [348] Collaborations, who measured its branching fraction with an uncertainty around 23 % [190]. In addition to B0s DsK, the chan
nels B0 D+ and B0s Ds+ are analysed. They are
characterised by a similar topology and therefore are good
Page 38 of 92 Eur. Phys. J. C (2013) 73:2373
Fig. 18 Invariant mass distributions of selected B [K]Dh
candidate events: (left) B candidates, (right) B+ candidates [6]. In the top plots, the track directly from the B vertex passes a kaon identication requirement and the B candidates are reconstructed assigning this track the kaon mass. The remaining events are placed in the bottom row and are reconstructed with a pion mass hypothesis. The dark
(red) curve represents the B DK events, the light (green) curve is
B D. The shaded contribution are partially reconstructed events
and the thin line shows the total t function which also includes a linear combinatoric component. The broken line represents the partially reconstructed B0s D0K+ decays where the pion is lost
0.0646 0.0043 0.0025, (71)
where the rst uncertainty is statistical and the second is systematic. Using the measured relative yield of B0 D+,
the known B0 D+ branching fraction [190], and the
recent fs/fd measurement [145], the branching fractions
B[parenleftbig]B0s Ds+[parenrightbig]
= [parenleftbig]2.95 0.05 0.17 +0.180.22[parenrightbig] 103, (72)
B[parenleftbig]B0s DsK[parenrightbig]
= [parenleftbig]1.90 0.12 0.13 +0.120.14[parenrightbig] 104 (73)
are obtained, where the rst uncertainty is statistical, the second is the experimental systematic uncertainty, and the third is from the fs/fd measurement. Both measurements are signicantly more precise than the previous world averages [190].
3.4.4 Measurements of using loop-mediated two-body B decays
CP violation in B0(s) decays plays a fundamental role in testing the consistency of the CKM paradigm in the SM and in probing virtual effects of heavy new particles.
With the advent of the B factories, the GronauLondon (GL) [350] isospin analysis of B decays has been
Fig. 19 Mass distribution of the B0s DsK candidate events [140].
The stacked background shapes follow the same top-to-bottom order in the legend and in the plot
control and normalisation channels. Particle identication criteria are used to separate the CF decays from the suppressed modes, and to suppress misidentied backgrounds.
The signal yields are obtained from unbinned extended maximum likelihood ts to the data. The ts include components for the combinatorial background and several sources of background from b hadron decays. The most important is the misidentied B0s Ds+ decay. Its shape is
xed from data using a reweighting procedure [349] while the yield is left free to oat. A similar procedure is applied to a simulated data sample to extract the shape of the B0 DK+ misidentied background. The t results are
shown in Fig. 19.
Correcting the raw signal yields for selection efciency differences gives
B(B0s DsK)
B(B0s Ds+) =
Eur. Phys. J. C (2013) 73:2373 Page 39 of 92
Table 6 Experimental data on B and B0s K+K decays.
The correlation column refers to that between Sf and Cf measurements. Except for the preliminary results in Ref. [356], all other measurements have been averaged by HFAG [44]. The CP asymmetry of
B+ +0 has been reported for completeness, although it has not
been used in the analysis. New results on time-dependent CP violation in B0 + reported by Belle at CKM2012 [358] are not included
Channel B 106 Sf (%) Cf (%) Corr. Ref.
B0 + 5.11 0.22 65 7 38 6 0.08 [359364]
B0 + 56 17 3 11 21 3 0.34 [356]
B0 00 1.91 0.23 43 24 [359, 363, 365]
B+ +0 5.48 0.35 2.6 3.9 [362, 363, 366]
B0s K+K 25.4 3.7 17 18 5 2 18 4 0.1 [356, 364, 367]
a precious source of information on the phase of the CKM matrix. Although the method allows a full determination of the weak phase and of the relevant hadronic parameters, it suffers from discrete ambiguities that limit its constraining power. It is however possible to reduce the impact of discrete ambiguities by adding information on hadronic parameters [351, 352]. In particular, as noted in Refs. [353355], the hadronic parameters entering the B0 + and the
B0s K+K decays are connected by U-spin, so that ex
perimental knowledge of B0s K+K can improve the ex
traction of the CKM phase with the GL analysis. Indeed, in Ref. [352], the measurement of B(B0s K+K) was used
to obtain an upper bound on one of the hadronic parameters.
LHCb has reported preliminary measurements of the time-dependent CP asymmetries using decays to CP eigenstates, namely B0 + and B0s K+K [356],
thereby permitting the use of the U-spin strategy proposed by Fleischer (F) [353355] to extract the CKM phase from a combined analysis of B0 + and the B0s K+K
decays. However, as shown explicitly below, this strategy alone suffers from a sizeable dependence on the breaking of U-spin symmetry. In Ref. [357], the authors propose to perform a combined analysis of the GL modes plus B0s K+K to obtain an optimal determination of the
CKM phase within the SM. They show that this combined strategy has a milder dependence on the magnitude of U-spin breaking, allowing for a more solid estimate of the theory error. The experimental data used for such a determination of are summarised in Table 6.
The time-dependent asymmetry for a B meson decay to a CP eigenstate f can be written, with the same notation as Eqs. (65) and (66),45 as
ACP(t) =
where Cf and Sf parametrise direct and mixing-induced CP violation respectively, and the quantity Df is constrained by the consistency relation
(Cf )2 + (Sf )2 + (Df )2 = 1. (75)
The LHCb preliminary results on direct and mixing-induced CP violation parameters in B0 + and B0s
K+K decays [356] are shown in Table 6. The measurements of C+ and S+ are compatible with those from the B factories, whereas CK+K and SK+K are measured for the rst time and are consistent with zero within the current uncertainties.
Beyond the SM, NP can affect both the B0(s)B0(s) amplitudes and the b d(s) penguin amplitudes. Taking the
phase of the mixing amplitudes from other measurements, for example from b c cs decays, one can obtain a con
straint on NP in b s (or b d) penguins. Alternatively,
assuming no NP in the penguin amplitudes, one can obtain a constraint on NP in mixing. The analysis discussed here is based on a simplied framework [357], using as input values sin 2 = 0.679 0.024 [44] and 2s = (0 5) [139] ob
tained from b c cs decays. The optimal strategy will be to
include the combined GL and Fleischer analysis in a global t of the CKM matrix plus possible NP contributions.
The GL and Fleischer analyses were formulated with different parametrisations of the decay amplitudes. In order to use the constraints in a global t one can write46
A[parenleftbig]B0 +[parenrightbig] = C[parenleftbig]ei dei[parenrightbig],
A[parenleftbig]B0 +[parenrightbig] = C[parenleftbig]ei dei[parenrightbig],
A[parenleftbig]B0 00[parenrightbig] =
C2[parenleftbig]T eiT ei + dei[parenrightbig],
Sf sin( mt) Cf cos( mt)
cosh( 2 t) + Df sinh( 2 t)
, (74)
C2[parenleftbig]T eiT ei + dei[parenrightbig],
46Note that the use here of the symbol C to denote a colour-suppressed amplitude is not related to its use to denote direct CP violation parameters in time-dependent analyses.
A[parenleftbig]B0 00[parenrightbig] =
45In the LHCb preliminary results on B0 + and B0s K+K
decays [356] a different notation has been used: Adirf Cf , Amixf Sf , A f Df .
Page 40 of 92 Eur. Phys. J. C (2013) 73:2373
Fig. 20 From left to right: PDF for obtained using the GL method as described in the text; PDF for obtained using the Fleischer method for = 0.1, 0.5 [357]. Here and in the following, dark (light) areas correspond to 68 % (95 %) probability regions
A[parenleftbig]B+ +0[parenrightbig] =
A(B0 +)2 + A[parenleftbig]B0 00[parenrightbig],
A(B0 +)2 + A[parenleftbig]B0 00[parenrightbig],
A[parenleftbig]B0s K+K[parenrightbig] = C
A[parenleftbig]B 0[parenrightbig] =
1 2/2
[parenleftbigg]ei +
1 2
2 d ei
[parenrightbigg],
[parenrightbigg],
(76)
where the magnitude of VubV ud has been reabsorbed in C, and the magnitude of VcbV cd/(VubV ud) has been reabsorbed in d. In the exact U-spin limit, one has C = C , d = d and
= . Isospin breaking in B has been neglected,
since its impact on the extraction of the weak phase is at the level of 1 [368371]. The physical observables entering the analysis are
B(B f ) = F (B)|
A[parenleftbig]B0s K+K[parenrightbig] = C
1 2/2
[parenleftbigg]ei +
1 2
2 d ei
C
C
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]fact =
A(B f )|2 + |A(B f )|2
2 ,
Cf = |
A(B f )|2 |A(B f )|2 |A(B f )|2 + |A(B f )|2
,
1.46 0.15, (78)
where the error obtained using light-cone QCD sum rule calculations [372] has been symmetrised. However, this can only serve as a reference value, since there are nonfactorisable contributions to C and C that could affect this estimate. In this analysis, the non-factorisable U-spin breaking is parametrised as follows
C = rfactrCC, Re[parenleftbig]d ei [parenrightbig] = rr Re[parenleftbig]dei[parenrightbig], Im[parenleftbig]d ei [parenrightbig] = ri Im[parenleftbig]dei[parenrightbig],
(77)
Sf =
2 Im(eiM(B) A(Bf )A(Bf )) 1 + |A(Bf )A(Bf )|2
,
s )(M2B0s 4M2K+)/(M2B0 4M2+) = 0.9112.
In the GL approach, one extracts the probability density function (PDF) for the angle = of the UT
from the measurements of B(B ), S+ , C+ and
C00 . Using the unitarity of the CKM matrix, it is possible to write the B decay amplitudes and observables
in terms of instead of and . However, for the purpose
of connecting B to B0s KK it is more convenient
to use the parametrisation in Eq. (76). In this way, (or, equivalently, ), is determined up to discrete ambiguities, that correspond however to different values of the hadronic parameters. As discussed in detail in Ref. [352], the shape of the PDF obtained in a Bayesian analysis depends on the allowed range for the hadronic parameters. For example, using the data in Table 6, solving for C and choosing at a priori distributions for d [0, 2], [, ], T [0, 1.5] and
T [, ] the PDF for in Fig. 20 is obtained, corre
sponding to = (68 15) ( [25, 87] at 95 % proba
bility). Using instead the Fleischer method, one can obtain a PDF for given a range for the U-spin breaking effects. In this method it was originally suggested to parametrise the U-spin breaking in C /C using the result one would obtain in factorisation, namely
rfact =
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
(79)
with rC, rr and ri uniformly distributed in the range [1 ,
1 + ].
In Fig. 20 the PDF for obtained with the Fleischer method for two different values of the U-spin breaking parameter = 0.1, 0.5 is shown. The method is very precise
for small amounts of U-spin breaking ( = 0.1), but be
comes clearly worse for = 0.5. Thus, a determination of
from the Fleischer method alone is subject to uncertainty on the size of U-spin breaking.
where M(B0) = 2, M(B0s) = 2s in the SM, and
F (B0) = 1, F (B+) = B+ /B
0 = 1.08, F (B0s) = B
0
s /
B0 (m2B0/m2B0
Eur. Phys. J. C (2013) 73:2373 Page 41 of 92
Fig. 21 From left to right: PDF for obtained using the combined method for = 0.1, 0.5; 68 % probability region for obtained using the
combined method (lled area) or the GL method (horizontal lines) as a function of [357]
Fig. 22 From left to right: PDFs for NP, d NP and NP obtained using the combined method with = 0.5 [357]
The result of the combined GL+F analysis is given in
Fig. 21, where the PDF for for = 0.1 and 0.5 is shown.
The result of the combined analysis is much more stable against the allowed amount of U-spin breaking. In Fig. 21 the 68 % probability region for obtained using the combined method as a function of is also shown, and compared to the GL result. The combined method shows a considerable gain in precision even for very large values of .
NP could affect the determination of in the combined method by giving (electroweak) penguin contributions a new CP-violating phase. If one assumes that the isospin analysis of the GL channels is still valid, barring order-of-magnitude enhancements of electroweak penguins in B , and if
one assumes for concreteness that NP enters only b s
penguins, in the framework of a global t, one can simultaneously determine and the NP contribution to b s
penguins. For the purpose of illustration, the value of from tree-level processes, tree = (76 9) is used as in
put [270],47 allowing inspection of the posterior for and
47Note that the value of quoted here differs from that obtained from the full CKM t (given in Table 2) due to the different inputs used.
for the NP penguin amplitude. Writing
A[parenleftbig]B0s K+K[parenrightbig]
= C
1 2/2
[parenleftbigg]e+i +
1 2
2
[parenleftbig]d ei + e+iNPd NPei
NP
[parenrightbig][parenrightbigg],
A[parenleftbig]B0s K+K[parenrightbig]
= C
(80)
1 2/2
[parenleftbigg]ei +
1 2
2
[parenleftbig]d ei + eiNPd NPei
NP
[parenrightbig][parenrightbigg],
and taking uniformly distributed d NP [0, 2] and NP, NP [, ] the PDFs shown in Fig. 22 are obtained for = 0.5.
This yields = (74 7), and a 95 % probability upper
bound on d NP around 1. Clearly, the bound is stronger for large values of NP.
Finally, B0s KK decays can also be used to extract
2s in the SM. The optimal choice in this respect is represented by B0s K()0K()0 (with B0 K()0K()0 as
Page 42 of 92 Eur. Phys. J. C (2013) 73:2373
U-spin related control channels to constrain subleading contributions), since in this channel there is no tree contribution proportional to ei [307, 308]. However, the combined analysis described above, in the framework of a global SM t, can serve for the same purpose. To illustrate this point, the GL+F analysis is performed, taking as input the SM t re
sult = (69.7 3.1) [270] and not using the measurement
of 2s from b c cs decays. In this way, 2s = (3 14)
is obtained for = 0.5. The analysis can also be performed
without using the measurement of , in this case the result is 2s = (6 14). With improved experimental accuracy,
this determination could become competitive with that from b c cs decays. Once results of time-dependent analyses
of the B0(s) K()0K()0 channels are available these may
also provide useful constraints.48
To conclude, the usual GL analysis to extract from B0 can be supplemented with the inclusion of the
B0s K+K modes, in the framework of a global CKM
t. The method optimises the constraining power of these decays and allows the derivation of constraints on NP contributions to penguin amplitudes or on the B0s mixing phase and illustrates these capabilities with a simplied analysis, neglecting correlations with other SM observables.
3.4.5 Studies of CP violation in multibody charmless b hadron decays
Multibody charmless b hadron decays can be used for a variety of studies of CP violation, including searches for NP and determination of the angle . Due to the resonant structure in multibody decays, these can offer additional possibilities to search for both the existence and features of NP.Model-independent analyses [374, 375] can be performed to rst establish the presence of a CP violation effect, and then to identify the regions of the phase space in which it is most pronounced.49 To further establish whether any observed CP violation can be accommodated within the Standard Model, amplitude analyses can be used to quantify the effects associated with resonant contributions to the decay. A number of methods have been proposed to determine from such processes [378387], in general requiring input not only from charged B decays, but also from B0 and B0s decays (to states
48The proposal of Ref. [308] has been recently critically reexamined in Ref. [373]. The present analysis shows no particular enhancement of the contribution proportional to ei in B0s K+K, in agreement with the expectation that B0s K()0K()0 should be penguin-
dominated to a very good accuracy.
49LHCb has presented preliminary results from model-independent searches for CP violation in B +K and B K+KK
at ICHEP 2012 [376], and in B + and B K+K
at CKM 2012 [377].
such as K0Sh+h and 0h+h ).50 The potential for LHCb to study multibody charmless 0b decays adds further possibilities for novel studies of CP violation effects.
3.4.6 Prospects of future LHCb measurements
As discussed above, the angle can be determined from both tree-dominated and loop-dominated processes. Comparisons of the values obtained provide tests of NP, and so precision measurements from both methods are needed. Among the tree-dominated processes, in addition to the modes discussed above, any channel that involves the interference of b cs and b ucs transitions is potentially
sensitive to . Many of these modes can be analysed in the upgraded phase of LHCb, including
1. B+ DK++ where, similarly to the B DK
mode, the neutral D can be reconstructed either in the two-body (ADS and GLW-like measurement) or multi-body (GGSZ-like measurement) nal state. The observation of the CF mode in LHCb data [389] indicates a yield only twice lower than that for the B DK mode,
which makes it competitive for the measurement of .51
However, two unknown factors affect the expected sensitivity. First, since this is a multibody decay, the overlap between the interfering amplitudes is in general less than 100 %; this is accounted for by a coherence factor between zero and unity which enters the interference term in Eqs. (54), (55), (59), (60) as an unknown parameter. Second, the value of rB can be different from that in
B DK and is as yet unmeasured, although it is ex
pected [318] that it can be larger in this decay than in B DK.
2. B0 DK+. Although the rate of these decays is
smaller that of B+ DK+, both interfering amplitudes
are colour-suppressed, therefore the expected value of rB is larger, rB 0.3. As a result, the sensitivity to should
be similar to that in the B DK modes.52 Depending
on the content of B0 D0K+ and B0 D0K+
amplitudes, the optimal strategy may involve Dalitz plot analysis of the B0 decay [390, 391]. In this case, control of amplitude model uncertainty will become essential for a precision measurement; it can be eliminated by studying the decays B0 DK+ with D K0S+
[392].
50LHCb has presented preliminary branching fraction measurements of B0(s) K0Sh+h decays at ICHEP 2012 [388].
51Preliminary results from a GLW-type analysis of this channel was presented at ICHEP 2012 [341].
52Preliminary results from a GLW-type analysis of B0 DK0 were
presented at ICHEP 2012 [340].
Eur. Phys. J. C (2013) 73:2373 Page 43 of 92
Table 7 Estimated precision of measurements with 50 fb1 for various charmed B decay modes
Decay mode sensitivity
B DK with D hh , D K 1.3
B DK with D K0S 1.9
B DK with D 4 1.7
B0 DK with D hh , D K0S 1.5
B DK with D hh 3
Time-dependent B0s DsK 2.0
Combined 0.9
3. B0s D. This mode is not self-tagging, but sensitivity
to can be obtained from untagged time-integrated measurements using several different neutral D decay modes [393, 394]. The rst evidence for the three-body decay B0s D0K+K has just been reported by LHCb [395],
and investigation of its resonant structure is in progress.4. B+c DD+s. B+c production in pp collisions is signi
cantly suppressed, however, in this mode the magnitude of CP violation is expected to be O(100 %): the two
interfering amplitudes are of the same magnitude because the b ucs amplitude is colour allowed, while
the b cs amplitude is colour suppressed [396399].
5. 0b D and 0b DpK. Measurement of from
analysis of the 0b D decay mode was proposed
in Ref. [400]. This method allows one to measure in a model-independent way by comparing the S- and P -wave amplitudes. However, this mode is problematic to reconstruct at LHCb because of the poorly dened 0b vertex (both particles from its decay are long-lived)
and low efciency of reconstruction. Alternatively, one can consider a similar measurement with the decay 0b DpK. A preliminary observation of this mode
in early LHCb data has been reported [401].
Table 7 shows the expected sensitivity to from tree level decays in the upgrade scenario. The LHCb upgrade is the only proposed experiment which will be able to reach sub-degree precision on .
Measurement of and 2s by means of the CP-violating observables from loop-mediated decays B0 + and
B0s K+K was discussed in Sect. 3.4.4. Extrapolating
the current sensitivity on C and S to the upgrade scenario, when 50 fb1 of integrated luminosity will be collected,
LHCb will be able to reach a statistical sensitivity stat(C)
stat(S) 0.008 in both B0 + and B0s K+K.
This corresponds to a precision on of 1.4, and on 2s of 0.01 rad, assuming perfect U-spin symmetry.
4 Mixing and CP violation in the charm sector
4.1 Introduction
The study of D mesons offers a unique opportunity to access up-type quarks in avour-changing neutral current (FCNC) processes. It probes scenarios where up-type quarks play a special role, such as supersymmetric models with alignment [402, 403]. It offers complementary constraints on possible NP contributions to those arising from the measurements of FCNC processes of down-type quarks (B or K mesons).
The neutral D system is the latest and last system of neutral mesons where mixing between particles and anti-particles has been established. The mixing rate is consistent with, but at the upper end of, SM expectations [404] and constrains many NP models [405]. More precise D0
D0 mixing measurements will provide even stronger constraints. However, the focus has been shifting to CP violation observables, which provide cleaner tests of the SM [406408]. First evidence for direct CP violation in the charm sector has been reported by the LHCb Collaboration in the study of the difference of the time-integrated asymmetries of D0 K+K and D0 + decay rates
through the parameter ACP [18]. No evidence of indirect
CP violation has yet been found. As discussed in detail below, these results on CP violation in the charm sector appear marginally compatible with the SM but contributions from NP are not excluded.
The mass eigenstates of neutral D mesons, |D1,2 , with
masses m1,2 and widths 1,2 can be written as linear combi
nations of the avour eigenstates |D1,2 = p|D0 q|D0 ,
with complex coefcients p and q which satisfy |p|2 +
|q|2 = 1. The average mass and width are dened as m
(m1 + m2)/2 and (1 + 2)/2. The D mixing param
eters are dened using the mass and width difference as xD (m2 m1)/ and yD (2 1)/2 . The phase
convention of p and q is chosen such that CP|D0 = |D0 .
First evidence for mixing of neutral D0 mesons was discovered in 2007 by Belle and BaBar [409, 410] and is now well established [44]: the no-mixing hypothesis is excluded at more than 10 for the world average (xD = 0.63 +0.190.20 %,
yD = 0.75 0.12 %).53
It is convenient to group hadronic charm decays into three categories. The CF decays, such as D0 K+, are
mediated by tree amplitudes, and therefore no direct CP violation effects are expected. The same is true for DCS decays, such as D0 K+, even though these are much
more rare. The SCS decays, on the other hand, can also have contributions from penguin amplitudes, and therefore direct
53At HCP 2012, LHCb presented the rst observation of charm mixing from a single measurement [411].
Page 44 of 92 Eur. Phys. J. C (2013) 73:2373
CP violation is possible, even though the penguin contributions are expected to be small. Within this classication, it should be noted that some decays to nal states containing K0S mesons, e.g. D0 K0S0, have both CF and DCS con
tributions which can interfere [412]. Within the SM, however, direct CP violation effects are still expected to be negligible in these decays.
LHCb is ideally placed to carry out a wide physics programme in the charm sector, thanks to the high production rate of open charm: with a cross-section of 6.10
0.93 mb [3, 4], one tenth of LHC interactions produce charm hadrons. Its ring-imaging Cherenkov detectors provide excellent separation between pions, kaons and protons in the momentum range between 2 and 100 GeV/c, and additional detectors also provide clean identication of muons and electrons. This allows high purity samples to be obtained both for hadronic and muonic decays. The large boost of the D hadrons produced at LHCb is benecial for time-dependent studies. LHCb has the potential to improve the precision on all the key observables in the charm sector in the next years.
In the remainder of this section the key observables in the charm sector are described, and the current status and near term prospects of the measurements at LHCb are reviewed. A discussion of the implications of the rst LHCb charm physics results follows, motivating improved measurements and studies of additional channels. The potential of the LHCb upgrade to make the precise measurements needed to challenge the theory is then described.
4.1.1 Key observables
Currently the most precise individual measurements of mixing parameters are those of the relative effective lifetime difference between D0 and D0 decays to CP eigenstates (
0.87 0.16 % [414]55 and is consistent with the value of
yD within the current accuracy.
The CP-violating observable A quanties the difference in decay rates of D0 and D0 to a CP eigenstate and is dened as
A =
+
[bracketrightbigg], (82)
where terms below O(104) have again been ignored [413]
and both mixing and direct CP contributions are assumed to be small. The parameter Ad describes the contribution from direct CP violation (|f /Af |2 1 Ad). The cur
rent world average of A is 0.02 0.16 % [44], consistent
with the hypothesis of no CP violation. Due to the smallness of xD and yD, A provides essentially the same information as a full time-dependent CP violation analysis of D0 K+K decays.
An alternative way to search for CP violation in charm mixing is with a time-dependent Dalitz plot analysis of D0 and D0 decays to K0S+ or K0SK+K. Such analyses have been carried out at the B factories [416, 417]. Also in these cases no CP violation was observed.
In time-integrated analyses the measured rate asymmetry is
ACP
CP
1 2(Am + Ad)yD cos xD sin
(D0 f ) (D0 f )
(D0 f ) + (D0 f )
adirCP A
t
, (83)
where the direct CP asymmetry contribution is dened as
adirCP |
Af |2 |f |2 |Af |2 + |f |2
and
) and avour specic nal states ( ), yCP, which is dened as
yCP =
+
2 1
1
2Ad (84)
and t denotes the average decay time of the observed can
didates.
A powerful way to reduce experimental systematic uncertainties is to measure the difference in time-integrated asymmetries in related nal states. For the two-body nal states K+K and +, this difference is given by
ACP ACP[parenleftbig]K+K[parenrightbig] ACP[parenleftbig]+[parenrightbig]
adirCP
[bracketrightbigg], (81)
where terms below O(104) have been ignored [413], CP
is the CP eigenvalue of the nal state, is the CP-violating relative phase between q/p andf /Af where
()
CP
[bracketleftbigg][parenleftbigg]1
1 8A2m
[parenrightbigg]yD cos
1
2(Am)xD sin
[parenleftbigg]1 + yD cos
t
[parenrightbigg]
Af are
the decay amplitudes, and Am represents a CP violation contribution from mixing (|q/p|2 1 Am).54 In the
limit of CP conservation yCP is equal to the mixing parameter yD. The resulting world average value for yCP is
54Am can be determined from asymmetries in semileptonic charm decays, with the assumption of vanishing direct CP violation.
+ [parenleftbig]aindCP + adirCPyD cos [parenrightbig]
(85)
where the CP-violating phase is assumed to be universal [418], a a(K+K) a(+), a (a(K+K) +
55New results presented by Belle at ICHEP 2012 [415] are not included in this average.
t
Eur. Phys. J. C (2013) 73:2373 Page 45 of 92
a(+))/2 and the indirect CP asymmetry parameter is dened as aindCP = (Am/2)yD cos + xD sin . The ratio
t / is equal to zero for the lifetime-unbiased B factory
measurements [419, 420] and is 0.098 0.003 for LHCb
[18] and 0.25 0.04 for CDF [421], therefore ACP is
largely a measure of direct CP violation.The current most accurate measurements of ACP are
from the LHCb and CDF Collaborations and are (0.82
0.21 0.11) % [18] and (0.62 0.21 0.10) % [422],
respectively.56 These results show rst evidence of CP violation in the charm sector: the world average is consistent with no CP violation at only 0.006 % C.L. [44].
4.1.2 Status and near-term future of LHCb measurements
LHCb has a broad programme of charm physics, including searches for rare charm decays (see Sect. 2), spectroscopy and measurements of production cross-sections and asymmetries (see Sect. 5). In this section only studies of mixing and CP violation are discussed. For reviews of the formalism, the reader is referred to Refs. [413, 424, 425] and the references therein, and for an overview of NP implications to Ref. [418].
Mixing and indirect CP violation occur only in neutral mesons. These are probed in a number of different decay modes, predominantlybut not exclusivelytime-dependent ratio measurements. In most cases, the same analysis yields measurements of both mixing and CP violation parameters, so these are considered together. By contrast, direct CP violation may occur in decays of both neutral and charged hadrons, and the primary sensitivity to it comes from time-integrated measurementsthough it may affect certain time-dependent asymmetries as well, as discussed in Sect. 4.7.1.
Several classes of mixing and indirect CP violation measurements are possible at LHCb, particularly:
Measurements of the ratios of the effective D0 lifetimes
in decays to quasi-avour-specic states (e.g. D0
K+) and CP eigenstates fCP (e.g. D0 KK+).
These yield yCP. Comparing the lifetime of D0 fCP
and D0 fCP yields the CP violation parameter A . Measurements of the time-dependence of the ratio of
wrong-sign to right-sign hadronic decays (e.g. D0
K+ vs. D0 K+). The ratio depends on y Dt and
(x 2D + y 2D)t2 (see, e.g., Ref. [424]), where x D = xD cos + yD sin ,y D = yD cos xD sin ,
56At ICHEP 2012, Belle also presented new results on ACP [423],
that are consistent with, but less precise than, those from LHCb and CDF.
and is the mode-dependent strong phase between the CF and DCS amplitudes. Note that (x 2D + y 2D) = x2D + y2D
rM. The mixing parameters can be measured independently for D0 and D0 to constrain indirect CP violation, and the overall asymmetry in wrong-sign decay rates for D0 and D0 gives the direct CP violation parameter Ad.
Time-dependent Dalitz plot ts to self-conjugate nal
states (e.g. D0 K0S+). These combine features of
the two methods above, along with simultaneous extraction of the strong phases relative to CP eigenstate nal states. Consequently they yield measurements of xD and yD directly. Likewise, the indirect CP violation parameters |q/p| and may be extracted, along with the asym
metry in phase and magnitude of each contributing amplitude (in a model-dependent analysis).
Measurements of the ratio of time-integrated rates of
wrong-sign to right-sign semileptonic decays (e.g. D0
D0 K+l
l vs. D0 Kl+l). These yield rM
and Am.
Within LHCb, analyses are planned or in progress for each of these methods. A measurement of yCP and A from the 2010 data sample has been published [19]. In addition, a preliminary result on the time-integrated wrong-sign rate in D0 K from the 2010 sample is available [426].57
A summary of what can be achieved with the 20102012 prompt charm samples is given in Table 8. Note that the observables are generally related to several physics parameters, such that the combined constraints are much more powerful than individual measurements. After analysing 2.5 fb1 of data, the mixing parameters xD and yD are expected to be determined at the level of O(104), and A to be mea
sured with a similar uncertainty. This will represent a signicant improvement in precision compared to the current world averages, which have uncertainties xD = 0.19 %,
yD = 0.12 %, and A = 0.23 %.
For direct CP violation, control of systematic uncertainties associated with production and efciency asymmetries is essential. To date, two techniques have been used to mitigate these effects:
Measurement of differences in asymmetry between two
related nal states, such that systematic effects largely cancelfor example, ACP(D0 KK+)ACP(D0
+) [18]. This is simplest with two-body or quasi-two-body decays. This is discussed in more detail in
Sect. 4.1.3.
Searching for asymmetries in the distributions of multi-
body decays, such that differences in overall normalisation can be neglected and effects related to lab-frame kinematics are largely washed outfor example, in the Dalitz plot distribution of D+ KK++ [427].
57Results of charm mixing parameters in wrong-sign D0 K+
decays have been presented at HCP 2012 [411].
Page 46 of 92 Eur. Phys. J. C (2013) 73:2373
Table 8 Projected statistical uncertainties with 1.0 and 2.5 fb1 of LHCb data. Yields are extrapolated based on samples used in analyses of 2011 data; sensitivities are projected from these yields assuming 1/N scaling based on reported yields by LHCb, and using published input from BaBar, Belle, and CDF. The projected CP-violation sensitivities may vary depending on the true values of the mixing parameters
Sample Observable Sensitivity (1.0 fb1)
Sensitivity (2.5 fb1)
Tagged KK yCP 5 104 4 104 Tagged yCP 10 104 7 104
Tagged KK A 5 104 4 104
Tagged A 10 104 7 104
Tagged WS/RS K x 2D 10 105 5 105
Tagged WS/RS K y D 20 104 10 104
Tagged K0S xD 5 103 3 103
Tagged K0S yD 3 103 2 103
Tagged K0S |q/p| 0.5 0.3
Tagged K0S 25 15
In the longer term, the goal is to extract the CP asymme-tries for D0 K+K and D0 + separately, along
with those for other decay modes. To achieve this, it will be necessary to determine the production and detector efciencies from data. Progress has been made in this area, notably in the D+s production asymmetry measurement [428], which involves determination of the pion reconstruction efciency from D+ D0+, D0 K++ decays
in which one of the D0 daughter pions is not used in the reconstruction.58 The detector asymmetries need to be determined as functions of the relevant variables, and similarly, the production asymmetries can vary as functions of trans-verse momentum and pseudorapidity. Understanding these systematic effects with the level of precision and granularity needed for CP asymmetry measurements is difcult and it cannot be assumed that these challenges will be solved in a short time scale. Moreover, production asymmetries can be determined only with the assumption of vanishing CP asymmetry in a particular (usually CF) control mode. Therefore ultimately the resulting measurements of CP asymmetries for individual decay modes are essentially ACP measure
ments relative to CF decays.
A summary of analyses that are in progress or planned with the 20112012 data is given below:
D0 KK+, +: Updates to the 0.6 fb1 ACP anal
ysis [18] are in progress, using both prompt charm and charm from semileptonic B decays (see Sect. 4.1.3). D+(s) K0Sh+, h+: A ACP-style analysis is possible by
comparing asymmetries in a CF control mode (e.g.
58The pion reconstruction efciency asymmetry has also been used in the determination of the D+ production asymmetry [429].
D+ K0S+) and the associated SCS mode (e.g.
D+ +), taking advantage of the inherent sym
metry of the K0S + and KK+ decays.59
The different kinematic distributions of the tracks (requiring binning or reweighting) and the CP asymmetry in the K0S decay need to be taken into account.
D+ ++, K+K+: A search for CP violation
in D+ K+K+ with the model-independent (so-
called Miranda) technique [374] was published with the 2010 data sample [427], comprising 0.04 fb1.
With such small data samples, detector effects are negligible. However, from studies of control modes such as D+s KK++ it is found that this is no longer
the case with 1.0 fb1 of data or more, so an update will require careful control of systematic effects. The ++ nal state should be more tractable, since the interaction asymmetry does not depend strongly on momentum.
D0 ++, KK++: Previous publications
have focused mainly on T -odd moments [430], but there is further information in the distribution of nal-state particles. A Miranda-style binned analysis or a comparable unbinned method [375] can be used.60
Baryonic decays: LHCb will collect large samples of charmed baryons, enabling novel searches for CP-violation effects [432]. Triggering presents a challenge, but trigger lines for several +c decay modes of the form h+ or phh + are already incorporated, allowing large samples to be recorded. In addition to the considerations outlined above for D meson decays, the large proton-antiproton interaction asymmetry and the possibility of polarisation in the initial state must be taken into account.
4.1.3 Experimental aspects of ACP and related
measurements
The raw asymmetry measured for D+-tagged D0 decays to a nal state f is dened as:
Araw(f )
N(D+ D0(f )+s) N(D D0(f )s) N(D+ D0(f )+s) + N(D D0(f )s)
, (86)
where N(X) refers to the number of reconstructed events of decay X after background subtraction. This raw asymmetry arises from several sources: the D+ production asymmetry AP, the asymmetry in selecting the tagging slow pion
59A small difference in kinematic distributions can occur in
KK+ due to crossing resonances.
60Preliminary results on the D0 ++ decay were presented
at ICHEP 2012 [431].
Eur. Phys. J. C (2013) 73:2373 Page 47 of 92
AD(+s), the asymmetry in selecting the D0 decay into the nal state AD(f ), and the CP asymmetry in the decay
ACP(f ).Consider the general case of a measured rate n, an ef
ciency (or other correction) , and the corrected rate N,
where the subscript refers to D0 or D0. Then:
N+
N =
n+/+
n/ =
n+
n
+
nKK,+ nKK,
[parenrightbigg][parenleftbigg]
+
[parenrightbigg],
. (87)
Dening a generic asymmetry Ax as
Ax
N,+ N, =
n,+ n,
[parenrightbigg][parenleftbigg]
+
[parenrightbigg]
x+ x x+ + x
nKK,+/nKK, n,+/n,
The nuisance asymmetries AP and AD(+s) cancel be
tween the K+K and + nal states because these are properties of the D+ and of the tagging slow pion, respectively, which do not depend on the decay of the D0 meson.
However, an articial correlation between these asymme-tries and the decay mode can arise if the asymmetry varies as a function of some variable63 (e.g. the momentum of the D+) and the reconstructed distributions in this variable are different for the K+K and + nal states (e.g. due to detector acceptance of the daughter tracks). In such a scenario, the two modes would populate regions with different raw asymmetries and so the nuisance asymmetries would not cancel fully. Two techniques have been used to address this:
the data can be partitioned into smaller kinematic regions
such that within each region the raw asymmetries are constant and/or the K+K and + kinematic distributions are equal;
the data can be reweighted such that the K+K and
+ kinematic distributions are equalised.
The rst approach was used in the published LHCb result, and the second in the CDF result [421].
There is another way in which the formalism could be broken: through the presence of peaking backgrounds which(a) fake the signal, (b) occur at different levels for the K+K and + nal states, and (c) have a different raw asymmetry from the signal. The signal extraction procedure used in the published LHCb analysis is a t to the mass difference from threshold m m((h+h)D
0 +s)
m(h+h) m(+). This is vulnerable to a class of back
ground in which a real D+ decay occurs and the correct slow pion is found but the D0 decay is partly misre-constructed, e.g. D0 K+0 misidentied as D0
KK+. This typically creates a background which peaks
63The discussion is framed in terms of kinematic variables, since there are clear mechanisms that could cause problems there, but the same logic can be applied to magnet polarity, trigger conditions, etc.
NKK,+/NKK,
N,+/N,+ =
,
gives the identity
x+
x =
1 + Ax
1 Ax
.
Then applying this to Eq. (87),
1 + An
1 An =
[parenrightbigg]. (88)
Applying the Taylor series expansion to Eq. (88), gives
1 + 2An + 2A2n + [parenrightbig]
= [parenleftbig]1 + 2AN + 2A2N + [parenrightbig][parenleftbig]1 + 2A + 2A2 + [parenrightbig], and thus
An = AN + A + [parenleftbig]terms of order A2[parenrightbig]. (89) Generalising this to include multiple asymmetries, the formula used in the published analysis [18] is obtained
Araw(f ) = ACP(f ) + AP + AD[parenleftbig]+s[parenrightbig] + AD(f ), (90) which is correct up to terms of second order in the asymmetries. In practise, for D0 h+h, the asymmetries are
AP 1 %, AD(+s) 12 %, and AD(f ) = 0 by construc
tion. Thus, the second-order correction is O(104).61 Fur
ther, AD(+s) and AP are the same for f = K+K and
f = + (leaving aside differences in kinematic distri
bution, considered below) and so many terms cancel in the difference:62
ACP = Araw[parenleftbig]K+K[parenrightbig] Araw[parenleftbig]+[parenrightbig]
ACP[parenleftbig]K+K[parenrightbig] ACP[parenleftbig]+[parenrightbig].
61Note that the LHCb dipole magnet creates regions of parameter space with large AD(+s), particularly at the left and right edges of the ac
ceptance. These regions are excluded with ducial cuts.
62Note in particular that if ACP(K+K) = ACP(+) = 0, the ap
proximation becomes exact at all orders.
At the present level of precision, with a statistical uncertainty of around 0.2 %, this approximation is perfectly adequate. However, when more data is accumulatedand certainly after the upgradeit will be necessary to change the analysis to take second-order terms into account. This can be done using the ratio formulation of Eq. (87), i.e.
NKK,+ NKK, =
1 + AN
1 AN
[parenrightbigg][parenleftbigg]1 + A
1 A
Page 48 of 92 Eur. Phys. J. C (2013) 73:2373
Table 9 Summary of absolute systematic uncertainties for ACP
Source Uncertainty
Fiducial requirement 0.01 %
Peaking background asymmetry 0.04 %
Fit procedure 0.08 %
Multiple candidates 0.06 %
Kinematic binning 0.02 %
Total 0.11 %
[bracketleftbigg]2D0[vextendsingle][vextendsingle]H
| C|=2[vextendsingle][vextendsingle]D0[angbracketrightbig]
+ D0[vextendsingle][vextendsingle]i
[integraldisplay] d4x T H| C|=1w(x)H| C|=1w(0)[vextendsingle][vextendsingle]D0[angbracketrightbig]
[bracketrightbigg],
(91)
1
2MDD
ImD0[vextendsingle][vextendsingle]i
yD =
[integraldisplay] d4x T H| C|=1w(x)H| C|=1w(0)[vextendsingle][vextendsingle]D0[angbracketrightbig].
in m but is broadly distributed in m(h+h). Only cases which lie within the narrow m(h+h) signal window will survive. This is more common for the K+K nal state than for +: the energy of a missing particle can be made up by misidentifying a pion as a kaon, but apart from
D0 e+e there is little that can fake the kinematics of
D0 +. In practise, the charged hadron identication
at LHCb suppresses these background greatly, and their raw asymmetries are not expected to be very different from the signal. In the published LHCb analysis, the impact of these backgrounds on the asymmetry was estimated by measuring their size and asymmetry in the h+h mass sidebands and computing the effect of such a background on the signal with a toy Monte Carlo study. The alternative approach would be to use a full 2D t to m(h+h) and m, which would distinguish this class of peaking background from the signal by its m(h+h) distribution.
The three issues discussed aboveterms entering at second order in the asymmetries, non-cancellation due to kinematic correlations, and peaking backgroundsare particular to this analysis and will require some changes to the procedure as larger data samples become available. In addition, there are more generic systematic uncertainties associated with the t procedure and with the handling of events with more than one candidate. These are summarised in Table 9.
4.2 Theory status of mixing and indirect CP violation
4.2.1 Theoretical predictions for D, mD and indirect CP violation in the Standard Model
As discussed in Sect. 4.1, mixing of charmed mesons provides outstanding opportunities to search for physics beyond the SM. New avour-violating interactions at some high-energy scale may, together with the SM interactions, mix the avour eigenstates giving mixing parameters that differ from their SM expectations. It is known experimentally that D0D0 mixing proceeds extremely slowly, which in the SM is usually attributed to the absence of super-heavy quarks.
Both SM and NP contributions to mass and width differences can be summarised as
xD =
1
2MDD Re
These formulae serve as the initial point of calculations of the mass and lifetime differences. They include contributions from local (at charm mass scale) C = 2 interactions
generated by the b-quark [433437] or NP particles and from SM-dominated time-ordered products of two C = 1
interaction Hamiltonians (see, however, Ref. [438]).
A simple examination of Eq. (91) reveals that the local C = 2 interactions only affect xD, thus one can conclude
that it is more likely that xD receives large NP contributions. Hence, it was believed that an experimental observation of xD yD would unambiguously reveal NP contributions to
charm mixing. This simple signal for NP was found to not be realised in nature, but it is interesting that the reverse relation, xD < yD with yD expected to be determined by the SM processes, might nevertheless signicantly affect the sensitivity to NP of experimental analyses of D mixing [439]. Also, it is important to point out that, contrary to the calculations of the SM contribution to mixing, the contributions of NP models can be calculated relatively unambiguously [405, 440, 441].
The calculation of the SM contribution to the mixing amplitudes is rather sophisticated. In the SM xD and yD are generated only at second order in avour SU(3)f breaking,
xD, yD sin2 C [bracketleftbig]SU(3)f breaking[bracketrightbig]2, (92) where C is the Cabibbo angle. Therefore, predicting the SM values of xD and yD depends crucially on estimating the size of SU(3)f breaking [404, 442].
There are currently two approaches, neither of which give very reliable results because mc is in some sense intermediate between heavy and light. The inclusive approach is based on the OPE. In the mc QCD limit, where QCD
is a scale characteristic of the strong interactions, mD and D can be expanded in terms of matrix elements of local operators [434437]. Such calculations typically yield xD, yD < 103. The use of the OPE relies on local quark-hadron duality (see, for example, Ref. [443]), and on QCD/Ereleased (with Ereleased mc) being small enough to
allow a truncation of the series. Moreover, a careful reorganisation of the OPE series is needed, as terms with smaller
Eur. Phys. J. C (2013) 73:2373 Page 49 of 92
powers of ms are numerically more important despite being more suppressed by powers of 1/mc [434437]. The numerically dominant contribution is composed of over twenty unknown matrix elements of dimension-12 operators, which are very hard to estimate. As a possible improvement of this approach, it would be important to perform lattice calculations of those matrix elements, as well as make perturbative QCD (pQCD) corrections to Wilson coefcients of those operators.
The exclusive approach sums over intermediate hadronic states, which may be modelled or t to experimental data [444449]. Since there are cancellations between states within a given SU(3)f multiplet, one needs to know the contribution of each state with high precision. However, the D meson is not light enough that its decays are dominated by a few nal states. In the absence of sufciently precise data on many decay rates and on strong phases, one is forced to use some assumptions. While most studies nd xD, yD < 103,
Refs. [444449] obtain xD and yD at the 102 level by arguing that SU(3)f violation is of order unity. Particular care should be taken if experimental data are used to estimate the mixing parameters, as the large cancellations expected in the calculation make the nal result sensitive to uncertainties in the experimental inputs. It was shown that phase space effects alone provide enough SU(3)f violation to induce xD, yD 102 [442]. Large effects in yD appear for
decays close to threshold, where an analytic expansion in SU(3)f violation is no longer possible; a dispersion relation can then be used to show that xD would receive contributions of similar order of magnitude. The dispersion calculation suffers from uncertainties associated with unknown (off-shell) q2-dependences of non-leptonic transition amplitudes and thus cannot be regarded as a precision calculation, although it provides a realistic estimate of xD. As a possible improvement of this approach, an estimate of SU(3)f breaking in matrix elements should be performed. In addition, a calculation with Vub = 0 should also be done, which
is important to understand the size of CP violation in charm mixing.
Based on the above discussion, it can be seen that it is difcult to nd a clear indication of physics beyond the SM in D0D0 mixing measurements alone. However, an observation of large CP violation in charm mixing would be a robust signal of NP.
CP violation in D decays and mixing can be searched for by a variety of methods. Most of the techniques that are sensitive to CP violation make use of the decay asymmetry ACP(f ) [418, 425]. For instance, time-dependent de
cay widths for D K are sensitive to CP violation in
mixing. In particular, a combined analysis of D K and
D KK can yield interesting constraints on CP-violating
parameters yCP and A , as discussed in Sect. 4.1.1.
With the D0D0 transition amplitudes dened as follows:
D0[vextendsingle][vextendsingle]H[vextendsingle][vextendsingle]D0[angbracketrightbig] =
M12 i 212,
D0[vextendsingle][vextendsingle]H[vextendsingle][vextendsingle]D0[angbracketrightbig] =
M12 i2 12,
(93)
then in the limit where direct CP violation is neglected, one can measure [418, 425] four quantities, xD, yD, Am, and , which are described by three physical variables,64
x12 =
2|M12|
, y12 = |
12|
,
(94)
This implies that there is a model-independent relation among experimental quantities [425, 450],
xD
yD =
1
2
12 = arg(M12/12).
Amtan . (95)
4.2.2 New physics in indirect CP violation
Indirect CP violation in charm mixing and decays is a unique probe for NP, since within the SM the relevant processes are described by the physics of the rst two generations to an excellent approximation. Hence, observation of CP violation in D0D0 mixing at a level higher than
O(103) (which is the SM contribution) would constitute an unambiguous signal of NP.
The commonly used theoretical parameters x12 and 12 dened in Eq. (94) can be expressed in terms of xD, yD and
|q/p| as:
x212 = x2D
(1 + |q/p|2)24|q/p|2 +
y2D
(1 |q/p|2)2 4|q/p|2
,
(96)
sin2 12 =
(x2D + y2D)2(1 |q/p|4)2
16x2Dy2D|q/p|4 + (x2D + y2D)2(1 |q/p|4)2
.
The latest t65 yields the following ranges [44]
xD [0.24, 0.99] %, yD [0.51, 0.98] %,
|q/p| [0.59, 1.26],
(97)
all at 95 % C.L. The t also provides 95 % C.L. ranges also for the theoretical parameters from Eq. (94):
x12 [0.25, 0.99] %, y12 [0.51, 0.98] %, 12 [bracketleftbig]8.4, 24.6[bracketrightbig].
(98)
64Among various possible phase denitions, only 12, the relative phase between M12 and 12, is convention-independent and so has physical consequences.
65Not including results presented at ICHEP 2012 or later.
Page 50 of 92 Eur. Phys. J. C (2013) 73:2373
It should be noted that the experimental precision on the CP violation parameters is more than two orders of magnitude away from their SM predictions.
It is reasonable to assume that there are no accidental strong cancellations between the SM and the NP contributions to M12. Useful bounds can thus be obtained by taking the NP contribution to saturate the upper limits in Eq. (98).The resulting constraints are presented in the xNP12/x12NP12 plane in Fig. 23. One can also translate the data into model-independent bounds on four-quark operators, as performed e.g. in Refs. [440, 441].
The generic NP analysis can also be applied to models with MFV, where new contributions to FCNCs originate only from the Yukawa matrices Yu,d. The relevant basis is then the up mass basis, where Yu is diagonal, so that avour violation comes from powers of YdY d. The leading contribution is to the operator (uLcL)2 ( is a colour index), and it is given in terms of its Wilson coefcient C1 by
C1 [bracketleftbig]y2s[parenleftbig]V
csVus[parenrightbig] + (1 + rGMFV) y2b[parenleftbig]V
cbVub[parenrightbig][bracketrightbig]2. (99)
Here rGMFV parameterises the effect of resummation of higher powers of the Yukawa matrices when these are important, namely in general MFV (GMFV) models [451].
The contribution to x12 in the linear MFV case (rGMFV =
0) is orders of magnitude below the current experimental sensitivity, assuming O(1) proportionality coefcient in
Eq. (99). Yet in the context of GMFV with two Higgs doublets and large tan , such that yb 1, observable signals
can be obtained, as shown in Fig. 23 for rGMFV in the range
[3, 3]. Note that strictly speaking rGMFV (and thus the re
sulting signal) is not bounded, but higher absolute values than those considered here are much less likely in realistic models. Indeed in the current example rGMFV [greaterorsimilar] 2 is excluded, as shown in the gure.
The available data on D0D0 mixing can also be used to constrain the parameter space of specic theories, such as SUSY and warped extra dimensions (WED) [452]. This has been done e.g. in Refs. [440, 441] or Refs. [453, 454] where the interplay between the constraints from the K and D systems is presented. Here the inuence of improving the current bounds is demonstrated.
Within a SUSY framework, one can focus on the rst two generations of the left-handed squark mass-squared matrix, m2Q, as the source of avour violation. As an additional
assumption, the framework can be aligned with the down sector, where the constraints are generically stronger. As in realistic alignment models (see e.g. Refs. [402, 455]), the off-diagonal element of m2Q in the down mass basis (which
induces s d FCNCs) is taken to be small but not zero,
with comparable real and imaginary parts. For concreteness, values of either 5C or 3C (with C being the Cabibbo angle)
are examined, where in both cases the dominant bounds still arise from D0D0 mixing and not from the K system [454]. The constrained parameter is the squark mass degeneracy, dened by
12Q
m
Fig. 23 Allowed region (shaded) in the xNP12/x12 sin NP12 plane. The red line corresponds to a GMFV prediction (see text for details) with rGMFV [3, 3]
Q2 m Q1
m
Q2 + m Q1
. (100)
Fig. 24 Bound on the squark mass degeneracy 12Q, dened in Eq. (100), as a function of the experimental constraint on CP violation in D0D0 mixing, parametrised by sin exp12. The alignment angle
from the down sector is 5C (left panel) or 3C (right panel). The solid blue line in each panel is for m Q = mg = 1 TeV and the dashed red
line is for m Q = mg = 1.5 TeV
Eur. Phys. J. C (2013) 73:2373 Page 51 of 92
In order to analyze the effect of improving the experimental constraints on indirect CP violation in charm (assuming that no such violation is actually observed), for simplicity the bound on x12 is kept xed as in Eq. (98), while that on 12 is varied. This is shown in Fig. 24 for the two alignment angles mentioned above and for two points in the SUSY parameter space m Q = mg = 1 and 1.5 TeV, where m Q is the average
squark mass and m
g is the gluino mass. The right edge of each of the four lines in the plots marks the current situation, where the dominant constraint is from mD. It is evident that after a certain level of improvement, the bound from CP violation becomes the important one, and this happens more quickly for a weaker alignment model (3C) than for 5C alignment. The reason is the larger phase in the former case.
To conclude, the experimental search for indirect CP violation in charm is one of the most promising channels for discovering NP or obtaining strong constraints. This is not negated by the large hadronic uncertainties in the D system, because of the very small SM short distance contribution to CP violation in D0D0 mixing.
4.3 The status of calculations of ACP
in the Standard Model
As discussed above, the LHCb Collaboration has measured a surprisingly large time-integrated CP asymmetry difference [18],
ACP ACP[parenleftbig]D0 KK+[parenrightbig] ACP[parenleftbig]D0 +[parenrightbig]
= (0.82 0.21 0.11) %, (101) which has recently been supported by a result from the
CDF collaboration [422].66 Inclusion of the BaBar and Belle measurements of the individual KK+ and + time-integrated CP asymmetries [419, 420] and the BaBar, Belle, and LHCb measurements of the indirect CP asymmetry A
[19, 410, 456] yields the world average for the direct CP asymmetry difference [44]
adirCP adirCP[parenleftbig]D0 KK+[parenrightbig] adirCP[parenleftbig]D0 +[parenrightbig]
= (0.67 0.16) %. (102)
The naive penguin-to-tree amplitude ratio is O([VcbVub/
VcsVus]S/) 104, yielding adirCP < 0.1 %. This has
led to extensive speculation in the literature that the measurement of adirCP is a signal for NP. This is a particularly exciting possibility, given that reasonable NP models can be constructed in which all related avour-changing neutral current (FCNC) constraints, e.g., from D0D0 mixing,
66New results presented at ICHEP 2012, including a new result from Belle on ACP [423], are not included in the averages discussed here.
are satised. A summary of NP interpretations is given in Sect. 4.4.1. First, a discussion of adirCP in the SM is given.
The naive expectation for the SM penguin-to-tree ratio is based on estimates of the short-distance penguins with b-quarks in the loops. In fact, there is consensus that a SM explanation for adirCP would have to proceed via dynamical enhancement of the long-distance penguin contraction
contributions to the penguin amplitudes, i.e., penguins with s and d quarks inside the loops. Research addressing the direct CP asymmetry in the SM has largely fallen into one of two categories: (i) avour SU(3)f or U-spin ts to the D decay rates, to check that an enhanced penguin amplitude can be accommodated [457463] (this, by itself, would not mean that adirCP is due to SM dynamics); (ii) rough estimates of the magnitudes of certain contributions to the long-distance penguin contractions [461, 464466], to check if, in fact, it is reasonable that SM dynamics could yield the enhanced penguin amplitudes returned by the SU(3)f or U-spin ts.
The results obtained using the avour symmetry decompositions can be summarised as follows. An SU(3)f analysis of the D P P decay amplitudes that incorporates CP vi
olation effects was rst carried out about 20 years ago [445, 457, 467]. Already in this study the possibility of large direct CP asymmetries was anticipated, e.g., as large as the percent level assuming that the penguins receive a large enhancement akin to the I = 1/2 rule in kaon decays. An updated
analysis, working to rst order in SU(3)f breaking, has been presented [458], making use of branching ratio measurements for the D K, and D0 KK+, K0 decay
modes. The authors concluded that adirCP can be easily reconciled with the measured branching ratios. This was also the conclusion of a study based on a diagrammatic SU(3)f amplitude decomposition [459], which considered a larger set of D P P decay modes. Again, this is only a state
ment about the possibility of accommodating the required amplitudes in the avour decomposition, not about their realisation via long distance QCD dynamics. Both studies ob-serve that a SM explanation of adirCP could be combined with precise measurements of the individual asymmetries adirCP(D0 KK+) and adirCP(D0 +) to obtain predictions for adirCP(D0 00). The conclusion, based on
current data, is that percent level asymmetries for the latter could be realised. Reference [459] also discusses implications for adirCP(D+ K+K0).
Studies employing U-spin symmetry [460, 461] necessarily focus on amplitude ts to the smaller set of decay modes D0 K+, K+, +, KK+, as the D0 is
a U-spin singlet, while the four nal states and the operators mediating these decays in the SM C = 1 effective Hamil
tonian each consist of a U-spin triplet and a singlet. Working to rst order in U-spin breaking, the four decay amplitudes
Page 52 of 92 Eur. Phys. J. C (2013) 73:2373
can be written as
A[parenleftbig]D0 K+[parenrightbig] = VcsV ud
[parenleftbigg]T
1
2T
[parenrightbigg],
A[parenleftbig]D0 +K[parenrightbig] = VcdV us
[parenleftbigg]T +
1
2T
[parenrightbigg],
A[parenleftbig]D0 +, K+K[parenrightbig]
=
(103)
1
2[parenleftbig]VcsV us VcdV ud[parenrightbig](T S)
VcbV ub[parenleftbigg]P
1
2P
[parenrightbigg],
where the U-spin triplet tree amplitude T and the singlet penguin amplitude P arise at 0th order in U-spin breaking, and T , S and P are the rst order U-spin breaking corrections, which transform in turn as a triplet, singlet, and singlet under U-spin. The singlet amplitude S accounts for the large rate difference (D0 KK+)/ (D0
+) = 2.8 (after accounting for phase space). A ra
tio S/T 0.5 is found in Refs. [460, 461], and in the
SU(3)f study of Ref. [458] which effectively contains the above U-spin decomposition. Realisation of Eq. (102) requires |P /T | 3, for O(1) strong phases and adirCP(D0
KK+) adirCP(D0 +), where the last relation be
comes an equality in the U-spin limit. This amounts to an order of magnitude enhancement of the penguin amplitude beyond the naive estimate.
The CP-averaged experimental sum-rule relation,
sum-rule = |A(D
0 +)
VcdVud |
|A(D0K+)VcdVus| + |A(D0K+)VcsVud|
1
0 KK+)
VcsVus | + |A(D
= (4.0 1.6) %, (104)
together with the observation of small (15 %) U-spin
breaking in A(D0 K+) vs. A(D0 K+), can be
interpreted as suggesting that U-spin is a good symmetry in these decays [461]. Other authors take the large difference between (D0 KK+) and (D0 +) or
S/T 0.5 as evidence for large U-spin breaking in SCS
decays. In Ref. [461], rather than interpreting the amount of U-spin breaking implied by S by comparing it to T , as in other works, S is compared to P . It is observed that whereas adirCP implies that P must be dominated by the sum of the long distance s- and d-quark penguin contractions, nominal U-spin breaking would imply that S must be dominated by their difference. A consistent picture emerges in which direct CP asymmetries of order a few per mille are not surprising given the size of (D0 KK+)/ (D0
+). However, as always in the avour decomposition approach, accommodation need not translate to realisation
by QCD dynamics. One consequence of this picture is that adirCP(D0 K0SK0S) could be as large as 0.6 % for O(1)
strong phases.
Finally, the estimates for the long-distance penguin contractions [466, 468] are reviewed to see if the required enhancement can be realised. Reference [468] employs the one-gluon exchange approximation. The essential ingredients are: (i) 1/Nc counting; (ii) D branching ratio data which shows that certain formally 1/mc power-suppressed amplitudes are of same order as their leading (1/mc)0 counterparts; (iii) translation of this breakdown of the 1/mc expansion to the penguin contraction amplitudes, in the approximation of a hard gluon exchange; (iv) use of a partonic quantity as a rough estimator of the hadronic interactions, e.g., nal state interactions, underlying the penguin contraction loops. This results in a rough estimate for adirCP at the few per mille level. The authors of Ref. [468] thus conclude that a SM explanation is plausible, given that their estimate suffers from large uncertainties. In Ref. [466] the penguin contractions are estimated using isospin and information from scattering and unitarity. A t of the CP-conserving contributions from the CP-averaged branching ratios provides information on the isospin amplitudes and the underlying renormalisation group invariant amplitude contributions. Allowing for three coupled channel contributions to , KK scattering the authors conclude that the observed asymmetries are marginally compatible with the SM.
To summarise, avour SU(3) or U-spin ts to the D
P P data can accommodate the enhanced penguin amplitudes required to reproduce adirCP. There is consensus that in this case adirCP(D0 00) could lie at the percent level,
while adirCP(D+ K+K0) could certainly lie at the few
per mille level. Under the assumption of nominal SU(3)f breaking in D P P decays, the enhancement of the long-
distance penguin contractions required to realise adirCP is
not surprising, given the large difference between the D0
KK+ and D0 + decay rates. It would of course
be of interest to extend the above CP violation studies to the SCS D V P and D V V decay modes. Finally,
among the works which have attempted to estimate directly the magnitudes of the long distance penguin contractions, there is no consensus on whether they can be enhanced by an order of magnitude beyond the naive penguin amplitude estimates, as would be required in order to explain adirCP.
Ultimately this question will have to be answered directly via lattice studies.
In the following section, future prospects are discussed. In subsequent sections, several denitive CP-violating signals for NP in SCS D decays will be discussed.
Eur. Phys. J. C (2013) 73:2373 Page 53 of 92
4.4 ACP in the light
of physics beyond the Standard Model
4.4.1 General considerations
Potential NP contributions to ACP can be parametrised in
terms of an effective Hamiltonian valid below the W and top mass scales
Heff-NP| C|=1 =
tr de
notes the traceless part. Then in the two generation limit, one can construct a single source of CP violation, given by J
i[Au, Ad] [470, 471]. The crucial observation is that J is in
variant under SO(2) rotations between the Au and Ad eigen-
bases. Introducing now SU(2)Q breaking NP effective operator contributions of the form QL = [(XL)ij Qi Qj ]L,
where Qi stands for the left-handed quark doublets, i and j are generation indices, XL is a traceless Hermitian avour matrix and L denotes a avour singlet current. It follows that the CP-violating contributions have to be proportional to J and thus invariant under avour rotations. The universality of CP violation induced by QL can be expressed ex
plicitly as [454]
Im[parenleftbig]XuL[parenrightbig]12 = Im[parenleftbig]XdL[parenrightbig]12 Tr(XL J ). (107) The above identity holds to a very good approximation even in the three-generation framework. In the SM, large values of Yb,t induce a SU(3)/SU(2) avour symmetry breaking pattern [451] which allows one to decompose XL under the residual SU(2) in a well dened way. Finally, residual SM SU(2)Q breaking is necessarily suppressed by small mass ratios mc,s/mt,b, and small CKM mixing angles. The most relevant implication of Eq. (107) is that it predicts a direct correspondence between SU(3)Q breaking NP contributions to ACP and / [454]. It follows immediately that strin
gent limits on possible NP contributions to the latter require SU(3)Q breaking contributions to the former to be below the per mille level (for RNP,i = O(1)). As a corollary, one can
show that within NP scenarios which only break SU(3)Q, existing stringent experimental bounds on new contributions to CP-violating rare semileptonic kaon decays K0L
0(, + ) put robust constraints on CP asymmetries of corresponding rare charm decays D (, + ). In par
ticular, the SU(3)Q-violating contribution to the CP asymmetry in D e+e has been shown to be less than 2 %
[454].
The viability of the remaining 4-quark operators in
Heff-NP| C|=1 as explanations of the experimental ACP value
depends crucially on their avour and chiral structure (a full list can be found in Ref. [469]). In particular, operators involving purely right-handed quarks are unconstrained in the effective theory analysis but may be subject to severe constraints from their UV sensitive contributions to D mixing observables. On the other hand, QED and QCD dipole operators are at present only weakly constrained by nuclear electric dipole moments (EDMs) and thus present the best candidates to address the ACP puzzle [469].
Finally, note that it was shown that the impact of universality of CP within the alignment framework is to limit the amount of CP violation in D0D0 mixing to below 20 %,
which is interestingly near the current bound. The expected progress in this measurement with the LHCb detector is therefore going to start probing this framework.
(YdY d)/tr, where Yq are the Yukawa matrices and /
CNP( )iQ( )i, (105)
where the relevant operators Q( )i are dened in Ref. [469].
Introducing the ratios RNP,iK, as the relevant NP hadronic amplitudes (matrix elements KK+, +|Q( )i|D ) nor
malised to the leading CP-conserving SM contributions and writing CNPi = v2EW/2NP, the relevant NP scale NP is
given by [469]
(10 TeV)22NP =
2 [summationdisplay]
i
GF
(0.61 0.17) 0.12 Im( RSM)Im( RNP,i) , (106)
where Ri = RiK + Ri and RSMK, parametrise the unknown
hadronic amplitude ratios associated with the CP-violating SM contributions. Comparing this estimate to the much higher effective scales probed by CP-violating observables in D mixing and also in the kaon sector, one rst needs to verify if such large contributions can still be allowed by other avour constraints. Within the effective theory approach, this can be estimated via so-called weak mixing of the effective operators. In particular, time-ordered correlators of Heff-NP| C|=1 with the SM effective weak Hamilto
nian can, at the one weak-loop order, induce important contributions to CP violation in both D meson mixing and kaon decays ( / ). On the other hand, analogous correlators quadratic in Heff-NP| C|=1 turn out to be either chirally sup
pressed and thus negligible, or yield quadratically divergent contributions, which are thus highly sensitive to particular UV completions of the effective theory [469].
4.4.2 Universality of CP violationin avour-changing decay processes
The strongest bounds can be derived for a particular class of operators, which transform non-trivially only under the SU(3)Q subgroup of the global SM quark avour symmetry GF = SU(3)Q SU(3)U SU(3)D, respected by the
SM gauge interactions. In particular one can prove that their CP-violating contributions to F = 1 processes (here F
generically represents a avour quantum number) have to be approximately universal between the up and down sectors [454]. Within the SM one can identify two unique sources of SU(3)Q breaking given by Au (YuY u)/tr and
Ad
Page 54 of 92 Eur. Phys. J. C (2013) 73:2373
4.4.3 Explanations of ACP within NP modelsSince the announcement of the LHCb result, several prospective explanations of ACP within various NP frameworks
have appeared. In the following the implications within some of the well-motivated NP models are discussed.
In the MSSM, the right size of the QCD dipole operator contributions can be generated with non-zero leftright up-type squark mixing contributions (u12)LR [418, 472, 473].
Such effects in ACP can be parametrised as [472]
[vextendsingle][vextendsingle] aSUSY
CP
[parenrightbigg], (108)
where m denotes a common squark and gluino mass scale.
At the same time dangerous contributions to D mixing observables are chirally suppressed. It turns out however that even the apparently small (u12)LR value required implies a highly nontrivial avour structure of the UV theory; in particular, large trilinear (A) terms and sizeable mixing among the rst two generation squarks (12) are required [472].
Im[parenleftbig]u12[parenrightbig]LR
[vextendsingle][vextendsingle]
0.6 %[parenleftbigg]| Im(u12)LR|103
[parenrightbigg][parenleftbigg]TeV
m
Im(A)12mc
m
[parenrightbigg]0.5 103. (109)
Similarly, WED models that explain the quark spectrum through avour anarchy [452, 474476] can naturally give rise to QCD dipole contributions affecting ACP as [477]
[vextendsingle][vextendsingle] aWED
CP
Im(A)3
[parenrightbigg][parenleftbigg]12 0.3
[parenrightbigg][parenleftbigg]TeV
m
[vextendsingle][vextendsingle]
0.6 %[parenleftbigg]Y5
6
2 3 TeV mKK
2 , (110)
where mKK is the KaluzaKlein (KK) scale and Y5 is the ve-dimensional Yukawa coupling in appropriate units. Reproducing the experimental value of ACP requires near-
maximal 5D Yukawa coupling, close to its perturbative bound [478, 479] of 4/NKK 7 for NKK = 3 pertur
bative KK states. In turn, this helps to suppress unrealistic tree-level contributions to CP violation in D0D0 mixing [440, 441]. This scenario can also be interpreted within the framework of partial compositeness in four dimensions, but generic composite models typically require smaller Yukawa couplings to explain ACP and consequently predict size
able contributions to CP violation in F = 2 processes
[480].
On the other hand, in the SM extension with a fourth family of chiral fermions ACP can be affected by 3 3 CKM
non-unitarity and b penguin operators
[vextendsingle][vextendsingle] a4th
gen CP
[vextendsingle][vextendsingle]
Im[parenleftbigg] b
[parenrightbigg]. (111)
However, due to the existing stringent constraints on the new CP-violating phases entering b [434, 481], only moderate effects comparable to the SM estimates are allowed [460].
Finally, it is possible to relate ACP to the anoma
lously large forwardbackward asymmetry in the t t system
measured at the Tevatron [482] through a minimal model. Among the single-scalar-mediated mechanisms that can explain the top data, only the t-channel exchange of a colour-singlet weak doublet, with a very special avour structure, is consistent with the total and differential t t cross-section,
avour constraints and electroweak precision measurements [483]. The required avour structure implies that the scalar unavoidably contributes at tree level to ACP [484]. The
relevant electroweak parameters are either directly measured, or xed by the top-related data, implying that, for a plausible range of the hadronic parameters, the scalar-mediated contribution is of the right size.
4.4.4 Shedding lighton direct CP violation via D V decays
The theoretical interpretation of ACP is puzzling: it is
above its naive estimate in the SM and it could well be a signal of NP, but it is not large enough to rule out a possible SM explanation. It is then important to identify possible future experimental tests able to distinguish standard vs. nonstandard explanations of ACP. Among the NP explana
tions of ACP, the most interesting ones are those based on
a new CP-violating phase in the C = 1 chromomagnetic
operator. A general prediction of this class of models, that could be used to test this hypothesis from data, is enhanced direct CP violation (DCPV) in radiative decay modes [485].
1. The rst key observation to estimate DCPV asymme-tries in radiative decay modes is the strong link between the C = 1 chromomagnetic operator (Q8
uLT agsGacR) and the C = 1 electromagnetic-
dipole operator (Q7 LQueF cR). In most ex
plicit new-physics models the short-distance Wilson coefcients of these two operators (C7,8) are expected to be similar. Moreover, even assuming that only a non-vanishing C8 is generated at some high scale, the mixing of the two operators from strong interactions implies C7,8 of comparable size at the charm scale. Thus if ACP
is dominated by NP contributions generated by Q8, it can be inferred that | Im[CNP7(mc)]| | Im[CNP8(mc)]| =
(0.20.8) 102.
2. The second important ingredient is the observation that in the Cabibbo-suppressed D V decays, where V is
a light vector meson with uu valence quarks (V = 0, ),
Q7 has a sizeable hadronic matrix element. More explicitly, the short-distance contribution induced by Q7, relative to the total (long-distance) amplitude, is substantially larger with respect to the corresponding relative weight of Q8 in D P +P decays. Estimating the SM
long-distance contributions from data, and evaluating the
d s
Eur. Phys. J. C (2013) 73:2373 Page 55 of 92
short-distance CP-violating contributions under the hypothesis that ACP is dominated by (dipole-type) NP,
leads to the following estimate for the maximal direct CP asymmetries in the D (, ) modes [485]:
[vextendsingle][vextendsingle]adir
CP
D (, ) [parenrightbig][vextendsingle][vextendsingle]max
= 0.04
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
Im[C7(mc)]
0.4 102
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
[bracketleftbigg] 105
B(D (, ) )
1/2
[lessorsimilar] 10 %. (112)
The case of the resonance, or better the K+K nal state with MKK close to the peak, is more involved since the matrix element of Q7 vanishes in the large mc limit for a pure ss state. However, a non-negligible CP asymmetry can be expected also in this case since:(1) the matrix element of Q7 is not expected to be identically zero because of sizeable O(QCD/mc) correc
tions; (2) nonresonant contributions due to (off-shell) and exchange can also contribute to the K+K nal state. Taking into account these effects, the following estimates for the maximal direct CP asymmetries are obtained [485]:
[vextendsingle][vextendsingle]adir
CP
D K+K [parenrightbig][vextendsingle][vextendsingle]max 2 %,
2mK < s < 1.05 GeV,
[vextendsingle][vextendsingle]adir
D K+K [parenrightbig][vextendsingle][vextendsingle]max 6 %,
1.05 GeV < s < 1.20 GeV.
(113)
In the rst bin, close to the peak, the leading contribution is due to the -exchange amplitude. The contribution due to the nonresonant amplitudes becomes more significant further from the peak, where the CP asymmetry can become larger.3. In order to establish the signicance of these results, two important issues have to be claried: (1) the size of the CP asymmetries within the SM, (2) the role of the strong phases.
As far as the SM contribution is concerned, it can rst be noticed that short-distance contributions generated by the operator Q7 are safely negligible. Using the result in Ref. [486], asymmetries are found to be below the 0.1 % level. The dominant SM contribution is expected from the leading non-leptonic four-quark operators, for which the general arguments discussed in Ref. [469] can be applied. The CP asymmetries can be decomposed as |aSMCP(f )| 2 Im(RSMf) 0.13 % Im(RSMf),
where |VcbVub/VcsVus| 0.0007 and RSMf is a ra
tio of suppressed over leading hadronic amplitudes, naturally expected to be smaller than one. This decomposition holds both for f = , KK and for f = V
channels. The SM model explanations of aCP require
RSM,KK 3. While this possibility cannot be excluded
from rst principles, a further enhancement of one order of magnitude in the D V mode is beyond any
reasonable explanation in QCD. As a result, an observation of |adirCP(D V )| [greaterorsimilar] 3 % would be a clear signal
of physics beyond the SM, and a clean indication of new CP-violating dynamics associated to dipole operators.
Having claried that large values of |adirCP(D V )|
would be a clear footprint of non-standard dipole operators, it can be asked if potential tight limits on |adirCP(D V )|
could exclude this non-standard framework. Unfortunately, uncertainty on the strong phases does not allow this conclusion to be drawn. Indeed the maximal values for the DCPV asymmetries presented above are obtained in the limit of maximal constructive interference of the various strong phases involved. In principle, this problem could be overcome via time-dependent studies of D(D) V de
cays or using photon polarisation, accessible via lepton pair conversion in D V ( + ); however, these types
of measurements are certainly more challenging from the experimental point of view.
4.4.5 Testing for CP-violating new physics in the I = 3/2 amplitudes
It is possible, at least in principle, to distinguish between NP and the SM as the origin of ACP. If ACP is due to
a chromomagnetic operator, i.e. due to I = 1/2 contribu
tions, one can measure CP violation in radiative D decays, as explained in the previous section. Examples of NP models that can be tested in this way are, e.g., avour-violating supersymmetric squark-gluino loops that mediate the c ug
transition [418, 472, 473]. On the other hand, if ACP is
due to I = 3/2 NP one can use isospin symmetry to write
sum rules for direct CP asymmetries in D decays [487]. If the sum rules are violated, then NP would be found. An example of a NP model that can be tested in this way is an addition of a single new scalar eld with nontrivial avour couplings [484].
The basic idea behind the I = 3/2 NP tests [487, 488]
is that in the SM the CP violation in SCS D decays arises from penguin amplitudes which are I = 1/2 transitions.
On the other hand, I = 3/2 amplitudes are CP-conserving
in the SM. Moreover, there are no I = 5/2 terms in the
SM short-distance effective Hamiltonian, and though such contributions can be generated by electromagnetic rescattering (as has been discussed in the context of B de
cays [489, 490]) they would also be CP conserving. Observing any CP violation effects in I = 3/2 amplitudes would
therefore be a clear signal of NP.
In the derivation of the sum rules it is important to pay attention to the potentially important effects of isospin breaking. Isospin symmetry is broken at O(102), which is also
CP
Page 56 of 92 Eur. Phys. J. C (2013) 73:2373
the size of the interesting CP asymmetries. There are two qualitatively different sources of isospin breaking: due to electromagnetic interactions, u and d quark masses, which are all CP-conserving effects, and due to electroweak penguin operators that are a CP-violating source of isospin breaking. The CP-conserving isospin breaking is easy to cancel in the sum rules. As long as the CP-conserving amplitudes completely cancel in the sum rules, which is the case in Ref. [487], the isospin breaking will only enter suppressed by the small CP violation amplitude and is therefore negligible. The electroweak penguin operators, on the other hand, are suppressed by /S O(102) compared to the
leading CP-violating but isospin conserving penguin contractions of the Q1,2 operators, and can thus also be safely neglected.
Among the SCS decays, the D , D , D
, D KK, and D+s K modes carry enough in
formation to construct tests of I = 3/2 NP. The sum rules
for D decays have the nice feature that the charged
decay D+ +0 is purely I = 3/2. In the SM there
fore
adirCP[parenleftbig]D+ +0[parenrightbig] = 0. (114)
If this CP asymmetry is measured to be nonzero, it would be a clear signal of I = 3/2 NP. However, if it is found
experimentally to be very small, it is still possible that this is only because the strong phase between the SM and NP amplitudes is accidentally small.
This possibility can be checked with more data if time-dependent D(t) + and D(t) 00 measure
ments become available,67 or if there is additional information on relative phases from a charm factory running on the (3770). The strategy amounts to measuring the weak phase of the I = 3/2 amplitude A3 via generalised trian
gle constructions that also take isospin breaking into account [487]. If
1 2A
+ + A
B decays), the search for I = 3/2 NP could be eas
ier experimentally in D decays since there are more
charged tracks in the nal state. The most promising observable where polarisation measurement is not needed is
ACP(D+ +0), which if found nonzero (after the cor
rection for the effect of nite decay widths) would signal I = 3/2 NP.
Another experimentally favourable probe is the isospin analysis of the D0 +0 Dalitz plot in terms of D
decays [493]. There are two combinations of measured amplitudes that are proportional to I = 3/2 amplitudes
A+0 + A
0+ = 32A3, A+ + 2A
00 + A+ = 6A3.
(116)
A measurement of the second sum can be obtained from the D0 +0 Dalitz plot. If the related CP asymmetry
|A+ + 2A00 + A+ |2
|A+ + 2A
00 + A+ |2
= 36[parenleftbig]|A3|2 |A3|2[parenrightbig], (117) is found to be nonzero, this would mean that the I = 3/2
NP contribution is nonzero. If it is found to vanish, however, it could be due to the strong phase difference being vanishingly small.
A denitive answer can be provided by another test that is directly sensitive to the weak phase of A3. This test is possible if the time-dependent D(t) +0 Dalitz plot
is measured. In this case the relative phases between the D0 and D0 amplitudes can be obtained (al
ternatively one could use time integrated entangled decays of (3770) at the charm factory). The presence of a weak phase in A3 can then be determined from the following sum-rule
(A+ + A+ + 2A
00 )
00
1 2A+
A
00
(A + A+ + 2A
00 )
= 3(A3 A3) (115)
is found to be nonzero, this would mean there is CP-violating NP in the I = 3/2 amplitude.
The above results apply also to D decays, but
for each polarisation amplitude separately. The corrections due to nite width can be controlled experimentally in the same way as in B decays [492]. As long as
the polarisations of the resonances are measured (or if the longitudinal decay modes dominate, as is the case in
67Time-dependent D(t) 00 measurements could in principle be
feasible using photon conversions [491].
= 6(A3 A3). (118)
A non-vanishing result for Eq. (118) would provide a denitive proof for I = 3/2 NP. A similar sum rule for the
CP asymmetries rather than the amplitudes was given in Eq. (117). In that case the time-integrated Dalitz plot sufces to determine the sum rule inputs.
The sum rules involving D K()K() decays are
somewhat more complex because there are at least three particles in the nal state. Nevertheless, it is possible to construct purely I = 3/2 matrix elements from appropriate
sums of decay amplitudes, and these can in principle be determined from amplitude analyses of the multibody nal states. It is also possible to search for CP violation in
Eur. Phys. J. C (2013) 73:2373 Page 57 of 92
I = 3/2 amplitudes using D+s K decays. The sum 2A[parenleftbig]D+s 0K+[parenrightbig] + A[parenleftbig]D+s +K0[parenrightbig] = 3A3, (119)
is I = 3/2 and can be measured from the common Dalitz
plot for D+s K0S+0 decay. Direct CP violation in this
sum, i.e.,
[vextendsingle][vextendsingle]
2A[parenleftbig]D+s 0K+[parenrightbig] + A[parenleftbig]D+s +K0[parenrightbig][vextendsingle][vextendsingle]2
[vextendsingle][vextendsingle]
2A[parenleftbig]Ds 0K[parenrightbig] + A[parenleftbig]Ds K0[parenrightbig][vextendsingle][vextendsingle]2
= 0, (120) would necessarily be due to I = 3/2 NP contributions.
Additional information on the absolute value of |A(D+s
+K0)| can be obtained from the D+s +K+ three-
body decay. Analogous tests using D+s K decays also
exist.
4.5 Potential for lattice computations of direct CP violation and mixing in the D0D0 system
In searches for NP using charmed mesons, it is obviously crucial to determine accurately the size of SM contributions. In the next few paragraphs the prospects for such a determination in the future using the methods of lattice QCD are discussed.
Lattice QCD provides a rst-principles method for determining the strong-interaction contributions to weak decay and mixing processes. It has developed into a precision tool, allowing determinations of the light hadron spectrum, decay constants, and matrix elements such as BK and BB with percent-level accuracy. For reviews and collections of recent results, see Refs. [109, 494]. The results provide conrmation that QCD indeed describes the strong interactions in the non-perturbative regime, as well as providing predictions that play an important role in searching for new physics by looking for inconsistencies in unitarity triangle analyses.
Results with high precision are, however, only available for processes involving single hadrons and a single insertion of a weak operator. For the D0 system, the high-precision quantities are thus the matrix elements describing the short-distance parts of D0D0 mixing and the matrix elements of four-fermion operators arising after integrating out NP. The methodology for such calculations is in place (and has been applied successfully to the K and B meson systems), and results are expected to be forthcoming in the next one to two years.
More challenging, and of course more interesting, are calculations of the decay amplitudes to and KK. For kaon physics, this is the present frontier of lattice calculations. One must deal with two technical challenges: (i) the fact that one necessarily works in nite volume so the states are not asymptotic two-particle states and (ii) the need to
calculate Wick contractions (such as the penguin-type contractions) which involve gluonic intermediate states in some channels. The former challenge has been solved in principle by the work of Lscher [495, 496] and Lellouch and Lscher [497] for the K case, while advances in lat
tice algorithms and computational power have allowed the numerical aspects of both challenges to be overcome. There are now well controlled results for the K ()I=2 am
plitude [498] and preliminary results for the K ()I=0
amplitude [499]. It is likely that results to 10 % accuracy
for all amplitudes will be available in a few years. Note that, once a lattice calculation is feasible, it will be of roughly equal difculty to obtain results for the CP-conserving and CP-violating parts.
To extend these results to the charm case, one must face a further challenge. This is that, even when one has xed the strong-interaction quantum numbers of a nal state, say to I = S = 0, the strong interactions necessarily bring in mul
tiple nal states when E = mD. For example, and KK
states mix with , 4, 6, etc. The nite-volume states that are used by lattice QCD are inevitably mixtures of all these possibilities, and one must learn how, in principle and in practise, to disentangle these states so as to obtain the desired matrix element. Recently, in Ref. [500], a rst step towards developing a complete method has been taken, in which the problem has been solved in principle for any number of two-particle channels, assuming that the scattering is dominantly S-wave. This is encouraging, and it may be that this method will allow semi-quantitative results for the amplitudes of interest to be obtained. Turning this method into practise is expected to take three to ve years due to a number of numerical challenges (in particular the need to calculate several energy levels with good accuracy). It is also expected to be possible to generalise the methodology to include four particle states; several groups are actively working on the theoretical issues. It is unclear at this stage, however, what time scale one should assign to this endeavour.
Finally, the possibility of calculating long-distance contributions to D0D0 mixing using lattice methods should be considered. Here the challenge is that there are two insertions of the weak Hamiltonian, with many allowed states propagating between them. Some progress has been made recently on the corresponding problem for kaons [501, 502] but the D0 system is much more challenging. The main problem is that, as for the decay amplitudes, there are many strong-interaction channels with E < mD. Further theoretical work is needed to develop a practical method.
4.6 Interplay of ACP with non-avour observables4.6.1 Direct CP violation in charm and hadronic electric dipole moments
Models in which the primary source of avour violation is linked to the breaking of chiral symmetry (leftright avour
Page 58 of 92 Eur. Phys. J. C (2013) 73:2373
mixing) are natural candidates to explain direct CP violation in SCS D meson decays, via enhanced C = 1 chromo-
magnetic operators. Interestingly, the chromomagnetic operator generates contributions to D0D0 mixing and / that are always suppressed by at least the square of the charm
Yukawa couplings, thus naturally explaining why they have remained undetected.
On the other hand, the dominant constraints are posed by the neutron and nuclear EDMs, which are expected to be close to their experimental bounds. This result is fairly robust because the Feynman diagram contributing to quark EDMs has essentially the same structure as that contributing to the chromomagnetic operator.
In the following the connection between adirCP and hadronic EDMs in concrete NP scenarios is discussed, following the analyses of Refs. [472, 473].
Supersymmetry The leading SUSY contribution to adirCP stems from loops involving up-squarks and gluinos and off-diagonal terms in the squark squared-mass matrix in the leftright up sector, the so-called (u12)LR mass-insertion. As can be seen from Eqs. (108)(109) and taking into account the large uncertainties involved in the evaluation of the matrix element, it can be concluded that a supersymmetric theory with left-right up-squark mixing can potentially explain the LHCb result.
Among the hadronic EDMs, the best constraints come from mercury and neutron EDMs. Their current experimental bounds are |dn| < 2.9 1026 e cm (90 % C.L.) and |dHg| < 3.1 1029 e cm (95 % C.L.). In the mass-insertion
approximation one can nd
|dn| 3 1026
[parenleftbigg]| Im(u11)LR|106
of the down-type quark masses entering (dij )LR. The only experimental bounds in tension with this scenario are those on |u,d11| coming from the neutron EDM.
Split families The severe suppression of (u21)effRL stemming from the charm mass can be partially avoided in a framework with split families, where the rst two generations of squarks are substantially heavier than t1,2 and bL, the only
squarks required to be close to the electroweak scale by naturalness arguments. In this case the effective couplings relevant to aSUSYCP can be decomposed as follows
u12[parenrightbig]effRL = [parenleftbig]u13[parenrightbig]RR[parenleftbig]u33[parenrightbig]RL[parenleftbig]u32[parenrightbig]LL,
u12[parenrightbig]effLR = [parenleftbig]u13[parenrightbig]LL[parenleftbig]u33[parenrightbig]RL[parenleftbig]u32[parenrightbig]RR.
(123)
Notice that this scenario takes advantage of the large (u33)LR Amt/ m which is assumed to be of order one.
The following two options can be considered to explain the LHCb results:
u32[parenrightbig]LL = O[parenleftbig]2[parenrightbig], [parenleftbig]u13[parenrightbig]RR = O[parenleftbig]2[parenrightbig]
[parenleftbig]u12[parenrightbig]effRL = O[parenleftbig]4[parenrightbig] = O[parenleftbig]103[parenrightbig],
u13[parenrightbig]LL = O[parenleftbig]3[parenrightbig], [parenleftbig]u32[parenrightbig]RR = O()
[parenleftbig]u12[parenrightbig]effLR = O[parenleftbig]4[parenrightbig] = O[parenleftbig]103[parenrightbig].
(124)
Gluinosquark loops yield an EDM (du) and a chromo-EDM (dcu) for the up quark proportional to d(c)u
Im[(u13)LL(u31)RR] and it turns out that
[vextendsingle][vextendsingle] aSUSY
CP
[vextendsingle][vextendsingle][vextendsingle][vextendsingle].
(125)
In conclusion, the EDM bounds require a strong hierarchical structure in the off-diagonal terms of the RR up-squark mass matrix, as happens in models predicting (uij )RR
(mui /muj )/|Vij |.
Supersymmetric avour models In models where the avour structure of the soft breaking terms is dictated by an approximate avour symmetry, (uLR)12 is generically avour-suppressed by (mc|Vus|/ m), which is of order a few times
104. There is however additional dependence on the ratio between avour-diagonal parameters, A/ m, and on un
known coefcients of order one, that can provide enhancement by a small factor. In most such models, the selection rules that set the avour structure of the soft breaking terms relate (uLR)12 to (dLR)12 and to (u,dLR)11, which are bounded from above by, respectively, / and EDM constraints. Since both / and EDMs suffer from hadronic uncertainties, small enhancements due to the avour-diagonal
[parenrightbigg][parenleftbigg]TeV
m
[vextendsingle][vextendsingle]
103
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
dn3 1026
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
Im(u32)RR 0.2
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
[parenrightbigg] e cm (121)
and therefore it has to be seen whether a concrete SUSY scenario can naturally account for the required level of suppression | Im(u11)LR| [lessorsimilar] 106.
Generalised trilinear terms While scenarios in which avour violation is restricted to the trilinear terms can be envisaged, it is natural to generalise the structure of Eq. (109) to all squarks and take
qij[parenrightbig]LR
103
Im(u31)RR
Aqijmqj
m , q = u, d, (122)
where qij are generic mixing angles. This pattern can be obtained when the matrices of the up and down trilinear coupling constants follow the same hierarchical pattern as the corresponding Yukawa matrices but they do not respect exact proportionality.
It is found that qij can all be of order unity not only in the up, but also in the down sector, thanks to the smallness
Eur. Phys. J. C (2013) 73:2373 Page 59 of 92
supersymmetric parameters cannot be ruled out. It is thus possible to accommodate ACP 0.006 in supersymmet
ric models that are non-minimally avour violating, but barring hadronic enhancements in charm decaysit takes a fortuitous accident to lift the supersymmetric contribution above the permille level [473].
New-physics scenarios with Z-mediated FCNC Effective FCNC couplings of the Z boson to SM quarks can appear in the SM with non-sequential generations of quarks, models with an extra U(1) symmetry or models with extra vector-like doublets and singlets. The effective FCNC Lagrangian can be written as
LZ-FCNCeff =
As in all the other frameworks, the most severe constraints are posed by the hadronic EDMs
|dn| 3 1026
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
Im[(ghL)ut(ghR)tu]
2 107
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
e cm. (132)
With scalar-mediated FCNCs, the potentially most interesting signals are the rare top decays t ch or t uh, if
kinematically allowed. In particular,
B(t qh) 0.4 102
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
(ghR)tq 101
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
2 , (133)
which could be within the reach of the LHC.
4.6.2 Interplay of collider physics and a new physics origin for ACP
The rst evidence for direct CP violation in SCS D decays may have interesting implications for NP searches around the TeV scale at the LHC. The NP contribution to adirCP can be fully parametrised by a complete set of C = 1 effective
operators at the charm scale. As shown by the authors of Ref. [469] only a few of these operators can accommodate the LHCb result without conicting with present bounds from D0D0 mixing and / . In particular four-fermion operators of the form Oq = (R cR)( qRqR) with q = u, d, s
are promising since they do not lead to avour violation in the down-type quark sector. The corresponding Wilson coefcients are dened as 1/2q. Assuming the SM expectation for adirCP is largely subdominant, the LHCb measurement suggests a scale of q 15 TeV [469].
There is an immediate interplay between charm decay and avour (and CP) conserving observables at much higher energies provided Oq arises from a heavy NP state ex
changed in the s-channel. Under this mild assumption Oq
factorises as the product of two quark currents and the same NP induces D0D0 mixing and quark compositeness through the (RcR)2 and ( qRqR)2 operators, respec
tively. Denoting their respective Wilson coefcients by c
and qq , the relation q = [radicalbig]cqq is predicted. The D0
D0 mixing bound on NP implies c [greaterorsimilar] 1200 TeV [441].
Combining this stringent C = 2 bound with the C = 1
scale suggested by adirCP thus generically requires qq [lessorsimilar]
200 GeV, which is a rather low compositeness scale for the light quark avours.
Quark compositeness can be probed at the LHC through dijet searches. Actually for the up or the down quark the low scale suggested by adirCP is already excluded by the Tevatron [503, 504]. On the other hand dijet searches are less sensitive to contact interactions involving only the strange quark since the latter, being a sea quark, has a suppressed parton distribution function in the proton. The authors of Ref. [505] showed that a rst estimation at the partonic level
g2 cos W qi
[bracketleftbig][parenleftbig]gZL[parenrightbig]ij PL + [parenleftbig]gZR[parenrightbig]ij PR[bracketrightbig]qj Z + h.c. (126)
The chromomagnetic operator is generated at the one-loop level, with leading contribution from Z-top exchange diagrams leading to
[vextendsingle][vextendsingle] aZ
-FCNC CP
[vextendsingle][vextendsingle]
0.6 %[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
Im[(gZL)ut(gZR)ct]
2 104
[vextendsingle][vextendsingle][vextendsingle][vextendsingle].
(127)
The presence of new CP-violating phases in the couplings (gZL,R)ij are also expected to generate hadronic EDMs. In particular, one can nd
|dn| 3 1026
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
Im[(gZL)ut(gZR)ut]
2 107
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
e cm, (128)
and therefore AZ-FCNCCP = O(102) only, provided
Im(gZR)ut/ Im(gZR)ct [lessorsimilar] 103.
In NP scenarios with Z-mediated FCNCs, the most interesting FCNC processes in the top sector are t cZ and
t uZ, which arise at the tree level. In particular,
B(t cZ) 0.7 102
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
(gZR)tc 101
[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
2 , (129)
which is within the reach of the LHC for the values of (gZR)tc relevant to AZ-FCNCCP.
New-physics scenarios with scalar-mediated FCNC Finally, it is instructive to analyse a new-physics framework with effective FCNC couplings to SM quarks of a scalar particle h. The effective Lagrangian reads
Lh-FCNCeff = qi[bracketleftbig][parenleftbig]ghL[parenrightbig]ij PL + [parenleftbig]ghR[parenrightbig]ij PR[bracketrightbig]qj h + h.c. (130) Also in this case the chromomagnetic operator is generated at the one-loop level, with a leading contribution from h-top exchange diagrams. This leads to
[vextendsingle][vextendsingle] aFCNC
CP
[vextendsingle][vextendsingle]
0.6 %[vextendsingle][vextendsingle][vextendsingle][vextendsingle]
Im[(ghL)ut(ghR)tc]
2 104
[vextendsingle][vextendsingle][vextendsingle][vextendsingle].
(131)
Page 60 of 92 Eur. Phys. J. C (2013) 73:2373
of the extra dijet production from a (sRsR)2 operator with
a scale of ss 200 GeV is marginally consistent, given the O(1) uncertainty of the problem, with the bounds from the ATLAS and CMS experiments [506, 507].
One concludes that an Os operator induced by a s-
channel exchanged NP can accommodate the adirCP measurement without conicting with C = 2, / and dijet
searches. Furthermore such a NP scenario makes several generic predictions both for charm and high-pT physics:(1) most of the CP asymmetry is predicted to be in the K+K channel, (2) CP violation in D0D0 mixing should be observed in the near future, and (3) an excess of dijets at the LHC is expected at a level which should be visible in the 2012 data.
4.7 Future potential of LHCb measurements
4.7.1 Requirements on experimental precision
The ultimate goal of mixing and CP violation measurements in the charm sector is to reach the precision of the SM predictions (or better). In some cases this requires measurements in several decay modes in order to distinguish enhanced contributions of higher order SM diagrams from effects caused by new particles.
Indirect CP violation is constrained by the observable A (see Eq. (82)). The CP-violating parameters in this observable are multiplied by the mixing parameters xD and yD, respectively. Hence, the relative precision on the CP-violating parameters is limited by the relative precision of the mixing parameters. Therefore, aiming at a relative precision below 10 % and taking into account the current mixing parameter world averages, the target precision would be 2 3 104. Indirect CP violation is expected in the SM at the
order of 104, and therefore the direct CP violation parameter contributing to A has to be measured to a precision of 103 in order to distinguish the two types of CP violation in
A .
Direct CP violation is not expected to be as large as the current world average of ACP in most other decay modes.
However, a few large CP violation signatures are expected in various models, as discussed in the previous sections.Estimations based on avour-SU(3) and U-spin symmetry lead to expectations of adirCP(D+ K+K0) [greaterorsimilar] 0.1 % and
adirCP(D0 K0SK0S) 0.6 %. Considerations assuming uni
versality of F = 1 transitions lead to a limit of adirCP(D
e+e) [lessorsimilar] 2 %. Enhanced electromagnetic dipole operators can lead to adirCP(D V ) of a few %, equivalent to the in
uence of chromomagnetic dipole operators on ACP. Ad
ditional information can be obtained from time-dependent studies of D V decays or from angular analyses of
D V l+l decays.
Analyses of I = 3/2 transitions involve asymmetry
measurements of several related decay modes. Examples are
the decays D , D , D , D KK, and
D+s K. The number of nal state particles in these de
cays varies from two to six (counting the pions from K0S decays) and many of these modes contain neutral pions in their nal state. The precision for modes involving neutral pions or photons will be limited by the ability of the calorimeter to identify these particles in the dense hadronic environment. An upgraded calorimeter with smaller Molire radius would greatly extend the physics reach in this area.68
In general, a precision of 5 104 or better for asymme
try differences as well as individual asymmetries is needed for measurements of other SCS charm decays. While measurements of time-integrated raw asymmetries at this level should be well within reach, the challenge lies in the control of production and detection asymmetries in order to extract the physics asymmetries of individual decay modes. This can be achieved by assuming that there is no signicant CP violation in CF decay modes.
4.7.2 Prospects of future LHCb measurements
Numbers of events in various channels are projected directly from the numbers reconstructed in the 2011 data set, in most cases. This involves assumptions that the prompt charm cross-section will increase by a factor of 1.8 when doubling the centre-of-mass energy from s = 7 TeV to
s = 14 TeV, that the integrated luminosity will increase
from 1 fb1 to 50 fb1, and that the trigger efciency for charm will increase by a factor of 2 as the current hardware trigger requirement is effectively removed (or substantially relaxed). Additionally, a factor of 3.5 times greater efciency in channels with K0S + daughters is pre
dicted based on progress made in the trigger software between 2011 and 2012. This primarily results from reconstructing candidates which decay downstream of the vertex detector. The results of this exercise are summarised in Table 10 for D0 decays and in Table 11 for D+ and D+s decays.
Estimating the physics reach with the projected data sets requires a number of assumptions. The statistical precision generally improves as 1/N. Estimating the systematic error, and therefore ultimate physics reach, is more of an art. It is often the case that data can be used to control systematic uncertainties at the level of the statistical error, but the extent to which this will be possible cannot be reliably predicted. In some cases controlling systematic uncertainties will require sacricing some of the statistics to work with cleaner signals or with signals which populate only parts of the detector where the performance is very well understood. Estimates of sensitivity to CP violation in mixing generally depend on the values of the mixing parametersthe larger the number of
68Such an upgrade to the calorimeter system is not in the baseline plan for the LHCb upgrade [25, 26].
Eur. Phys. J. C (2013) 73:2373 Page 61 of 92
Table 10 Numbers of D0 and D+ D0+ signal events observed
in the 2011 data in a variety of channels and those projected for 50 fb1. These channels can be used for mixing studies, for indirect
CP violation studies, and for direct CP violation studies. As discussed in the text, the numbers of events in any one channel can vary from one analysis to another, depending on the level of cleanliness required.Hence, all numbers should be understood to have an inherent variation of a factor of 2. To control systematic uncertainties with the very high level of precision that will be required by the upgrade, it may be necessary to sacrice some of the statistics
Mode 2011 yield (103 events)
50 fb1 yield (106 events)
Untagged D0 K+ 230 000 40 000
D+ D0+; D0 K+ 40 000 7 000 D+ D0+; D0 K+ 130 20
D0 KK+ 25 000 4 600 D0 + 6 500 1 200
D+ D0+; D0 KK+ 4 300 775 D+ D0+; D0 + 1 100 200
D+ D0+; D0 K0S+ 300 180 D+ D0+; D0 K0SKK+ 45 30
D+ D0+; D0 K++ 7 800 1 400 D+ D0+; D0 KK++ 120 20
D+ D0+; D0 ++ 470 85 D+ D0+; D0 K+X 4 000
D+ D0+; D0 K+X 0.1
mixed events, the larger the effective statistics contributing to the corresponding CP violation measurement.
The estimated statistical precisions for parameters of mixing and CP violation in the D0 system are presented in Table 12. The precision for measuring (x 2D, y D) using the time-dependence of the wrong-sign (WS) to right-sign (RS) K rate comes from extrapolating the BaBar [409] and Belle [508] sensitivities.69 The precision for measuring rM using the ratio of WS to RS K events assumes the central value to be 2.5 105. The S/B ratio is assumed to be 30
times better than reported by BaBar [509] for their similar Ke analysis. Background can be reduced by a factor of 10 using LHCbs excellent vertex resolution to remove candidates with decay time less than twice the D0 lifetimea requirement which only modestly reduces the WS signal as its decay time distribution has the form dN/dt t2e t. In
addition, the excellent vertex resolution and the decay time requirement allow the neutrino momentum, and hence the D+ D0 mass difference to be measured with better res
olution than was possible in the e+e experiments. BaBar demonstrated that using a doubly-tagged sample of semilep-tonic decay candidates provides the same mixing sensitivity
69The LHCb measurements of charm mixing parameters from wrong-sign K decays [411] are consistent with the estimated sensitivities.
Table 11 Numbers of D+ and D+s signal events observed in the 2011 data in a variety of channels and those projected for 50 fb1. These channels can be used for direct CP violation studies. As discussed in the text, the numbers of events in any one channel can vary from one analysis to another, depending on the level of cleanliness required. To control systematic uncertainties with the very high level of precision that will be required by the upgrade, it may be necessary to sacrice some of the statistics
Mode 2011 yield
(103 events)
50 fb1 yield (106 events)
D+ K++ 60 000 11 000 D+ K++ 200 40
D+ KK++ 6 500 1 200 D+ + 2 800 500
D+ ++ 3 200 575 D+ K0S+ 1 500 1 000
D+ K0SK+ 525 330 D+ KK+K+ 60 10
D+s KK++ 8 900 1 600 D+s +, ( KK+) 5 350 1 000
D+s ++ 2 000 360 D+s K++
D+s K++ 555 100 D+s KK+K+ 50 10
D+s K0SK+ 410 260 D+s K0S+ 33 20
as the more traditional singly-tagged sample [510]. By combining singly- and doubly-tagged samples, it should be possible to effectively double the statistics.
The projected sensitivities for the two-body direct CP violation measurements are relatively solid: the 2011 ACP
measurements provide benchmark samples with full analysis cuts including ducial cuts necessary to control systematic uncertainties for measuring ACP. The systematic er
rors for the separate ACP(KK+) and ACP(+) mea
surements will be more challenging and may require sacricing statistical precision. The projections for measuring yCP and A using KK+ and + should also be robust as the same samples will be used for these analyses as for the ACP measurements.
The projected precision for measuring (xD, yD) from D0 K0S+ comes from scaling the Belle [416] and
BaBar [511] sensitivities. The statistical precisions could be even better as LHCbs prompt sample will be enhanced at higher decay times where the mixing effects are larger. By contrast, D0 mesons from semileptonic B decays should be unbiased in this variable, providing a useful sample at lower decay times.
The estimated statistical precisions for DCPV in D+ measurements are presented in Table 13. The estimates for the phase-space integrated CP violation rates are scaled by
Page 62 of 92 Eur. Phys. J. C (2013) 73:2373
Table 12 Estimated statistical uncertainties for mixing and CP violation measurements which can be made with the projected samples for 50 fb1 described in Table 10
Sample Parameter(s) Precision
WS/RS K (x 2D, y D) O[(105, 104)]
WS/RS K rM O(5 107) WS/RS K |p/q|D O(1 %)
D+ D0+; D0 KK+, + ACP 0.015 % D+ D0+; D0 KK+ ACP 0.010 %
D+ D0+; D0 + ACP 0.015 %
D+ D0+; D0 K0S+ (xD, yD) (0.015 %, 0.010 %)
D+ D0+; D0 KK+, (+) yCP 0.004 % (0.008 %) D+ D0+; D0 KK+, (+) A 0.004 % (0.008 %)
D+ D0+; D0 KK++ AT 2.5 104
Table 13 Estimated statistical uncertainties for CP violation measurements which can be made with the projected D+ samples for 50 fb1 described in Table 11
Sample Parameter(s) Precision
D+ K0SK+ Phase-space integrated CP violation 104
D+ KK++ Phase-space integrated CP violation 5 105
D+ ++ Phase-space integrated CP violation 8 105
D+ KK++ CP violation in phases, amplitude model (0.010.10)
D+ KK++ CP violation in fraction differences, amplitude model (0.010.10) %
D+ ++ CP violation in phases, amplitude model (0.010.10)
D+ ++ CP violation in fraction differences, amplitude model (0.010.10) %
D+ KK++ CP violation in phases, model-independent (0.010.10)
D+ KK++ CP violation in fraction differences, model-independent (0.010.10) %
D+ ++ CP violation in phases, model-independent (0.010.10)
D+ ++ CP violation in fraction differences, model-independent (0.010.10) %
1/N and are then increased by a factor of two to allow for using tighter cuts to control systematic uncertainties. The estimates for measuring CP violation in the magnitudes and phases of quasi-two-body amplitudes contributing to three-body nal states come from scaling the BaBar sensitivities for time-integrated CP violation in D0 +0 and
D0 KK+0 by 1/N. The angular moments of the
cosine of the helicity angle of the D decay products reect the spin and mass structure of the intermediate resonant and nonresonant amplitudes with no explicit model dependence. The difference between the angular moment distributions observed in D0 and D0 decays provides sensitivity to CP violation in the magnitudes (or fractions) and phases of amplitudes about equal to that of model-dependent ts.The angular moment differences are robust, in the sense that they are model-independent, but they are less specic compared to the results from model-dependent analyses: they indicate only the spins and mass ranges where particle and antiparticle amplitudes differ, but do not identify a specic CP-violating intermediate state or how much it varies. The sensitivity to CP violation in any contributing amplitude depends on how much it contributes to the three-body decay, and also on the other amplitudes with which it interferes.
For this reason, ranges of sensitivity are indicated rather than single values. No sensitivities for CP violation measurements in three-body D+s decay channels are estimated explicitly. They can be estimated roughly by extrapolating from the numbers for D+ decays by scaling by 1/N.
These estimates should be degraded slightly as the lifetime of the D+ is about twice that of the D+s meson, making it easier to select clean D+ samples.
4.8 Conclusion
LHCb has proven its capability of performing high-precision charm physics measurements. The experiment is ideally suited for CP violation searches and for measurements of decay-time-dependent processes such as mixing.
Finding evidence for a non-zero value of ACP has
raised the question of whether or not this may be interpreted as the rst hint of physics beyond the SM at the LHC. Within the SM the central value can only be explained by significantly enhanced penguin amplitudes. This enhancement is conceivable when estimating avour SU(3) or U-spin breaking effects from ts to D P P data. However, attempts at
estimating the long distance penguin contractions directly
Eur. Phys. J. C (2013) 73:2373 Page 63 of 92
have not yielded conclusive results to explain the enhancement.
Lattice QCD has the potential of assessing the penguin enhancement directly. However, several challenges arise which make these calculations impossible at the moment.Following promising results on K decays, additional
challenges arise in the charm sector as and KK states mix with , 4, 6 and other states. Possible methods have been proposed and results may be expected in three to ve years time.
General considerations on the possibility of interpreting ACP in models beyond the SM have led to the conclu
sion that an enhanced chromomagnetic dipole operator is required. These operators can be accommodated in minimal supersymmetric models with non-zero left-right up-type squark mixing contributions or, similarly, in warped extra dimensional models. Tests of these interpretations beyond the SM are needed. One promising group of channels are radiative charm decays where the link between the chromo-magnetic and the electromagnetic dipole operator leads to predictions of enhanced CP asymmetries of several percent.These can be measured to sufcient precision at the LHCb upgrade.
Another complementary test is to search for contributions beyond the SM in I = 3/2 amplitudes. This class
of amplitudes leads to several isospin relations which can be tested in a range of decay modes, e.g. D , D ,
D KK, etc. Several of these measurements, such as the
Dalitz plot analysis of the decay D0 +0, can be
performed at LHCb.
Beyond charm physics, the chromomagnetic dipole operators would affect the neutron and nuclear EDMs, which are expected to be close to the current experimental bound. Similarly, rare FCNC top decays are expected to be enhanced, if kinematically allowed. Furthermore, quark compositeness can be related to the ACP measurement and tested in di
jet searches. Current results favour the NP contribution to be located in the D0 KK+ decay as the strange quark
compositeness scale is less well constrained. Measurements of the individual asymmetries of sufcient precision will be possible at the LHCb upgrade.
The charm mixing parameters have not yet been precisely calculated in the SM. An inclusive approach based on an operator product expansion relies on the expansion scale being small enough to allow convergence and furthermore involves the calculation of a large number of unknown matrix elements. An exclusive approach sums over intermediate hadronic states and requires very precise branching ratio determinations of these nal states which are currently not available. Contrary to the SM, contributions beyond the SM can be calculated reliably. With the SM contribution to indirect CP violation being <104, the LHCb upgrade is ideally suited to cover the parameter space available for enhanced
asymmetries beyond the SM. Measurements in several complementary modes will permit the extraction of the underlying theory parameters with high precision.
The LHCb upgrade will allow to constrain CP asymme-tries and mixing observables to a level of precision which, in most of the key modes, cannot be matched by any other experiment foreseen on a similar timescale. This level of precision should permit us not only to discover CP violation in charm decays but also to unambiguously understand its origin.
5 The LHCb upgrade as a general purpose detector in the forward region
The previous sections have focussed on avour physics observables that are sensitive to physics beyond the SM. However, LHCb has excellent potential in a range of other important topics. As discussed in this section, the detector upgrade will further enhance the capability of LHCb in these areas, so that it can be considered as a general purpose detector in the forward region. LHCb may also be able to make a unique contribution to the eld of heavy ion physics, by studying soft QCD and heavy avour production in pA collisions. The rst pA run of the LHC will clarify soon the potential of LHCb in this eld.
5.1 Quarkonia and multi-parton scattering
The mechanism of heavy quarkonium production is a longstanding problem in QCD. An effective eld theory, non-relativistic QCD (NRQCD), provides the foundation for much of the current theoretical work. According to NRQCD, the production of heavy quarkonium factorizes into two steps: a heavy quarkantiquark pair is rst created perturbatively at short distances and subsequently evolves non-perturbatively into quarkonium at long distances. The NRQCD calculations depend on the colour-singlet (CS) and colour-octet (CO) matrix elements, which account for the probability of a heavy quarkantiquark pair in a particular colour state to evolve into heavy quarkonium. The CS model [512, 513], which provides a leading-order (LO) description of quarkonia production, was rst used to describe experimental data. However, it underestimates the observed cross-section for single J/ production at high pT at the Tevatron [514]. To resolve this discrepancy the CO mechanism was introduced [515]. The corresponding matrix elements were determined from the large-pT data as the CO cross-section falls more slowly than that for CS. More recent higher-order calculations [516519] close the gap between the CS predictions and the experimental data [520] reducing the need for large CO contributions.
Traditionally, quarkonia production studies at hadron colliders have focussed on the study of J/, (2S) and (nS)
Page 64 of 92 Eur. Phys. J. C (2013) 73:2373
Fig. 25 Invariant mass distribution of selected candidates from 25 pb1 of data collected in 2010 [524]. The (1S), (2S) and (3S)
states are clearly resolved. The results of a maximum likelihood t are superimposed
decays to dimuon or dielectron pairs [520]. The LHCb programme so far has followed this pattern with measurements of many cross-sections already published [521525]. As an example of the quality of the data, Fig. 25 shows the mass distribution. By the time of the upgrade in 2018, data samples corresponding to several fb1 will have been collected at s = 7, 8 and 14 TeV and the results will be domi
nated by systematic uncertainties. Therefore, new probes of quarkonia production will be pursued. Two possibilities are detailed here: multiple quarkonia production and quarkonia production via hadronic decay modes. These studies will prot from the higher integrated luminosity and improved trigger. These modes provide clear signals in the detector and will be relatively uneffected by the increased pile-up.
As the cross-sections for charmonium production at the LHC are large [521523, 525], the question of multiple production of these states in a single protonproton collision naturally arises. Studies of double hidden charm and hidden and associated open charm production have been proposed as probes of the quarkonium production mechanism [526]. In protonproton collisions contributions from other mechanisms, such as double parton scattering (DPS) [527529] or the intrinsic charm content of the proton [530], are possible. First studies of both processes have been carried out with the current LHCb data; more details can be found in Refs. [304, 531].
LO colour singlet calculations for the gg J/J/
process in perturbative QCD exist and give results consistent with the data [532534]. In the LHCb ducial region (2 < yJ/ < 4.5, pTJ/ < 10 GeV/c, where yJ/ and pTJ/
represent the rapidity and transverse momentum of the J/, respectively) these calculations predict the J/J/ production cross-section to be 4.1 1.2 nb [534] in agree
ment with the measured value of 5.1 1.0 nb [531]. Simi-
Table 14 Expected cross-sections in the LHCb acceptance and yields for double quarkonia production with 50 fb1 at s = 14 TeV
Mode gg [nb] Yield [SPS] DPS [nb] Yield [DPS]
J/ J/ 7.2 270 000 11 430 000
J/ (2S) 3.2 14 000 4.0 19 000
(2S) (2S) 0.4 180 0.6 300
J/ c0 4.3 200
J/ c1 6.6 14 000
J/ c2 8.6 11 000
J/ (1S) 0.0036 360 0.27 20 000
J/ (2S) 0.0011 90 0.07 5300
J/ (3S) 0.0005 50 0.035 2000
(1S) (1S) 0.014 1100 0.0027 200
lar calculations exist for the case of double (1S) production. For the case of J/ plus (1S) production no leading order diagrams contribute and hence the rate is expected to be suppressed in Single Parton Scattering (SPS). This leads to an unnatural ordering of the cross-section values: J/J/gg > (1S) (1S)gg > (1S)J/gg.
The DPS contributions to all these double onia production modes can be estimated, neglecting partonic correlations in the proton, as the product of the measured cross-sections of the sub-processes involved divided by an effective cross-section [527529, 535]. The value of the latter is determined from multi-jet events at the Tevatron to be DPSeff = 14.5 1.7+1.72.3 mb [536]. At s = 7 TeV the con
tribution from this source to the total cross-section is similar in size to the LO contribution from SPS. For DPS the ordering of the cross-section values is: J/J/DPS > (1S)J/DPS >
(1S) (1S)DPS.
The expected cross-sections for a few double quarkonia processes, together with their yields, are summarized in Table 14. Measurements of the cross-sections and properties in these modes will allow the two contributions to be disentangled.
As well as probing the production mechanism these studies are sensitive to a potential rst observation of tetraquark states [534] and of b and b states decaying in the double J/ mode. Based on the cross-sections and branching ratios given in Ref. [537], 500 (1500) fully reconstructed b0(1P ) (b2(1P )) are expected with the upgraded detector and these decays will be visible at LHCb. In the case of the b state, several estimates exist, based on values of the branching ratio b J/J/ ranging from 106 to 108
[538], corresponding to yields of 0.02 to 5 events.
The upgraded detector is expected to have excellent hadron identication capabilities both ofine and at the trigger level. As discussed in Ref. [539], this allows charmonium studies to be performed in hadronic decay modes. A particularly convenient mode is the pp nal state. This
Eur. Phys. J. C (2013) 73:2373 Page 65 of 92
is accessible for the J/, c, cJ , hc and (2S) mesons.
Extrapolating from studies with the current detector large inclusive samples of these decays will be collected. For example around 0.5 million c pp will be collected.
Hadronic decays of heavy bottomonium have received less attention in the literature [538]. The high mass implies a large phase space for many decay modes, but consequently the branching ratio for each individual mode is reduced. In Ref. [538] it is estimated that the b DD branching frac
tion is 105 and the b DD rate may be a factor of
ten higher. Though no specic studies have been performed, based on the studies of double open charm production given in Ref. [304] it is plausible that an b signal will be detected in this mode with the upgraded detector.
5.2 Exotic meson spectroscopy
The spectroscopy of bound states formed by heavy quark antiquark pairs (c or b quarks), has been extensively studied from both theoretical and experimental points of view since the discovery of the J/ state in 1974 [540, 541] and the discovery of the (1S) state in 1977 [542]. Until recently, all experimentally observed charmonium (c c) and bottomo
nium (b b) states matched well with expectations.
However, in 2003, a new and unexpected charmonium state was observed by the Belle experiment [543] and then conrmed independently by the BaBar [544], CDF [545] and D0 [546] experiments. This new particle, referred to as the X(3872), was observed in B X(3872)K decays,
in the decay mode X(3872) J/+ and has a mass
indistinguishable (within uncertainties) from the D0D0 threshold [520]. Several of the X(3872) parameters are unknown (such as its spin) or have large uncertainties, but this state does not match any predicted charmonium state [520]. The discovery of the X(3872) has led to a resurgence of interest in exotic spectroscopy and subsequently many new states have been claimed. For example: the Y family, Y (4260), Y (4320) and Y (4660), of spin parity 1, or the puzzling charged Z family, Z(4050)+, Z(4250)+ and
Z(4430)+, so far observed only by the Belle experiment [547549], and not conrmed by BaBar [550, 551]. The nature of these states has drawn much theoretical attention and many models have been proposed. One possible explanation is that they are bound molecular states of open charm mesons [552]. Another is that these are tetraquarks [553] states formed of four quarks (e.g. c, c, one light quark and
one light anti-quark). Other interpretations have been postulated such as quarkgluon hybrid [553] or hadrocharmonium models [554], but experimental data are not yet able to conclude denitely. For reviews, see Refs. [520, 552, 554 558].
The bottomonium system should exhibit similar exotic states to the charmonium case. The Belle experi-
ment recently reported the observation of exotic bottomonium charged particles Zb(10610)+ and Zb(10650)+ in the decays Zb (nS)+ and Zb hb(nP )+ [559].
Evidence for a neutral isopartner has also been reported [560].70 These states appear similar to, but narrower than, the Z(4430)+ observed in the charmonium case. In addition, neutral states analogous to the X(3872) and the Y states are expected in the bottomonium system.
Studies of the X(3872) have already been performed with the current detector [562]. The 50 fb1 of integrated luminosity collected with the upgraded detector will contain over one million X(3872) J/ candidates, by far the
largest sample ever collected and allow study of this meson with high precision. A signicant fraction of the X(3872) sample will originate from the decays of B mesons (the remainder being promptly produced) allowing the quantum numbers and other properties to be determined. With such a large sample the missing 3D2 state of the charmonium system [563] will be also be observed and studied with high precision.
Another study being pursued with the current detector is to clarify the status of the Z(4430)+ state. If conrmed, the
Z(4430)+ will be copiously produced at s = 14 TeV and
the larger data set will allow detailed study of its properties in different B decay modes, thus setting the basis for all future searches for exotic charged states.
Similar to the charmonium-like states, exotic bottomonium states will mainly be searched for in the (nS)+
channel, with (nS) +. The excellent resolution
observed in the (nS) analysis [524] allows efcient separation of the three states, which is crucial in searching for exotic bottomonium states in these channels.
All these studies, and searches for other exotica such as pentaquarks will prot from the increased integrated luminosity.
5.3 Precision measurements of b- and c-hadron properties
A major focus of activity with the current LHCb detector is the study of the properties of beauty and charm hadrons. This is a wide ranging eld including studies of properties such as mass and lifetime, observation of excited b hadrons and the measurements of branching ratios. These studies provide important input to pQCD models. Three topics are considered here: b decays to charmonia, B+c, and b-baryon decays.
One important eld being studied with the current detector is exclusive b decays to charmonia. Studies of these modes are important to improve understanding of the shape of the momentum spectrum of J/ produced in b hadron
70At ICHEP 2012, Belle reported observations of the Zb states decay
ing to BB() [561].
Page 66 of 92 Eur. Phys. J. C (2013) 73:2373
decays, as measured by the B factories [564, 565]. To explain the observed excess at low momentum, new contributions to the total b J/X rate are needed. Several
sources have been proposed in the literature: intrinsic charm [566], baryonium formation [567] and as yet unobserved exotic states [568]. One of the rst proposed explanations for the excess was a contribution from an intrinsic charm component to the b-hadron wave-function [566]. This would lead to an enhancement of b-hadron decays to J/ in association with open charm. The B-factories have set limits on such decays at the level of 105 [190], which considerably restricts, but does not exclude, contributions from intrinsic charm models. The branching ratios of these decays have been estimated in pQCD [569]. In the case of B0 J/D0
the branching ratio has been estimated to be 7107. If this
value is correct, several hundred fully reconstructed events will be collected with the upgraded detector. Similar decay modes are possible for B0s and B+c mesons though no limits (or predictions) exist.
Another possibility to explain the shape of the J/ spectrum is contributions from exotic strange baryonia formed in decays such as B+ J/0p. This decay has been ob-
served by BaBar [570], with a branching ratio of (1.18
0.31) 105. The related decay B0 J/pp is unob
served, with an upper limit on the branching ratio of 8.3
107 at 90 % condence level [571]. At present, these decays are experimentally challenging due to the low Q-values involved. The larger data samples available at the time of the upgrade, together with improved proton identication at low momentum, may lead to their observation.
Compared to the case of B0 and B+, the B0s sector is less well explored both experimentally and theoretically.
Decays such as B0s J/K0K0 and B0s J/
should be observable with the present detector. With the upgraded apparatus, the decay modes B0s J/K0SK0S and
B0s J/ will also become accessible. The latter chan
nel is interesting as the low Q-value will allow a precision determination of the B0s mass.
As the lowest bound state of two heavy quarks b and c, the B+c meson forms a unique avoured, weakly decaying quarkonium system. Studies of the properties of B+c mesons such as the mass, lifetime and two-body non-leptonic decay modes are being performed with the current detector.As an example, Fig. 26 shows the signals observed for B+c J/+ and B+c J/3+. The large data set col
lected with the upgraded detector will allow these studies to be pursued with higher precision together with rst studies of CP and triple-product asymmetries in the B+c system. In
Table 15 the expected yields of selected decay modes are estimated extrapolating from the yields of B+c J/+
and B+c J/3+ observed with the current detector. As
well as studies of the branching ratios and searches for NP, these modes will allow precision measurements of the B+c
Fig. 26 Invariant mass distribution of (top) B+c J/3+ and (bot
tom) B+c J/+ candidates using 0.8 fb1 of integrated luminos
ity collected in 2011 [572]. The results of maximum likelihood ts are superimposed
Table 15 Branching ratios and expected yields for selected B+c decays to nal states containing a J/ or (2S) meson. The branching ratios for the J/ modes are taken from Ref. [573], with the additional constraint of the ratio of the B+c J/3+ to B+c J/+ reported
in Ref. [572]. The (2S) mode branching ratios are estimated assuming that they are 0.5 of the J/ values, as observed in many modes (see for example Ref. [574]). Only dimuon modes are considered for the J/ and (2S), and only the K+K+ (K++) modes are considered for the D+s (D+) modes. The B+c K+K0 numbers are
taken from Ref. [575]
Mode Branching ratio Expected yield [50 fb1]
B+c J/+ 2 103 52 000
B+c J/3+ 5 103 17 000
B+c J/K+ (12) 104 30004000
B+c J/K+1 3 105 1000
B+c (2S)+ 1 103 3000
B+c (2S)3+ 2.5 103 1000
B+c J/D+s (23) 103 14001900
B+c J/D+ (513) 104 8100
B+c K+K0 106 500
mass and lifetime to be made. Based on ongoing studies with the current detector, a statistical precision of 0.1 MeV/c2 on
the mass will be achieved. The uncertainty on the mass will most likely be dominated by systematic errors related to the momentum scale. Precision of 104 on this variable would translate to an uncertainty of 0.3 MeV/c2 on the mass. Measurements of the B+c lifetime using the J/+ decay are
Eur. Phys. J. C (2013) 73:2373 Page 67 of 92
Fig. 27 Invariant mass spectrum of 0b+ [583]. The points with error bars are the data, the solid line is the result of a t to this distribution, and the dashed line is the tted background contribution
ongoing. Extrapolating these results to 50 fb1, a statistical
precision of 0.004 ps will be achieved.
The large B+c data set will open possibilities for many other studies. Decay modes of the B+c meson to a B0s or B0 meson together with a pion or kaon will also be accessible.
Studies of the B+c B0s+ decay have been started with
the data collected in 2011 where a handful of events are expected. As discussed in Ref. [573], semileptonic B+c decays to B0s can be used to provide a clean tagged decay source for CP violation studies. Finally, signals of the currently unexplored excited B+c meson states are expected to be ob-served [576579]. As discussed in Ref. [575] observation of the B+c decay is extremely challenging due to the soft photon produced in the decay to the ground state. The prospects for observation of the rst P-wave multiplet decays decaying radiatively to the ground state are more promising.
Large samples of b baryons decaying to nal states containing charmonia will also be collected. Precision measurements of the properties of the already known states will be possible. For example, extrapolating the preliminary studies with 0.3 fb1 discussed in Ref. [580], 10 000 b J/
and 2000 b J/ events will be collected. This will
allow the b (b) mass to be measured to a precision of 0.1 MeV/c2 (0.5 MeV/c2). Precise b-baryon lifetime measurements, that will allow tests of the heavy quark expansion [147, 581, 582], should also be possible. Studies of excited b baryons, for example determination of the quantum numbers of the b baryons that have recently been observed by
LHCb (Fig. 27) [583], will also be made.
Baryonic states containing two heavy quarks will also be observable. The lightest of these, the cc isodoublet, have an estimated cross-section of O(102) nb [584, 585] and so
should be visible with 5 fb1 collected with the current detector. However, the statistics may be marginal for follow-on analyses: measurements of the lifetime and ratios of branching fractions, searches for excited states, and so forth. They will certainly be insufcient for angular analyses aimed at
conrming the quark model predictions for the spin-parity of these states. These studies will require the statistics and improved triggering of the LHCb upgrade. Heavier states such as the cc, bc, and bb have still smaller production cross-sections [585]. First studies towards bc detection are in progress. These indicate that at best a handful of events can be expected in 5 fb1, but that this state should be observable with the upgrade.
5.4 Measurements with electroweak gauge bosons
Two of the most important quantities in the LHC electroweak physics programme are the sine of the effective electroweak mixing angle for leptons, sin2 lepteff, and the mass of the W -boson, mW . Thanks to its unique forward coverage, an upgraded LHCb can make important contributions to this programme. The forward coverage of LHCb also allows a probe of electroweak boson production in a different regime from that of ATLAS and CMS, and the range of accessible physics topics is not limited to electroweak bosons. For example, t t production proceeds predominantly
by gluongluon fusion in the central region, but has a significant contribution from quarkantiquark annihilation in the forward region, giving a similar production regime to that studied at the Tevatron.
5.4.1 sin2 lepteff
The value of sin2 lepteff can be extracted from AFB, the forwardbackward asymmetry of leptons produced in Z decays. The raw value of AFB measured in dimuon nal states at the LHC is about ve times larger than at an e+e collider, due to the initial state couplings, and so, in principle, it can be measured with a better relative precision, given equal amounts of data. The measurement however requires knowledge of the direction of the quark and antiquark that created the Z boson, and any uncertainty in this quantity results in a dilution of the observed value of AFB. This dilution is very signicant in the central region, as there is an approximately equal probability for each proton to contain the quark or anti-quark that is involved in the creation of the Z, leading to an ambiguity in the denition of the axis required in the measurement. However, the more forward the Z boson is produced, the more likely it is that it follows the quark direction; for rapidities y > 3, the Z follows the quark direction in around 95 % of the cases. Furthermore, in the forward region, the partonic collisions that produce the Z are nearly always between u-valence and-sea quark or
d-valence and d-sea quark. The s s contribution, with a less
well-known parton density function, is smaller than in the central region. Consequently, the forward region is the optimum environment in which to measure AFB at the LHC.
Preliminary studies [586] have shown that with a 50 fb1 data sample collected by the LHCb upgrade, AFB could be
Page 68 of 92 Eur. Phys. J. C (2013) 73:2373
Fig. 28 LHCb Z and W production results from 37 pb1 at s =
7 TeV [588]. Left: Z + peak. Right: W+ W production
asymmetry, where the bands correspond to the experimental uncertainties (only indicated within the LHCb acceptance), and the data points
give predictions for various different parton density function sets. Note that the kinematic range of the ATLAS and CMS experiments only extends up to lepton pseudorapidities of 2.5
measured with a statistical precision of around 0.0004. This would give a statistical uncertainty on sin2 lepteff of better than 0.0001, which is a signicant improvement in precision on the current world average value. It is also worth remarking that the two most precise values entering this world average at present, the forwardbackward b b asym
metry measured at LEP (sin2 lepteff = 0.23221 0.00029),
and the left-right asymmetries measured at SLD with polarised beams (sin2 lepteff = 0.23098 0.00026), are over 3
discrepant with each other [587]. LHCb will be able to bring clarity to this unsatisfactory situation.
More work is needed to identify the important systematic uncertainties on the AFB measurement. One source of error is the uncertainty in the parton density functions. With current knowledge this contribution would lead to an uncertainty of almost double the statistical precision estimate above, but this will reduce when the differential cross-section measurements from the LHC of the W and Z bosons, and those of DrellYan dimuon production at lower masses, are included in the global ts to the parton density functions. LHCb has already embarked on this measurement programme. Figure 28 (left) shows the Z + peak ob
tained with 37 pb1 of data [588]. Figure 28 (right) shows the measured asymmetry between W+ and W production as a function of lepton pseudorapidity. This measurement is already approaching the accuracy of the theoretical uncertainties. The W and Z measurements described in Ref. [588] are being used to constrain parton density functions by some groups [589]. A preliminary measurement of lower mass DrellYan production [590] will extend these constraints to lower Q2 (masses above 5 GeV/c2 are currently considered) and Bjorken x.
5.4.2 mW
Decreasing the uncertainty on mW from its present error of15 MeV/c2 is one of the most challenging tasks for the
LHC (it may also be reduced further at the Tevatron). Although no studies have yet been made of determining mW with LHCb itself, it is evident that the experiment can give important input to the measurements being made at ATLAS and CMS [591]. A signicant and potentially limiting external uncertainty on mW will again come from the knowledge of the parton density functions. These are less constrained in the kinematic range accessible to LHCb, so that precise measurements of W+, W, Z and DrellYan production in this region can be used to improve the global picture.
Improved determinations of the shapes of the differential cross-sections are particularly important. One specic area of concern arises from the knowledge of the heavy quarks in the proton. Around 2030 % of W production in the central region is expected to involve s and c quarks, making the understanding of this component very important for the mW measurement. LHCb can make a unique contribution to improving the knowledge of the heavy-quark parton density functions by exploiting its vertexing and particle identication capabilities to tag the relatively low-pT nal-state quarks produced in processes such as gs Wc, gc Zc,
gb Zb, gc c and gb b. These processes provide
direct probes of the strange, charm and bottom partons, and can be probed at high and low values of Bjorken x inside the LHCb acceptance.
5.4.3 t t production
Understanding the nature of top production, and in particular the asymmetry in t t events reported by Fermilab [592596],
is of prime concern. As for the measurement of sin2 lepteff, identifying the forward direction of events is crucial. The
LHCb acceptance for identifying both leptons from t t de
cays is far smaller than that of ATLAS and CMS (typically 2 % rather than 70 %, according to PYTHIA generator level studies). However, the higher q q production fraction and
Eur. Phys. J. C (2013) 73:2373 Page 69 of 92
better determined direction in the LHCb forward acceptance combine to suggest that competitive measurements can be achieved. With the integrated luminosity offered by the upgrade, statistical precision will no longer be an issue, and LHCb measurements of the t t asymmetry will offer a com
petitive and complementary test of Tevatron observations [597].
5.5 Searches for exotic particles with displaced vertices
Different theoretical paradigms have been proposed to solve the so-called hierarchy problem, the most discussed being SUSY. There are, however, many other ideas including various models involving extra dimensions, Technicolour and little Higgs models. These ideas approach the hierarchy problem from the direction of strong dynamics [598].
A growing subset of models features new massive long-lived particles with a macroscopic distance of ight. They can be produced by the decay of a single-produced resonance, such as a Higgs boson or a Z [599, 600], from the decay chain of SUSY particles [601], or by a hadronisation-type mechanism in models where the long-lived particle is a bound state of quarks from a new conning gauge group, as discussed in Ref. [599]. In the last case, the multiplicity of long-lived particles in an event can be large, while only one long-lived particle is expected to be produced in other models. The decay modes may also vary depending on the nature of the particle, from several jets in the nal state [600] to several leptons [602] or lepton plus jets [603]. A comprehensive review of the experimental signatures is given in Ref. [604].
The common feature amongst these models is the presence of vertices displaced from the interaction region. Such signatures are well suited to LHCb, and in particular to the upgraded experiment, which will be able to select events with displaced vertices at the earliest trigger level.
As an example, consider the hidden valley (HV) model already discussed in Ref. [25]. In this model the hidden sector, or v-sector, contains two new heavy quarks: U and C.Strassler and Zurek [601] suggest that an exotic Higgs boson could decay with a signicant branching fraction to a pair of 0v particles, where the 0v is the neutral member of the isotriplet of v-isospin 1 hadrons formed by U and C quarks. The 0v can decay in SM particles and if the mass of the spinless 0v is below the ZZ threshold it will decay dominantly into bb pairs due to helicity conservation. Here the 0v widths are determined by their lifetime which could be very long, resulting in narrow states. The nal state would consist of four b-jets, each pair being produced from a displaced vertex corresponding to the 0v decay as illustrated in
Fig. 29. If these decays exist, the lower limit on the Higgs mass set by LEP would be misleading, as it assumes the prompt decay of the Higgs to bb to be dominant.
Fig. 29 Decay of a Higgs via a scalar eld into two 0v particles, with 0v charge equal to zero, which subsequently decay into bb jets.
(Adapted from Ref. [601])
The potential of LHCb to search for such exotic Higgs decays at s = 14 TeV has been discussed in Ref. [25],
and is briey summarised here. The benchmark model uses mH = 120 GeV/c2, m
0
v = 35 GeV/c2 and
v = 10 ps. By
combining vertex and jet reconstruction, the capacity to reconstruct this nal state is shown using full simulation of the detector, assuming 0.4 interactions per crossing. Backgrounds to this signal from other processes, such as the production of two pairs of b b quarks, have been considered and
found to be negligible.
During 2010 and 2011 data taking, an inclusive displaced vertex trigger has been introduced in the second level of the software trigger. Preliminary studies [605] have demonstrated that for an output rate below 1 % of the overall trigger bandwidth, the efciency of the whole trigger chain on events with two ofine reconstructible 0v vertices with a minimum mass of 6 GeV and good vertex quality is of the order of 80 %. This strategy has been tested up to on average two visible interactions per crossing which is what is expected for the upgraded experiment.
The analysis of the trigger output showed that once vertices arising from hadronic interactions with material are rejected, the dominant background is compatible with b hadron decay vertices as shown in Fig. 30. Those b hadron vertices are reconstructed with large masses because of the presence of fake or cloned tracks. With the present detector, it is difcult to keep the trigger rate down for single candidate events without using tight cuts on the mass and the displacement of the candidates. In the previous model, the trigger efciency for events with a single long-lived particle reconstructible in LHCb is only about 20 %. This efciency is expected to decrease for models where the mass of the long-lived particle is smaller. In addition, the number of events with at least one 0v state in the acceptance is three times higher than the number of events with two 0v particles. Improving the single candidate efciency would increase sensitivity to this model. It would also give a better coverage for the models where only one long-lived particle is produced.
In the upgraded detector, the track fake rate in the vertex detector is expected to be below one percent [26], compared to 6 % in the present detector. Other upgrades to the tracking detectors will also help to reduce the fake rate. Moreover
0
Page 70 of 92 Eur. Phys. J. C (2013) 73:2373
Fig. 30 Left: Distribution in x and z, for |y| < 1 mm, of the recon
structed vertices. The visible structures reect the geometry of the vertex detector, with the pairs of silicon sensors appearing as pairs of vertical bands and the corrugated (RF) foil as the two wave shapes. The green shaded region represents the ducial vacuum volume in which candidates are accepted. Right: Flight distance of ofine reconstructed
vertices in events outside the matter region. Data are compatible with b b background. The black points are for data in 36 pb1 [605], the red
line is a full simulation of b b production and the green dashed line is
a full simulation of the HV benchmark channel. The blue dashed line shows a simulation of a model with baryon number violating neutralino couplings
the use of an improved description for the complex RF foil shape will give a better control on the background arising from hadronic interactions. It will enable the use of the true shape of the RF foil, rather than the loose ducial volume cut used at present, which depending on the considered lifetime, rejects 1030 % of the long-lived particles. Those improvements would allow to decrease the thresholds on the single candidates trigger and therefore increase the reach of such searches.
As discussed in Ref. [25] the coupling of vertex information to jet reconstruction will allow to reduce the physical backgrounds. Studies are on-going on this matter. Assuming a Higgs production cross-section at s = 14 TeV of
50 pb, an integrated luminosity of 50 fb1 and a geometric efciency of 10 %, 250 000 Higgs bosons will be produced in LHCb. If H0 0v0v is a dominant decay mode, then
LHCb will be in an excellent position to observe this signal, taking advantage of the software triggers ability to select high-multiplicity events with good efciency.
5.6 Central exclusive production
Central exclusive production (CEP) processes provide a promising and novel way to study QCD and the nature of new particles, from low mass glueball candidates up to the Higgs boson itself. The CEP of an object X in a pp collider may be written as follows
pp p + X + p,where the + signs denote the presence of large rapidity
gaps. At high energies the t-channel exchanges giving rise to these processes can only be zero-charge colour singlets. Known exchanges include the photon and the pomeron. Another possibility, allowed in QCD, but not yet observed, is
the odderon, a negative C-parity partner to the pomeron with at least three gluons. The most attractive aspect of CEP reactions is that they offer a very clean environment in which to measure the nature and quantum numbers of the centrally produced state X.
Central exclusive [606], dijet [607, 608] and c [609] production has been observed at the Tevatron. LHCb has presented preliminary results on candidate dimuon events compatible with CEP [610]. Figure 31 shows the invariant mass of CEP c candidates. These are events in which only a J/ + decay and a candidate are reconstructed,
with no other activity (inconsistent with noise) seen elsewhere in the detector. Important observables in CEP are the relative production rates of c0, c1 and c2. As is evident from Fig. 31, the invariant mass resolution of LHCb is sufcient for this measurement.
Although not part of the baseline for the LHCb upgrade, additional instrumentation is being considered which could improve the potential of LHCb to study CEP processes. For example, the inclusion of forward shower counters (FSCs) on both sides of the interaction point, as proposed in Ref. [612], would be able to detect showers from very forward particles interacting in the beam pipe and surrounding material. The absence of a shower would indicate a rapidity gap and be helpful in increasing the purity of a CEP sample. More ambitiously, the deployment of semi-conductor detectors very close to the beam, within Roman pots, several hundred meters away from the interaction point, as proposed for other LHC experiments [613] would also be benecial for LHCb. The ability to measure the directions of the deected protons in the CEP interaction provides invaluable information in determining the quantum numbers of the centrally produced state.
Several important physics goals have been identied for the LHCb CEP programme:
Eur. Phys. J. C (2013) 73:2373 Page 71 of 92
Fig. 31 Preliminary LHCb results on central exclusive c production [610]. The J/ invariant mass in data is compared to the expectation of the SuperCHIC Monte Carlo generator [611], which has been normalised to the observed number of events. The relative proportions of c0, c1 and c2 are 12 %, 36 % and 52 % respectively
Accumulation and characterisation of large samples of
exclusive c c and b b events. A full measurement pro
gramme of these standard candles will be essential to understand better the QCD mechanism of CEP [614], and may provide vital input if CEP is used for studies of Higgs and other new particles [615].
Searches for structure in the mass spectra of decay states
such as K+K, 2+2, K+K+ and p p. A par
ticular interest of this study would be the hunt for glue-balls, which are a key prediction of QCD.
Observation and study of exotic particles in CEP pro
cesses. For example, a detailed study of the CEP process pp p + X(3872) + p would provide a valuable
new tool to aid understanding of this state. This and other states could be searched for in, for example, decays containing DD, which if observed would shed light onto the nature of the parent particle [614].
There are several reasons which make LHCb a suitable detector for realising these goals, particularly with the upgraded experiment:
Even when running at a luminosity of 1033 cm2 s1
LHCb will have low pileup compared to ATLAS and CMS. This will be advantageous in triggering and reconstructing low mass CEP states.
The higher integrated luminosity that will be collected by
the upgraded detector will allow studies to be performed on states that are inaccessible with only a few fb1. This is true, for example, of central exclusive b production, which is expected to be a factor of 1000 less than that
of c mesons [614].
The particle identication capabilities of the LHCb ring-
imaging Cherenkov detector system allow centrally produced states to be cleanly separated into decays involving pions, kaons and protons.
The low pT acceptance of LHCb, and high bandwidth
trigger, will allow samples of relatively low mass states to be collected and analysed.
6 Summary
As described in the previous sections, LHCb has produced world-leading results across its physics programme, using the 1.0 fb1 data sample of s = 7 TeV pp collisions col
lected in 2011. The inclusion of the data collected at s =
8 TeV during 2012 will enable further improvements in precision in many key avour physics observables. However, an upgrade to the detector is needed to remove the bottleneck in the trigger chain that currently prevents even larger increases in the collected data sample. The upgraded detector with trigger fully implemented in software is to be installed during the 2018 long shutdown of the LHC, and will allow a total data set of 50 fb1 to be collected. With such a data sample, LHCb will not only reach unprecedented precision for a wide range of avour physics observables, but the exible trigger will allow it to exploit fully the potential of a forward physics experiment at a hadron collider.
In this section, some highlights of the LHCb physics output so far, and their implications on the theoretical landscape, are summarised. The sensitivity of the upgraded detector to key observables is then given, before a concluding statement on the importance of the LHCb upgrade to the global particle physics programme.
6.1 Highlights of LHCb measurements and their implications
6.1.1 Rare decays
Among rare decays, the LHCb limit on the rate of the decay
B0s + [13] places stringent limits on NP models that
enhance the branching fraction. The measurement
B[parenleftbig]B0s +[parenrightbig]
< 4.5 109 (95 % condence level), (134) can be compared to the SM prediction B(B0s +)SM =
(3.1 0.2) 109 [116].71 This result puts severe con
straintsfar beyond the ATLAS and CMS search limits on supersymmetric models with large values of tan , i.e. of the ratio of vacuum expectation values of the Higgs doublets (see, for example, Refs. [116, 129, 162]).
71It should be noted that the measured value is the time-integrated branching fraction, and the SM prediction should be increased by around 10 % to allow a direct comparison [136].
Page 72 of 92 Eur. Phys. J. C (2013) 73:2373
The measurement of the forwardbackward asymmetry in B0 K0+ [15] has to be viewed as the start of
a programme towards a full angular analysis of these decays. The full analysis will allow determination of numerous NP-sensitive observables (see, for example, Refs. [53, 54]).The measurements that will be obtained from such an analysis, as well as similar studies of related channels, such as B0s + [69], allow model-independent constraints
on NP, manifested as limits on the operators of the effective Hamiltonian (see, for example, Refs. [42, 43]). Indeed, the rst results already impose important constraints. Studies of radiative decays such as B0s [16, 17] provide addi
tional information since they allow to measure the polarisation of the emitted photon, and are therefore especially sensitive to models that predict new right-handed currents. Similarly, studies of observables such as isospin asymmetries [77] are important since they allow to pin down in which operators the NP effects occur.
Several new opportunities with rare decays at LHCb are becoming apparent. The observation of B+ ++
[86], the rarest B decay yet discovered, enables a new approach to measure the ratio of CKM matrix elements
|Vtd/Vts|. Decays to nal states containing same-sign lep-
tons [197] allow searches for Majorana neutrinos complementary to those based on neutrinoless double beta decay.LHCb can also reach competitive sensitivity for some lepton avour violating decays such as + ++ [191].
6.1.2 CP violation in the B sector
Measurements of the neutral B meson mixing parameters provide an excellent method to search for NP effects, due to the low theoretical uncertainties associated to several observables. The LHCb measurements of the CP-violating phase, s, and the width difference, s, in the B0s system [10, 139, 219, 232] signicantly reduce the phase space for
NP:
s = 0.002 0.083 0.027 rad, s = 0.116 0.018 (stat) 0.006 (syst) ps1.
(135)
However deviations from the SM predictions [119, 221] are still possible. Effects of O(0.1) are typical of some well-
motivated NP models that survive the present ATLAS and CMS bounds (such as in Ref. [37]). The experimental uncertainty on s is still a factor of 40 larger than that on the prediction, therefore improved measurements are needed to reach the level of sensitivity demanded by theory. It should also be noted that compared to the CP-violating phase in the B0 system (2), s is much more precisely predicted, and therefore presents stronger opportunities for NP searches.
In addition, to understand the origin of the anomalous dimuon asymmetry seen by D0 [159], improved measurements of semileptonic asymmetries in both B0s and B0 systems are needed. LHCb has just released its rst results
on the B0s asymmetry [248], demonstrating the potential to search for NP effects with more precise measurements.
Moreover, a constraint on, or a measurement of, the rate of the decay B0s + is important to provide knowl
edge of possible NP contributions to 12 (see, for example, Refs. [153, 155]).
Among the B0 mixing parameters, improved measurements of both d (i.e., sin 2) and d are needed. Reducing the uncertainty on the former will help to improve the global ts to the CKM matrix [252, 266], and may clarify the current situation regarding the tension between various inputs to the ts (see, for example, Ref. [267]). Another crucial observable is the angle , which, when measured in the tree-dominated B DK processes, provides a benchmark
measurement of CP violation. The rst measurements from LHCb already help to improve the uncertainty on [6, 7]: further improvements are both anticipated and needed.
Comparisons of values of from loop-dominated processes with the SM benchmark from tree-dominated processes provide important ways to search for new sources of CP violation. In particular, the study of B0s K+K
and B0 + decays [356], which are related by U-
spin, allows a powerful test of the consistency of the observables with the SM [355, 357]. Similarly, the U-spin partners B0s K0K0 [303] and B0 K0K0 are among the
golden channels to search for NP contributions in b sq q
penguin amplitudes [308]. Another important channel in this respect is B0s [304], for which the CP-violating ob
servables are predicted with low theoretical uncertainty in the SM. Studies of CP violation in multibody b hadron decays [376, 377] offer additional possibilities to search for both the existence and features of NP.
6.1.3 Charm mixing and CP violation
In the charm sector, the evidence for CP violation in the observable ACP has prompted a large amount of theoretical
work. The measurement
ACP = ACP[parenleftbig]K+K[parenrightbig] ACP[parenleftbig]+[parenrightbig]
= (0.82 0.21 0.11) %, (136)
is different from zero by 3.5 standard deviations [18]. While
ACP represents a time-integrated CP asymmetry, ACP
originates predominantly from direct CP violation. The emergent consensus is that while an asymmetry of the order of 1 % is rather unlikely in the SM, it cannot be ruled out that QCD effects cause enhancements of that size. Further measurements are needed in order to establish if NP effects are present in the charm sector. Among the anticipated results are updates of the ACP measurement as well
as of the individual CP asymmetries in D0 K+K and
Eur. Phys. J. C (2013) 73:2373 Page 73 of 92
D0 +. It is of great interest to look for direct CP vi
olation in decays to other nal states, and in decays of other charmed hadrons (D+, D+s and +c).
The SM predictions are somewhat cleaner for indirect CP violation effects, and therefore it is also essential to search for CP violation in charm mixing. New results from time-dependent analyses of D0 K+K [19] and D0
K0S+ will improve the current knowledge, and additional channels will also be important with high statistics.
Several authors have noted correlations between CP violation in charm and various other observables (for example, Refs. [469, 484]). These correlations appear in, and differ between, certain theoretical models, and can therefore be used to help identify the origin of the effects. Observables of interest in this context include those that can be measured at high-pT experiments, such as t t asymmetries, as well
as rare charm decays. Among the latter, it has been noted that CP asymmetries are possible in radiative decays such as D0 [485], and that searches for decays involving
dimuons, such as D0 + [178] and D+ ++
are well motivated.
6.1.4 Measurements exploiting the unique kinematic acceptance of LHCb
The unique kinematic region covered by the LHCb acceptance enables measurements that cannot be performed at other experiments, and that will continue to be important in the upgrade era. These include probes of QCD both in production, such as studies of multi-parton scattering [531, 616], and in decay, such as studies of exotic hadrons like the X(3872) [562] and the putative Z(4430)+ state. Conventional hadrons can also be studied with high precision: one important goal will be to establish the existence of doubly heavy baryons. Central exclusive production of conventional and exotic hadrons can also be studied; the sensitivity of the upgraded experiment will be signicantly enhanced due to the software trigger.
Measurements of production rates and asymmetries of electroweak gauge bosons in the LHCb acceptance are important to constrain parton density functions [588]. With high statistics, LHCb will be well placed to make a precision measurement of the sine of the effective electroweak mixing angle for leptons, sin2 lepteff, from the forwardbackward asymmetry of leptons produced in the Z + decay.
Improved knowledge of parton density functions, as can be obtained from studies of production of gauge bosons in association with jets [617], will help to reduce limiting uncertainties on the measurement of the W boson. These studies are also an important step towards a top physics programme at LHCb, which will become possible once the LHC energy approaches the nominal 14 TeV.
The importance of having a detector in the forward region can be illustrated with the recent discovery by ATLAS
and CMS of a new particle that may be the Higgs boson. It is now essential to determine if this particle has the couplings to bosons, leptons and quarks expected in the SM. In particular, at the observed mass the highest branching ratio is expected to be for H b bhowever this is a difcult
channel for ATLAS and CMS due to the large SM background. LHCb with its excellent b-hadron sensitivity will be able to search for such decays. The forward geometry of LHCb is also advantageous to observe new long-lived particles that are predicted in certain NP models, including some with extended Higgs sectors. Although limits can be set with the current detector [605], this is an area that benets significantly from the exible software trigger of the upgraded experiment. Models with extended Higgs sectors also produce characteristic signals in avour physics observables, which emphasises the need for the LHCb upgrade as part of the full exploitation of the LHC.
6.2 Sensitivity of the upgraded LHCb experiment to key observables
As mentioned in Sect. 1, the LHCb upgrade is necessary to progress beyond the limitations imposed by the current hardware trigger that, due to its maximum output rate of 1 MHz, restricts the instantaneous luminosity at which data can most effectively be collected. To overcome this, the upgraded detector will be read out at the maximum LHC bunch-crossing frequency of 40 MHz so that the trigger can be fully implemented in software. The upgraded detector will be installed during the long shutdown of the LHC planned for 2018. A detailed description of the upgraded LHCb experiment can be found in the Letter of Intent (LoI) [25], complemented by the recent framework technical design report (FTDR) [26], which sets out the timeline and costing for the project. A summary has been prepared for the European Strategy Preparatory Group [618].
The sensitivity to various avour observables is summarised in Table 16, which is taken from the FTDR [26]. This is an updated version of a similar summary that appears as Table 2.1 in the LoI [25]. The measurements considered include CP-violating observables, rare decays and fundamental parameters of the CKM unitarity triangle. More details about these observables are given below. The current precision, either from LHCb measurements or averaging groups [44, 252, 266], is given and compared to the estimated sensitivity with the upgrade. As an intermediate step, the estimated precision that can be achieved prior to the upgrade is also given for each observable. For this, a total integrated luminosity of 1.0 (1.5, 4.0) fb1 at pp centre-of-mass collision energy s = 7 (8, 13) TeV recorded in 2011
(2012, 20152017) is assumed. Another assumption is that the current efciency of the muon hardware trigger can be maintained at higher s, but that higher thresholds will be
Page 74 of 92 Eur. Phys. J. C (2013) 73:2373
Table 16 Statistical sensitivities of the LHCb upgrade to key observables. For each observable the current sensitivity is compared to that which will be achieved by LHCb before the upgrade, and that which will be achieved with 50 fb1 by the upgraded experiment. Systematic
uncertainties are expected to be non-negligible for the most precisely
measured quantities. Note that the current sensitivities do not include
new results presented at ICHEP 2012 or CKM2012
Type Observable Current precision LHCb 2018 Upgrade (50 fb1)
Theory uncertainty
B0s mixing 2s(B0s J/) 0.10 [139] 0.025 0.008 0.003
2s(B0s J/f0(980)) 0.17 [219] 0.045 0.014 0.01
assl 6.4 103 [44] 0.6 103 0.2 103 0.03 103 Gluonic penguins 2effs(B0s ) 0.17 0.03 0.02
2effs(B0s K0K0) 0.13 0.02 < 0.02 2eff(B0 K0S) 0.17 [44] 0.30 0.05 0.02
Right-handed currents 2effs(B0s ) 0.09 0.02 <0.01
eff(B0s )/B
0
s 5 % 1 % 0.2 %
Electroweak penguins S3(B0 K0+; 1 < q2 < 6 GeV2/c4) 0.08 [68] 0.025 0.008 0.02
s0AFB(B0 K0+) 25 % [68] 6 % 2 % 7 %
AI(K+; 1 < q2 < 6 GeV2/c4) 0.25 [77] 0.08 0.025 0.02
B(B+ ++)/B(B+ K++) 25 % [86] 8 % 2.5 % 10 %
Higgs penguins B(B0s +) 1.5 109 [13] 0.5 109 0.15 109 0.3 109
B(B0 +)/B(B0s +) 100 % 35 % 5 % Unitarity triangle angles (B D()K()) 1012 [252, 266] 4 0.9 negligible
(B0s DsK) 11 2.0 negligible
(B0 J/K0S) 0.8 [44] 0.6 0.2 negligible Charm CP violation A 2.3 103 [44] 0.40 103 0.07 103
ACP 2.1 103 [18] 0.65 103 0.12 103
necessary for other triggers, reducing the efciency for the relevant channels by a factor of 2 at s = 14 TeV.
In LHCb measurements to date, the CP-violating phase in B0s mixing, measured in both J/ and J/f0(980) nal states, has been denoted s. In the upgrade era it will be necessary to remove some of the assumptions that have been made in the analyses to date, related to possible penguin amplitude contributions, and therefore the observables in b c cs transitions are denoted by 2s = s, while
in b q qs (q = u, d, s) transitions the notation 2effs is
used. This parallels the established notation used in the B0 system (the , , convention for the CKM unitarity triangle angles is used). The penguin contributions are expected to be small, and therefore a theory uncertainty on 2s(B0s J/) 0.003 is quoted, comparable to the
theory uncertainty on 2(B0 J/K0S). However, larger
effects cannot be ruled out at present. Data-driven methods to determine the penguin amplitudes are also possible [246, 277, 284]: at present these given much larger estimates of the uncertainty, but improvement can be anticipated with increasing data samples. The avour-specic asymmetry in the B0s system, assl in Table 16, probes CP violation in mix-
ing. The sl subscript is used because the measurement uses semileptonic decays.
Sensitivity to the emitted photon polarisation is encoded in the effective lifetime, eff of B0s decays, together
with the effective CP-violation parameter 2effs. Two of the most interesting of the full set of angular observables in
B0 K0+ decays [62], are S3, which is related to
the transverse polarisation asymmetry [63], and the zero-crossing point (s0) of the forwardbackward asymmetry. As discussed above, isospin asymmetries, denoted AI , are also of great interest.
In the charm sector, it is important to improve the precision of ACP, described above, and related measurements
of direct CP violation. One of the key observables related to indirect CP violation is the difference in inverse effective lifetimes of D0 K+K and D0 K+K decays, A .
The extrapolations in Table 16 assume the central values of the current measurements, or the SM where no measurement is available. While the sensitivities given include statistical uncertainties only, preliminary studies of systematic effects suggest that these will not affect the conclusions signicantly, except in the most precise measurements,
Eur. Phys. J. C (2013) 73:2373 Page 75 of 92
such as those of assl, A and ACP. Branching fraction
measurements of B0s mesons require knowledge of the ratio of fragmentation fractions fs/fd for normalisation [145].The uncertainty on this quantity is limited by knowledge of the branching fraction of D+s K+K+, and improved
measurements of this quantity will be necessary to avoid a limiting uncertainty on, for example, B(B0s +). The
determination of 2s from B0s J/ provides an exam
ple of how systematic uncertainties can be controlled for measurements at the LHCb upgrade. In the most recent measurement [139], the largest source of systematic uncertainty arises due to the constraint of no direct CP violation that is imposed in the t. With larger statistics, this constraint can be removed, eliminating this source of uncertainty. Other sources, such as the background description and angular acceptance, are already at the 0.01 rad level, and can be reduced with more detailed studies.
Experiments at upgraded e+e B factories and elsewhere will study avour-physics observables in a similar time-frame to the LHCb upgrade. However, the LHCb sample sizes in most exclusive B and D nal states will be far larger than those that will be collected elsewhere, and the LHCb upgrade will have no serious competition in its study of B0s decays, b-baryon decays, mixing and CP violation. Similarly the yields in charmed-particle decays to nal states consisting of only charged tracks cannot be matched by any other experiment. On the other hand, the e+e environment is advantageous for inclusive studies and for measurements of decay modes including multiple neutral particles [619 623], and therefore enables complementary measurements to those that will be made with the upgraded LHCb experiment.
6.3 Importance of the LHCb upgrade
The study of deviations from the SM in quark avour physics provides key information about any extension of the SM. It is already known that the NP needed to stabilize the electroweak sector must have a non-generic avour structure in order to be compatible with the tight constraints of avour-changing processes, even if the precise form of this structure is still unknown. Hopefully, ATLAS and CMS will detect new particles belonging to these models, but the couplings of the theory and, in particular, its avour structure, cannot be determined only using high-pT data.
Therefore, the LHCb upgrade will play a vital role in any scenario. It allows the exploration of NP phase space that a priori cannot be studied by high energy searches. Future plans for full exploitation of the LHC should be consistent with a co-extensive LHCb programme.
Acknowledgements The LHCb Collaboration expresses its gratitude to its colleagues in the CERN accelerator departments for the excellent performance of the LHC. LHCb thanks the technical and
administrative staff at the LHCb institutes, and acknowledges support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 and Region Auvergne (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); ANCS/IFA (Romania); MinES, Rosatom, RFBR and NRC Kurchatov Institute (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). LHCb also acknowledges the support received from the ERC under FP7. The Tier1 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom). LHCb is thankful for the computing resources put at its disposal by Yandex LLC (Russia), as well as to the communities behind the multiple open source software packages that are depended upon.
The work of A. Datta was supported by the National Science Foundation under Grant No. NSF PHY-1068052. D.M. Straub was supported by the EU ITN Unication in the LHC Era, contract PITNGA-2009-237920 (UNILHC). We thank D. Gorbunov for useful comments.
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
References
1. A.A. Alves Jr. et al. (LHCb Collaboration), The LHCb detector at the LHC. J. Instrum. 3, S08005 (2008)
2. R. Aaij et al. (LHCb Collaboration), Measurement of (pp
b bX) at s = 7 TeV in the forward region. Phys. Lett. B 694,
209 (2010). arXiv:1009.27313. LHCb Collaboration, Prompt charm production in pp collisions at s = 7 TeV, LHCb-CONF-2010-013
4. R. Aaij et al. (LHCb Collaboration), Prompt charm production in pp collisions at s = 7 TeV. Nucl. Phys. B (2013). doi:10.1016/
http://dx.doi.org/10.1016/j.nuclphysb.2013.02.010
Web End =j.nuclphysb.2013.02.010 . arXiv:1302.2864,5. B. Adeva et al. (LHCb Collaboration), Roadmap for selected key measurements of LHCb. arXiv:0912.4179
6. R. Aaij et al. (LHCb Collaboration), Observation of CP violation in B DK decays. Phys. Lett. B 712, 203 (2012). arXiv:
1203.36627. R. Aaij et al. (LHCb Collaboration), A model-independent Dalitz plot analysis of B DK with D K0Sh+h (h = , K)
decays and constraints on the CKM angle . Phys. Lett. B 718, 43 (2012). arXiv:1209.58698. R. Aaij et al. (LHCb Collaboration), First evidence of direct CP violation in charmless two-body decays of B0s mesons. Phys.
Rev. Lett. 108, 201601 (2012). arXiv:1202.62519. R. Aaij et al. (LHCb Collaboration), Measurement of b-hadron branching fractions for two-body decays into charmless charged hadrons. J. High Energy Phys. 10, 037 (2012). arXiv:1206.2794
10. R. Aaij et al. (LHCb Collaboration), Measurement of the CP-violating phase s in the decay B0s J/. Phys. Rev. Lett.
108, 101803 (2012). arXiv:1112.318311. R. Aaij et al. (LHCb Collaboration), Search for the rare decays B0s + and B0 +. Phys. Lett. B 699, 330 (2011).
arXiv:1103.246512. R. Aaij et al. (LHCb Collaboration), Search for the rare decays B0s + and B0 +. Phys. Lett. B 708, 55 (2012).
arXiv:1112.1600
Page 76 of 92 Eur. Phys. J. C (2013) 73:2373
13. R. Aaij et al. (LHCb Collaboration), Strong constraints on the rare decays B0s + and B0 +. Phys. Rev. Lett.
108, 231801 (2012). arXiv:1203.449314. R. Aaij et al. (LHCb Collaboration), First evidence for the decay B0s +. Phys. Rev. Lett. 110, 021801 (2013). arXiv:1211.
267415. R. Aaij et al. (LHCb Collaboration), Differential branching fraction and angular analysis of the decay B0 K0+. Phys.
Rev. Lett. 108, 181806 (2012). arXiv:1112.351516. R. Aaij et al. (LHCb Collaboration), Measurement of the ratio of branching fractions B(B0 K0 )/B(B0s ). Phys. Rev.
D 85, 112013 (2012). arXiv:1202.626717. R. Aaij et al. (LHCb Collaboration), Measurement of the ratio of branching fractions B(B0 K0 )/B(B0s ) and direct
CP asymmetry in B0 K0 . Nucl. Phys. B 867, 1 (2013).
arXiv:1209.031318. R. Aaij et al. (LHCb Collaboration), Evidence for CP violation in time-integrated D0 hh+ decay rates. Phys. Rev. Lett. 108,
111602 (2012). arXiv:1112.093819. R. Aaij et al. (LHCb Collaboration), Measurement of mixing and CP violation parameters in two-body charm decays. J. High Energy Phys. 04, 129 (2012). arXiv:1112.4698
20. N. Cabibbo, Unitary symmetry and leptonic decays. Phys. Rev.
Lett. 10, 531 (1963)
21. M. Kobayashi, T. Maskawa, CP violation in the renormalizable theory of weak interaction. Prog. Theor. Phys. 49, 652 (1973)
22. J.H. Christenson, J.W. Cronin, V.L. Fitch, R. Turlay, Evidence for the 2 decay of the K02 meson. Phys. Rev. Lett. 13, 138 (1964)
23. V. Gligorov, C. Thomas, M. Williams, The HLT inclusive B triggers, LHCb-PUB-2011-016
24. R. Aaij et al., The LHCb trigger and its performance. arXiv: 1211.3055
25. LHCb Collaboration, Letter of Intent for the LHCb Upgrade.
CERN-LHCC-2011-001.LHCC-I-018
26. LHCb Collaboration, Framework TDR for the LHCb Upgrade.
CERN-LHCC-2012-007.LHCB-TDR-012
27. E. Majorana, Teoria simmetrica dellelettrone e del positrone.
Nuovo Cimento 14, 171 (1937)
28. A. Atre, T. Han, S. Pascoli, B. Zhang, The search for heavy Majorana neutrinos. J. High Energy Phys. 05, 030 (2009). arXiv:0901. 3589
29. G. Cvetic, C. Dib, S.K. Kang, C.S. Kim, Probing Majorana neutrinos in rare K and D, Ds, B, Bc meson decays. Phys. Rev. D 82, 053010 (2010). arXiv:1005.4282
30. S. Fajfer, J.F. Kamenik, N. Kosnik, b dd s transition and con
straints on new physics in B-decays. Phys. Rev. D 74, 034027 (2006). http://arxiv.org/abs/arXiv:hep-ph/0605260
Web End =arXiv:hep-ph/0605260 31. D. Pirjol, J. Zupan, Predictions for b ss d, and b dd s de
cays in the SM and with new physics. J. High Energy Phys. 02, 028 (2010). arXiv:0908.315032. L. Hofer, D. Scherer, L. Vernazza, B0s 0 and B0s 0 as
a handle on isospin-violating new physics. J. High Energy Phys. 02, 080 (2011). arXiv:1011.631933. N. Uraltsev, Heavy quark expansion in beauty and its decays. http://arxiv.org/abs/arXiv:hep-ph/9804275
Web End =arXiv:hep-ph/9804275
34. A.J. Buras, Flavor physics and CP violation. http://arxiv.org/abs/arXiv:hep-ph/0505175
Web End =arXiv:hep-ph/ 0505175
35. A.J. Buras et al., Universal unitarity triangle and physics beyond the standard model. Phys. Lett. B 500, 161 (2001). http://arxiv.org/abs/arXiv:hep-ph/0007085
Web End =arXiv:hep-ph/ 0007085
36. G. DAmbrosio, G.F. Giudice, G. Isidori, A. Strumia, Minimal avor violation: an effective eld theory approach. Nucl. Phys.B 645, 155 (2002). http://arxiv.org/abs/arXiv:hep-ph/0207036
Web End =arXiv:hep-ph/0207036
37. R. Barbieri et al., U(2) and minimal avour violation in super-symmetry. Eur. Phys. J. C 71, 1725 (2011). arXiv:1105.2296
38. S. Descotes-Genon, D. Ghosh, J. Matias, M. Ramon, Exploring New Physics in the C7C 7 plane. J. High Energy Phys. 06, 099 (2011). arXiv:1104.3342
39. W. Altmannshofer, P. Paradisi, D.M. Straub, Model-independent constraints on new physics in b s transitions. J. High Energy
Phys. 04, 008 (2012). arXiv:1111.125740. C. Bobeth, G. Hiller, D. van Dyk, C. Wacker, The decay B
K + at low hadronic recoil and model-independent B = 1
constraints. J. High Energy Phys. 01, 107 (2012). arXiv:1111. 255841. F. Beaujean, C. Bobeth, D. van Dyk, C. Wacker, Bayesian t of exclusive b s
decays: the Standard Model operator basis.J. High Energy Phys. 08, 030 (2012). arXiv:1205.183842. W. Altmannshofer, D.M. Straub, Cornering new physics in b s
transitions. J. High Energy Phys. 08, 121 (2012). arXiv:1206. 027343. T. Hurth, F. Mahmoudi, The minimal avour violation benchmark in view of the latest LHCb data. Nucl. Phys. B 865, 461 (2012). arXiv:1207.0688
44. Y. Amhis et al. (Heavy Flavor Averaging Group), Averages of b-hadron, c-hadron, and -lepton properties as of early 2012. arXiv:1207.1158, updated results and plots available at: http://www.slac.stanford.edu/xorg/hfag/
Web End =http://www.slac.stanford.edu/xorg/hfag/
45. M. Misiak et al., Estimate of B( B Xs ) at O(2s). Phys. Rev.
Lett. 98, 022002 (2007). http://arxiv.org/abs/arXiv:hep-ph/0609232
Web End =arXiv:hep-ph/0609232 46. M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, QCD factorization for B decays: strong phases and CP viola
tion in the heavy quark limit. Phys. Rev. Lett. 83, 1914 (1999). http://arxiv.org/abs/arXiv:hep-ph/9905312
Web End =arXiv:hep-ph/9905312 47. M. Beneke, G. Buchalla, M. Neubert, C.T. Sachrajda, QCD factorization for exclusive, nonleptonic B meson decays: general arguments and the case of heavy light nal states. Nucl. Phys. B 591, 313 (2000). http://arxiv.org/abs/arXiv:hep-ph/0006124
Web End =arXiv:hep-ph/0006124
48. C.W. Bauer, S. Fleming, D. Pirjol, I.W. Stewart, An effective eld theory for collinear and soft gluons: heavy to light decays. Phys. Rev. D 63, 114020 (2001). http://arxiv.org/abs/arXiv:hep-ph/0011336
Web End =arXiv:hep-ph/0011336
49. C.W. Bauer, D. Pirjol, I.W. Stewart, Soft collinear factorization in effective eld theory. Phys. Rev. D 65, 054022 (2002). http://arxiv.org/abs/arXiv:hep-ph/0109045
Web End =arXiv:hep-ph/0109045
50. M. Beneke, T. Feldmann, D. Seidel, Systematic approach to exclusive B V + , V decays. Nucl. Phys. B 612, 25 (2001).
http://arxiv.org/abs/arXiv:hep-ph/0106067
Web End =arXiv:hep-ph/0106067 51. M. Beneke, T. Feldmann, D. Seidel, Exclusive radiative and electroweak b d and b s penguin decays at NLO. Eur. Phys. J.
C 41, 173 (2005). http://arxiv.org/abs/arXiv:hep-ph/0412400
Web End =arXiv:hep-ph/0412400 52. J. Charles et al., Heavy-to-light form factors in the nal hadron large energy limit of QCD. Phys. Rev. D 60, 014001 (1999). http://arxiv.org/abs/arXiv:hep-ph/9812358
Web End =arXiv:hep-ph/9812358
53. U. Egede et al., New observables in the decay mode Bd K0 + . J. High Energy Phys. 11, 032 (2008). arXiv:0807. 258954. U. Egede et al., New physics reach of the decay mode B K0 + . J. High Energy Phys. 10, 056 (2010). arXiv:1005. 057155. J. Matias, F. Mescia, M. Ramon, J. Virto, Complete anatomy of
Bd K0( K) + and its angular distribution. J. High
Energy Phys. 04, 104 (2012). arXiv:1202.426656. A. Khodjamirian, T. Mannel, A. Pivovarov, Y.-M. Wang, Charm-loop effect in B K() + and B K . J. High Energy
Phys. 09, 089 (2010). arXiv:1006.494557. B. Grinstein, D. Pirjol, Exclusive rare B K + decays at
low recoil: controlling the long-distance effects. Phys. Rev. D 70, 114005 (2004). http://arxiv.org/abs/arXiv:hep-ph/0404250
Web End =arXiv:hep-ph/0404250 58. M. Beylich, G. Buchalla, T. Feldmann, Theory of B
K() + decays at high q2: OPE and quarkhadron duality. Eur. Phys. J. C 71, 1635 (2011). arXiv:1101.5118
Eur. Phys. J. C (2013) 73:2373 Page 77 of 92
59. N. Isgur, M.B. Wise, Weak transition form-factors between heavy mesons. Phys. Lett. B 237, 527 (1990)
60. Z. Liu et al., A lattice calculation of B K() form factors,
in Proceedings of CKM2010, the 6th International Workshop on the CKM Unitarity Triangle, University of Warwick, UK, 610 September 2010. arXiv:1101.272661. F. Krger, L.M. Sehgal, N. Sinha, R. Sinha, Angular distribution and CP asymmetries in the decays B K+ee+ and B
+ee+. Phys. Rev. D 61, 114028 (2000). http://arxiv.org/abs/arXiv:hep-ph/9907386
Web End =arXiv:hep-ph/ 990738662. W. Altmannshofer et al., Symmetries and asymmetries of B
K+ decays in the Standard Model and beyond. J. High Energy Phys. 01, 019 (2009). arXiv:0811.121463. F. Krger, J. Matias, Probing new physics via the transverse amplitudes of B0 K0( K+) + at large recoil. Phys.
Rev. D 71, 094009 (2005). http://arxiv.org/abs/arXiv:hep-ph/0502060
Web End =arXiv:hep-ph/0502060 64. C. Bobeth, G. Hiller, G. Piranishvili, CP asymmetries in B K( K) and untagged Bs, Bs ( K+K) decays
at NLO. J. High Energy Phys. 07, 106 (2008). arXiv:0805.252565. C. Bobeth, G. Hiller, D. van Dyk, The benets of B K +
decays at low recoil. J. High Energy Phys. 07, 098 (2010). arXiv: 1006.501366. C. Bobeth, G. Hiller, D. van Dyk, More benets of semileptonic rare B decays at low recoil: CP violation. J. High Energy Phys. 07, 067 (2011). arXiv:1105.0376
67. M. Benzke, S.J. Lee, M. Neubert, G. Paz, Long-distance dominance of the CP asymmetry in B Xs,d decays. Phys. Rev.
Lett. 106, 141801 (2011). arXiv:1012.316768. LHCb Collaboration, Differential branching fraction and angular analysis of the B0 K0+ decay. LHCb-CONF-2012-008
69. LHCb Collaboration, Measurement of the ratio of branching fractions for B0s and B0s J/. LHCb-CONF-
2012-00370. J.-T. Wei et al. (Belle Collaboration), Measurement of the differential branching fraction and forwardbackward asymmetry for B K() + . Phys. Rev. Lett. 103, 171801 (2009). arXiv:
0904.077071. T. Aaltonen et al. (CDF Collaboration), Measurements of the angular distributions in the decays B K()+ at CDF. Phys.
Rev. Lett. 108, 081807 (2012). arXiv:1108.069572. S. Descotes-Genon, J. Matias, M. Ramon, J. Virto, Implications from clean observables for the binned analysis of B Kll at
large recoil. J. High Energy Phys. 01, 048 (2013). arXiv:1207. 275373. A. Bharucha, W. Reece, Constraining new physics with B
K+ in the early LHC era. Eur. Phys. J. C 69, 623 (2010). arXiv:1002.431074. C. Hambrock, G. Hiller, Extracting B K form factors from
data. Phys. Rev. Lett. 109, 091802 (2012). arXiv:1204.444475. T. Aaltonen et al. (CDF Collaboration), Observation of the baryonic avor-changing neutral current decay b +. Phys.
Rev. Lett. 107, 201802 (2011). arXiv:1107.375376. J.P. Lees et al. (BaBar Collaboration), Measurement of branching fractions and rate asymmetries in the rare decays B
K() + . Phys. Rev. D 86, 032012 (2012). arXiv:1204.393377. R. Aaij et al. (LHCb Collaboration), Measurement of the isospin asymmetry in B K()+ decays. J. High Energy Phys. 07,
133 (2012). arXiv:1205.342278. C. Bobeth, G. Hiller, G. Piranishvili, Angular distributions of B K + decays. J. High Energy Phys. 12, 040 (2007).
arXiv:0709.417479. D. Becirevic, N. Kosnik, F. Mescia, E. Schneider, Complementarity of the constraints on New Physics from B0s + and
from B Kl+l decays. Phys. Rev. D 86, 034034 (2012).
arXiv:1205.581180. J.P. Lees et al. (BaBar Collaboration), Evidence for an excess of B D()
decays. Phys. Rev. Lett. 109, 101802 (2012). arXiv:1205.5442
81. A. Matyja et al. (Belle Collaboration), Observation of B0
D+ decay at Belle. Phys. Rev. Lett. 99, 191807 (2007). arXiv:0706.442982. A. Bozek et al. (Belle Collaboration), Observation of B+ D0+ and evidence for B+ D0+ at Belle. Phys. Rev.
D 82, 072005 (2010). arXiv:1005.230283. G. Hiller, F. Krger, More model independent analysis of b
s processes. Phys. Rev. D 69, 074020 (2004). http://arxiv.org/abs/arXiv:hep-ph/0310219
Web End =arXiv:hep-ph/ 031021984. N. Taniguchi et al. (Belle Collaboration), Measurement of branching fractions, isospin and CP-violating asymmetries for exclusive b d modes. Phys. Rev. Lett. 101, 111801 (2008).
arXiv:0804.477085. P. del Amo Sanchez et al. (BaBar Collaboration), Study of B
X decays and determination of |Vtd/Vts|. Phys. Rev. D 82,
051101 (2010). arXiv:1005.408786. R. Aaij et al. (LHCb Collaboration), First observation of the decay B+ ++. J. High Energy Phys. 12, 125 (2012).
arXiv:1210.264587. T. Feldmann, J. Matias, Forwardbackward and isospin asymmetry for B K + decay in the standard model and in super-
symmetry. J. High Energy Phys. 01, 074 (2003). http://arxiv.org/abs/arXiv:hep-ph/0212158
Web End =arXiv:hep-ph/ 021215888. A. Khodjamirian, T. Mannel, Y.-M. Wang, B K + decay
at large hadronic recoil. J. High Energy Phys. (2013). doi:10. 1007/JHEP02(2013)010. arXiv:1211.023489. D. Atwood, M. Gronau, A. Soni, Mixing induced CP asymme-tries in radiative B decays in and beyond the standard model. Phys. Rev. Lett. 79, 185 (1997). http://arxiv.org/abs/arXiv:hep-ph/9704272
Web End =arXiv:hep-ph/9704272
90. D. Atwood, T. Gershon, M. Hazumi, A. Soni, Mixing-induced CP violation in B P1P2 in search of clean new physics sig
nals. Phys. Rev. D 71, 076003 (2005). http://arxiv.org/abs/arXiv:hep-ph/0410036
Web End =arXiv:hep-ph/0410036 91. F. Muheim, Y. Xie, R. Zwicky, Exploiting the width difference in Bs . Phys. Lett. B 664, 174 (2008). arXiv:0802.0876
92. F. Legger, T. Schietinger, Polarized radiative b decays at LHCb. CERN-LHCB-2006-013
93. G. Hiller, M. Knecht, F. Legger, T. Schietinger, Photon polarization from helicity suppression in radiative decays of polarized b to spin-3/2 baryons. Phys. Lett. B 649, 152 (2007). http://arxiv.org/abs/arXiv:hep-ph/0702191
Web End =arXiv:hep http://arxiv.org/abs/arXiv:hep-ph/0702191
Web End =ph/0702191
94. Y.-M. Wang, Y. Li, C.-D. Lu, Rare decays of 0b and
0b l+l in the light-cone sum rules. Eur. Phys. J. C 59,
861 (2009). arXiv:0804.064895. T. Mannel, Y.-M. Wang, Heavy-to-light baryonic form factors at large recoil. J. High Energy Phys. 12, 067 (2011). arXiv:1111. 1849
96. T. Feldmann, M.W.Y. Yip, Form factors for b transitions
in the soft-collinear effective theory. Phys. Rev. D 85, 014035 (2012). arXiv:1111.184497. M. Gronau, Y. Grossman, D. Pirjol, A. Ryd, Measuring the photon polarization in B K . Phys. Rev. Lett. 88, 051802
(2002). http://arxiv.org/abs/arXiv:hep-ph/0107254
Web End =arXiv:hep-ph/0107254 98. M. Gronau, D. Pirjol, Photon polarization in radiative B decays. Phys. Rev. D 66, 054008 (2002). http://arxiv.org/abs/arXiv:hep-ph/0205065
Web End =arXiv:hep-ph/0205065
99. D. Atwood, T. Gershon, M. Hazumi, A. Soni, Clean signals of CP-violating and CP-conserving New Physics in B P V de
cays at B factories and hadron colliders. http://arxiv.org/abs/arXiv:hep-ph/0701021
Web End =arXiv:hep-ph/0701021 100. E. Kou, A. Le Yaouanc, A. Tayduganov, Determining the photon polarization of the b s using the B K1(1270)
(K) decay. Phys. Rev. D 83, 094007 (2011). arXiv:1011. 6593101. B. Aubert et al. (BaBar Collaboration), Measurement of B decays to K . Phys. Rev. D 75, 051102 (2007). http://arxiv.org/abs/arXiv:hep-ex/0611037
Web End =arXiv:hep-ex/ 0611037102. H. Yang et al. (Belle Collaboration), Observation of B+
K1(1270)+ . Phys. Rev. Lett. 94, 111802 (2005). http://arxiv.org/abs/arXiv:hep-ex/0412039
Web End =arXiv:hep-ex/ 0412039
Page 78 of 92 Eur. Phys. J. C (2013) 73:2373
103. C. Bobeth, T. Ewerth, F. Krger, J. Urban, Analysis of neutral Higgs boson contributions to the decays B(s) + and B K + . Phys. Rev. D 64, 074014 (2001). http://arxiv.org/abs/arXiv:hep-ph/0104284
Web End =arXiv:hep-ph/
0104284
104. C. Bobeth, A.J. Buras, F. Krger, J. Urban, QCD corrections to
B Xd,s , Bd,s + , K and KL + in the
MSSM. Nucl. Phys. B 630, 87 (2002). http://arxiv.org/abs/arXiv:hep-ph/0112305
Web End =arXiv:hep-ph/0112305 105. A.J. Buras, P.H. Chankowski, J. Rosiek, L. Slawianowska,
Md,s, B0d,s + and B Xs in supersymmetry at large
tan . Nucl. Phys. B 659, 3 (2003). http://arxiv.org/abs/arXiv:hep-ph/0210145
Web End =arXiv:hep-ph/0210145 106. F. Mahmoudi, SuperIso v2.3: a program for calculating avor physics observables in supersymmetry. Comput. Phys. Commun. 180, 1579 (2009). arXiv:0808.3144107. E. Gamiz et al. (HPQCD Collaboration), Neutral B meson mixing in unquenched lattice QCD. Phys. Rev. D 80, 014503 (2009). arXiv:0902.1815108. C. Bernard et al., B and D meson decay constants. PoS LAT
TICE2008, 278 (2008). arXiv:0904.1895109. J. Laiho, E. Lunghi, R.S. Van de Water, Lattice QCD inputs to the CKM unitarity triangle analysis. Phys. Rev. D 81, 034503 (2010). arXiv:0910.2928, updated results and plots available at: http://www.latticeaverages.org/
Web End =http://www.latticeaverages.org/ 110. J. Simone et al. (Fermilab Lattice and MILC Collaborations),
The decay constants fDs , fD+ , fBs and fB from lattice QCD.
PoS LATTICE2010, 317 (2010)
111. A. Bazavov et al. (Fermilab Lattice and MILC Collaborations), B- and D-meson decay constants from three-avor lattice QCD.
Phys. Rev. D 85, 114506 (2012). arXiv:1112.3051112. E.T. Neil et al. (Fermilab Lattice Collaboration, MILC Collaboration), B and D meson decay constants from 2 + 1 avor im
proved staggered simulations. PoS LATTICE2011, 320 (2011). arXiv:1112.3978113. P. Dimopoulos et al. (ETM Collaboration), Lattice QCD determination of mb, fB and fBs with twisted mass Wilson fermions.
J. High Energy Phys. 01, 046 (2012). arXiv:1107.1441114. C. McNeile et al., High-precision fBs and heavy quark effective theory from relativistic lattice QCD. Phys. Rev. D 85, 031503 (2012). arXiv:1110.4510115. H. Na et al., B and Bs meson decay constants from lattice QCD.
Phys. Rev. D 86, 034506 (2012). arXiv:1202.4914116. A.J. Buras, J. Girrbach, BSM models facing the recent LHCb data: a rst look. Acta Phys. Pol. B 43, 1427 (2012). arXiv:1204. 5064117. A.J. Buras, J. Girrbach, D. Guadagnoli, G. Isidori, On the Standard Model prediction for B(Bs,d +). Eur. Phys. J. C 72,
2172 (2012). arXiv:1208.0934118. A.J. Buras, M.V. Carlucci, S. Gori, G. Isidori, Higgs-mediated
FCNCs: natural avour conservation vs. minimal avour violation. J. High Energy Phys. 10, 009 (2010). arXiv:1005.5310 119. J. Charles et al., Predictions of selected avor observables within the Standard Model. Phys. Rev. D 84, 033005 (2011). arXiv:1106.4041120. F. Mahmoudi, S. Neshatpour, J. Orloff, Supersymmetric constraints from Bs + and B K+ observables. J.
High Energy Phys. 08, 092 (2012). arXiv:1205.1845121. S.R. Choudhury, N. Gaur, Dileptonic decay of Bs meson in
SUSY models with large tan . Phys. Lett. B 451, 86 (1999). http://arxiv.org/abs/arXiv:hep-ph/9810307
Web End =arXiv:hep-ph/9810307 122. K.S. Babu, C. Kolda, Higgs mediated B0 + in minimal
supersymmetry. Phys. Rev. Lett. 84, 228 (2000). http://arxiv.org/abs/arXiv:hep-ph/9909476
Web End =arXiv:hep-ph/ 9909476123. J. Ellis, K.A. Olive, V.C. Spanos, On the interpretation of Bs
+ in the CMSSM. Phys. Lett. B 624, 47 (2005). http://arxiv.org/abs/arXiv:hep-ph/0504196
Web End =arXiv:hep http://arxiv.org/abs/arXiv:hep-ph/0504196
Web End =ph/0504196 124. M. Carena et al., Constraints on B and Higgs physics in minimal low energy supersymmetric models. Phys. Rev. D 74, 015009 (2006). http://arxiv.org/abs/arXiv:hep-ph/0603106
Web End =arXiv:hep-ph/0603106
125. J. Ellis, S. Heinemeyer, K.A. Olive, G. Weiglein, Light heavy
MSSM Higgs bosons at large tan . Phys. Lett. B 653, 292 (2007). arXiv:0706.0977126. F. Mahmoudi, New constraints on supersymmetric models from b s . J. High Energy Phys. 12, 026 (2007). arXiv:0710.3791
127. E. Golowich et al., Relating Bs mixing and Bs + with
New Physics. Phys. Rev. D 83, 114017 (2011). arXiv:1102.0009 128. A.G. Akeroyd, F. Mahmoudi, D. Martinez Santos, The decay
Bs +: updated SUSY constraints and prospects. J. High
Energy Phys. 12, 088 (2011). arXiv:1108.3018129. O. Buchmueller et al., Supersymmetry in light of 1/fb of LHC data. Eur. Phys. J. C 72, 1878 (2012). arXiv:1110.3568130. S. Chatrchyan et al. (CMS Collaboration), Search for B0s
+ and B0 + decays. J. High Energy Phys. 04, 033
(2012). arXiv:1203.3976131. M. Blanke et al., Rare and CP-violating K and B decays in the littlest Higgs model with T -parity. J. High Energy Phys. 01, 066 (2007). http://arxiv.org/abs/arXiv:hep-ph/0610298
Web End =arXiv:hep-ph/0610298 132. M. Blanke et al., Rare K and B decays in a warped extra dimension with custodial protection. J. High Energy Phys. 03, 108 (2009). arXiv:0812.3803133. W. Liu, C.-X. Yue, H.-D. Yang, Rare decays Bs + and
B K + in the topcolor-assisted technicolor model. Phys.
Rev. D 79, 034008 (2009). arXiv:0901.3463134. M. Bauer, S. Casagrande, U. Haisch, M. Neubert, Flavor physics in the RandallSundrum model: II. Tree-level weak-interaction processes. J. High Energy Phys. 09, 017 (2010). arXiv:0912. 1625135. A.J. Buras et al., Lepton avour violation in the presence of a fourth generation of quarks and leptons. J. High Energy Phys. 09, 104 (2010). arXiv:1006.5356136. K. de Bruyn et al., Probing new physics via the B0s
+ effective lifetime. Phys. Rev. Lett. 109, 041801 (2012). arXiv:1204.1737137. K. de Bruyn et al., Branching Ratio Measurements of Bs Decays.
Phys. Rev. D 86, 014027 (2012). arXiv:1204.1735138. S. Descotes-Genon, J. Matias, J. Virto, An analysis of Bd,s mixing angles in presence of new physics and an update of B0s
K0 K0. Phys. Rev. D 85, 034010 (2012). arXiv:1111.4882
139. LHCb Collaboration, Tagged time-dependent angular analysis of
B0s J/ decays at LHCb. LHCb-CONF-2012-002
140. R. Aaij et al. (LHCb Collaboration), Measurements of the branching fractions of the decays B0s DsK and B0s
Ds+. J. High Energy Phys. 06, 115 (2012). arXiv:1204.1237 141. R. Aaij et al. (LHCb Collaboration), Measurement of the ratio of fragmentation functions fs/fd and the dependence on B meson kinematics. J. High Energy Phys. (2013). doi:10.1007/ JHEP04(2013)001. arXiv:1301.5286142. R. Fleischer, N. Serra, N. Tuning, A new strategy for B0s branching ratio measurements and the search for New Physics in B0s
+. Phys. Rev. D 82, 034038 (2010). arXiv:1004.3982143. R. Fleischer, N. Serra, N. Tuning, Tests of factorization and
SU(3) relations in B decays into heavy-light nal states. Phys. Rev. D 83, 014017 (2011). arXiv:1012.2784144. J.A. Bailey et al., Bs Ds/B D semileptonic form-factor
ratios and their application to B(B0s +). Phys. Rev. D 85,
114502 (2012). arXiv:1202.6346145. R. Aaij et al. (LHCb Collaboration), Measurement of b hadron production fractions in 7 TeV pp collisions. Phys. Rev. D 85, 032008 (2012). arXiv:1111.2357146. I.I. Bigi, M.A. Shifman, N. Uraltsev, A.I. Vainshtein, High power n of m(b) in beauty widths and n = 5 innity limit. Phys. Rev.
D 56, 4017 (1997). http://arxiv.org/abs/arXiv:hep-ph/9704245
Web End =arXiv:hep-ph/9704245 147. I. Bigi, T. Mannel, N. Uraltsev, Semileptonic width ratios among beauty hadrons. J. High Energy Phys. 09, 012 (2011). arXiv: 1105.4574
Eur. Phys. J. C (2013) 73:2373 Page 79 of 92
148. J.P. Alexander et al. (CLEO Collaboration), Absolute measurement of hadronic branching fractions of the D+s meson. Phys.
Rev. Lett. 100, 161804 (2008). arXiv:0801.0680149. M. Wang (Belle Collaboration), Charm decays at Belle, talk given at ICHEP 2012, Melbourne, July 5th 2012, slides available online150. G. Aad et al. (ATLAS Collaboration), Search for the decay B0s
+ with the ATLAS detector. Phys. Lett. B 713, 387 (2012). arXiv:1204.0735151. T. Aaltonen et al. (CDF Collaboration), Search for Bs +
and Bd + decays with CDF II. Phys. Rev. Lett. 107,
191801 (2011). arXiv:1107.2304152. C.W. Bauer, N.D. Dunn, Comment on new physics contributions to s12. Phys. Lett. B 696, 362 (2011). arXiv:1006.1629153. C. Bobeth, U. Haisch, New physics in s12: (sb) (
) operators.
arXiv:1109.1826154. A. Dighe, A. Kundu, S. Nandi, Possibility of large lifetime differences in neutral B meson systems. Phys. Rev. D 76, 054005 (2007). arXiv:0705.4547155. A. Dighe, A. Kundu, S. Nandi, Enhanced Bs Bs lifetime differ-
ence and anomalous like-sign dimuon charge asymmetry from new physics in Bs +. Phys. Rev. D 82, 031502 (2010).
arXiv:1005.4051156. A.K. Alok, S. Baek, D. London, Neutral gauge boson contributions to the dimuon charge asymmetry in B decays. J. High Energy Phys. 07, 111 (2011). arXiv:1010.1333157. J.E. Kim, M.-S. Seo, S. Shin, The D0 same-charge dimuon asymmetry and possibile new CP violation sources in the Bs Bs system. Phys. Rev. D 83, 036003 (2011). arXiv:1010.5123158. H.D. Kim, S.-G. Kim, S. Shin, D0 dimuon charge asymmetry from Bs system with Z couplings and the recent LHCb result.
arXiv:1205.6481159. V.M. Abazov et al. (D0 Collaboration), Measurement of the anomalous like-sign dimuon charge asymmetry with 9 fb1 of p p collisions. Phys. Rev. D 84, 052007 (2011). arXiv:1106.6308
160. R. Aaij et al. (LHCb Collaboration), A study of the Z production cross-section in pp collisions at s = 7 TeV using tau nal
states. J. High Energy Phys. 01, 111 (2013). arXiv:1210.6289 161. R. Aaij et al. (LHCb Collaboration), Measurement of the CP asymmetry in B0 K0+ decays. Phys. Rev. Lett. 110,
031801 (2013). arXiv:1210.4492
162. F. Mahmoudi, Direct and indirect searches for New Physics, in
Proceedings of Moriond QCD (2012). arXiv:1205.3099163. F. Mahmoudi, SuperIso: a program for calculating the isospin asymmetry of B K in the MSSM. Comput. Phys. Com
mun. 178, 745 (2008). arXiv:0710.2067164. S. Chatrchyan et al. (CMS Collaboration), Search for supersymmetry at the LHC in events with jets and missing transverse energy. Phys. Rev. Lett. 107, 221804 (2011). arXiv:1109.2352 165. CMS Collaboration, Search for supersymmetry with the razor variables at CMS, CMS-PAS-SUS-12-005, 2012166. D.A. Demir, K.A. Olive, M. Voloshin, The forward backward asymmetry of B (, K) + : Supersymmetry at work. Phys.
Rev. D 66, 034015 (2002). http://arxiv.org/abs/arXiv:hep-ph/0204119
Web End =arXiv:hep-ph/0204119 167. A. Behring, C. Gross, G. Hiller, S. Schacht, Squark avor implications from B K()l+l. J. High Energy Phys. 08, 152
(2012). arXiv:1205.1500168. O. Buchmueller et al., The CMSSM and NUHM1 in light of7 TeV LHC, B0s + and XENON100 data. Eur. Phys. J.
C 72, 2243 (2012). arXiv:1207.7315169. A. Crivellin, U. Nierste, Supersymmetric renormalisation of the
CKM matrix and new constraints on the squark mass matrices. Phys. Rev. D 79, 035018 (2009). arXiv:0810.1613170. O. Buchmueller et al., Higgs and supersymmetry. Eur. Phys. J. C
72, 2020 (2012). arXiv:1112.3564
171. A. Djouadi et al. (MSSM Working Group), The minimal super-symmetric standard model: group summary report. http://arxiv.org/abs/arXiv:hep-ph/9901246
Web End =arXiv:hep http://arxiv.org/abs/arXiv:hep-ph/9901246
Web End =ph/9901246
172. A. Arbey, M. Battaglia, F. Mahmoudi, Constraints on the MSSM from the Higgs sector: a pMSSM study of Higgs searches, B0s
+ and dark matter direct detection. Eur. Phys. J. C 72, 1906 (2012). arXiv:1112.3032173. LHCb Collaboration, Search for the rare decays B0(s) at
the LHC with the ATLAS, CMS and LHCb experiments. LHCb-CONF-2012-017174. G. Aad et al. (ATLAS Collaboration), Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B 716, 1 (2012). arXiv:1207.7214175. S. Chatrchyan et al. (CMS Collaboration), Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B 716, 30 (2012). arXiv:1207.7235176. G. Burdman, E. Golowich, J. Hewett, S. Pakvasa, Rare charm decays in the standard model and beyond. Phys. Rev. D 66, 014009 (2002). http://arxiv.org/abs/arXiv:hep-ph/0112235
Web End =arXiv:hep-ph/0112235 177. E. Golowich, J. Hewett, S. Pakvasa, A.A. Petrov, Relating D0
D0 mixing and D0 l+l with New Physics. Phys. Rev. D 79,
114030 (2009). arXiv:0903.2830178. LHCb Collaboration, Search for the D0 + decay with
0.9 fb1 at LHCb. LHCb-CONF-2012-005
179. G. Buchalla et al., B, D and K decays. Eur. Phys. J. C 57, 309
(2008). arXiv:0801.1833180. S. Fajfer, N. Kosnik, S. Prelovsek, Updated constraints on new physics in rare charm decays. Phys. Rev. D 76, 074010 (2007). arXiv:0706.1133181. V.M. Abazov et al. (D0 Collaboration), Search for avor-changing-neutral-current D meson decays. Phys. Rev. Lett. 100, 101801 (2008). arXiv:0708.2094182. I.I. Bigi, A. Paul, On CP asymmetries in two-, three- and four-body D decays. J. High Energy Phys. 03, 021 (2012). arXiv: 1110.2862183. L. Cappiello, O. Cata, G. DAmbrosio, Standard Model prediction and new physics tests for D0 h+hl+l (h = , K:
l = e, ). arXiv:1209.4235
184. G. Ecker, A. Pich, The longitudinal muon polarization in KL
+. Nucl. Phys. B 366, 189 (1991)185. G. Isidori, R. Unterdorfer, On the short distance constraints from
KL,S +. J. High Energy Phys. 01, 009 (2004). arXiv:
http://arxiv.org/abs/arXiv:hep-ph/0311084
Web End =hep-ph/0311084 186. S. Gjesdal et al., Search for the decay K0S . Phys. Lett. B
44, 217 (1973)187. R. Aaij et al. (LHCb Collaboration), Search for the rare decay
KS +. J. High Energy Phys. 01, 090 (2013). arXiv:1209.
4029188. W.J. Marciano, T. Mori, J.M. Roney, Charged lepton avour violation experiments. Annu. Rev. Nucl. Part. Sci. 58, 315 (2008) 189. M. Raidal et al., Flavour physics of leptons and dipole moments.
Eur. Phys. J. C 57, 13 (2008). arXiv:0801.1826190. K. Nakamura et al. (Particle Data Group), Review of particle physics. J. Phys. G 37, 075021 (2010), and 2011 partial update for the 2012 edition191. LHCb Collaboration, Search for the lepton avour violating decay +. LHCb-CONF-2012-015
192. LHCb Collaboration, Search for the lepton avour violating and baryon number violating decays p+ and
p. LHCb-CONF-2012-027193. J.C. Pati, A. Salam, Lepton number as the fourth color. Phys.
Rev. D 10, 275 (1974), Phys. Rev. D 11, 703 (1975). Erratum 194. L.G. Landsberg, Is it still worth searching for lepton avor violation in rare kaon decays? Phys. At. Nucl. 68, 1190 (2005). arXiv: http://arxiv.org/abs/arXiv:hep-ph/0410261
Web End =hep-ph/0410261
Page 80 of 92 Eur. Phys. J. C (2013) 73:2373
195. D. Gorbunov, M. Shaposhnikov, How to nd neutral leptons of the nuMSM? J. High Energy Phys. 10, 015 (2007). arXiv:0705. 1729
196. R. Aaij et al. (LHCb Collaboration), Search for the lepton number violating decays B+ ++ and B+ K++.
Phys. Rev. Lett. 108, 101601 (2012). arXiv:1110.0730197. R. Aaij et al. (LHCb Collaboration), Searches for Majorana neutrinos in B decays. Phys. Rev. D 85, 112004 (2012). arXiv: 1201.5600198. Y. Kahn, M. Schmitt, T.M.P. Tait, Enhanced rare pion decays from a model of MeV dark matter. Phys. Rev. D 78, 115002 (2008). arXiv:0712.0007199. R. Dermisek, J.F. Gunion, Consistency of LEP event excesses with an h aa decay scenario and low-ne-tuning next-to-
minimal supersymmetric Standard Models. Phys. Rev. D 73, 111701 (2006). http://arxiv.org/abs/arXiv:hep-ph/0510322
Web End =arXiv:hep-ph/0510322 200. C. Bouchiat, P. Fayet, Constraints on the parity-violating couplings of a new gauge boson. Phys. Lett. B 608, 87 (2005). arXiv: http://arxiv.org/abs/arXiv:hep-ph/0410260
Web End =hep-ph/0410260 201. C. Boehm et al., MeV dark matter: has it been detected? Phys.
Rev. Lett. 92, 101301 (2004). http://arxiv.org/abs/arXiv:astro-ph/0309686
Web End =arXiv:astro-ph/0309686 202. D.S. Gorbunov, V.A. Rubakov, Kaon physics with light sgoldstinos and parity conservation. Phys. Rev. D 64, 054008 (2001). http://arxiv.org/abs/arXiv:hep-ph/0012033
Web End =arXiv:hep-ph/0012033 203. O. Adriani et al. (PAMELA Collaboration), An anomalous positron abundance in cosmic rays with energies 1.5100 GeV.Nature 458, 607 (2009). arXiv:0810.4995204. J. Chang et al., An excess of cosmic ray electrons at energies of
300800 GeV. Nature 456, 362 (2008)205. H.K. Park et al. (HyperCP Collaboration), Evidence for the decay + p+. Phys. Rev. Lett. 94, 021801 (2005).
http://arxiv.org/abs/arXiv:hep-ex/0501014
Web End =arXiv:hep-ex/0501014 206. N. Deshpande, G. Eilam, J. Jiang, On the possibility of a new boson X0(214 MeV) in + p+. Phys. Lett. B 632, 212
(2006). http://arxiv.org/abs/arXiv:hep-ph/0509081
Web End =arXiv:hep-ph/0509081 207. D. Gorbunov, V. Rubakov, On sgoldstino interpretation of HyperCP events. Phys. Rev. D 73, 035002 (2006). http://arxiv.org/abs/arXiv:hep-ph/0509147
Web End =arXiv:hep-ph/ 0509147208. C.Q. Geng, Y.K. Hsiao, Constraints on the new particle in +
p+. Phys. Lett. B 632, 215 (2006). http://arxiv.org/abs/arXiv:hep-ph/0509175
Web End =arXiv:hep-ph/0509175 209. X.-G. He, J. Tandean, G. Valencia, Does the HyperCP evidence for the decay p+ indicate a light pseudoscalar
Higgs boson? Phys. Rev. Lett. 98, 081802 (2007). http://arxiv.org/abs/arXiv:hep-ph/0610362
Web End =arXiv:hep-ph/ 0610362210. LHCb Collaboration, Search for the rare decays B0s
++ and B0d ++. LHCb-CONF-2012-010
211. S. Demidov, D. Gorbunov, Flavor violating processes with sgoldstino pair production. Phys. Rev. D 85, 077701 (2012). arXiv:1112.5230
212. H.J. Hyun et al. (Belle Collaboration), Search for a low mass particle decaying into + in B0 K0X and B0 0X at
Belle. Phys. Rev. Lett. 105, 091801 (2010). arXiv:1005.1450 213. M. Freytsis, Z. Ligeti, J. Thaler, Constraining the axion portal with B Kl+l. Phys. Rev. D 81, 034001 (2010). arXiv:0911.
5355214. A.D. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the Universe. Pisma Zh. Eksp. Teor. Fiz. 5, 32 (1967), also available as JETP Lett. 5, 24 (1967)215. U. Nierste, Three lectures on meson mixing and CKM phenomenology. arXiv:0904.1869216. A. Lenz, Theoretical update of B-mixing and lifetimes. arXiv:
1205.1444217. A. Lenz, Theoretical status of Bs-mixing and lifetimes of heavy hadrons. Nucl. Phys. B, Proc. Suppl. 177178, 81 (2008). arXiv:0705.3802
218. R. Aaij et al. (LHCb Collaboration), Measurement of the CP violating phase s in B0s J/f0(980). Phys. Lett. B 707, 497
(2012). arXiv:1112.3056219. R. Aaij et al. (LHCb Collaboration), Measurement of the CP-violating phase s in Bs J/+ decays. Phys. Lett. B
713, 378 (2012). arXiv:1204.5675220. A. Lenz, U. Nierste, Numerical updates of lifetimes and mixing parameters of B mesons, in Proceedings of CKM2010, the 6th International Workshop on the CKM Unitarity Triangle, University of Warwick, UK, 610 September (2010). arXiv:1102.4274 221. A. Lenz, U. Nierste, Theoretical update of B0sB0s mixing.
J. High Energy Phys. 06, 072 (2007). http://arxiv.org/abs/arXiv:hep-ph/0612167
Web End =arXiv:hep-ph/0612167 222. M. Beneke et al., Next-to-leading order QCD corrections to the lifetime difference of B0s mesons. Phys. Lett. B 459, 631 (1999).
http://arxiv.org/abs/arXiv:hep-ph/9808385
Web End =arXiv:hep-ph/9808385 223. M. Ciuchini et al., Lifetime differences and CP violation parameters of neutral B mesons at the next-to-leading order in QCD.J. High Energy Phys. 08, 031 (2003). http://arxiv.org/abs/arXiv:hep-ph/0308029
Web End =arXiv:hep-ph/0308029 224. M. Beneke, G. Buchalla, I. Dunietz, Width difference in the
B0sB0s system. Phys. Rev. D 54, 4419 (1996). http://arxiv.org/abs/arXiv:hep-ph/9605259
Web End =arXiv:hep-ph/ 9605259225. M. Beneke, G. Buchalla, A. Lenz, U. Nierste, CP asymmetry in avor specic B decays beyond leading logarithms. Phys. Lett. B 576, 173 (2003). http://arxiv.org/abs/arXiv:hep-ph/0307344
Web End =arXiv:hep-ph/0307344 226. LHCb Collaboration, Measurement of ms in the decay B0s
Ds(K+K)+ using opposite-side and same-side avour tagging algorithms. LHCb-CONF-2011-050227. V.M. Abazov et al. (D0 Collaboration), Search for CP violation in B0s +DsX decays in p p collisions at s = 1.96 TeV.
Phys. Rev. D 82, 012003 (2010). arXiv:0904.3907228. A. Abulencia et al. (CDF Collaboration), Observation of B0sB0s oscillations. Phys. Rev. Lett. 97, 242003 (2006). http://arxiv.org/abs/arXiv:hep-ex/0609040
Web End =arXiv:hep-ex/
0609040229. R. Aaij et al. (LHCb Collaboration), Measurement of the B0s
B0s oscillation frequency ms in B0s Ds(3) decays. Phys.
Lett. B 709, 177 (2012). arXiv:1112.4311230. A.S. Dighe, I. Dunietz, R. Fleischer, Extracting CKM phases and
B0sB0s mixing parameters from angular distributions of nonlep-tonic B decays. Eur. Phys. J. C 6, 647 (1999). http://arxiv.org/abs/arXiv:hep-ph/9804253
Web End =arXiv:hep-ph/
9804253231. I. Dunietz, R. Fleischer, U. Nierste, In pursuit of new physics with B0s decays. Phys. Rev. D 63, 114015 (2001). http://arxiv.org/abs/arXiv:hep-ph/0012219
Web End =arXiv:hep-ph/
0012219232. R. Aaij et al. (LHCb Collaboration), Determination of the sign of the decay width difference in the Bs system. Phys. Rev. Lett.
108, 241801 (2012). arXiv:1202.4717
233. Y. Xie, P. Clarke, G. Cowan, F. Muheim, Determination of 2s in
B0s J/K+K decays in the presence of a K+K S-wave
contribution. J. High Energy Phys. 09, 074 (2009). arXiv:0908. 3627234. R. Aaij et al. (LHCb Collaboration), Analysis of the resonant components in B0s J/+. Phys. Rev. D 86, 052006
(2012). arXiv:1204.5643235. R. Fleischer, R. Knegjens, G. Ricciardi, Anatomy of B0s,d
J/f0(980). Eur. Phys. J. C 71, 1832 (2011). arXiv:1109.1112 236. R. Aaij et al. (LHCb Collaboration), Measurement of the B0s effective lifetime in the J/f0(980) nal state. Phys. Rev. Lett.
109, 152002 (2012). arXiv:1207.0878237. T. Aaltonen et al. (CDF Collaboration), Measurement of the CP-violating phase J/s in B0s J/ decays with the CDF II
detector. Phys. Rev. D 85, 072002 (2012). arXiv:1112.1726 238. V.M. Abazov et al. (D0 Collaboration), Measurement of the
CP-violating phase J/s using the avor-tagged decay B0s
J/ in 8 fb1 of p p collisions. Phys. Rev. D 85, 032006
(2012). arXiv:1109.3166
Eur. Phys. J. C (2013) 73:2373 Page 81 of 92
239. R. Aaij et al. (LHCb Collaboration), Opposite-side avour tagging of B mesons at the LHCb experiment. Eur. Phys. J. C 72, 2022 (2012). arXiv:1202.4979
240. LHCb Collaboration, Performance of avor tagging algorithms optimised for the analysis of B0s J/. LHCb-CONF-2012-
026241. LHCb Collaboration, Optimization and calibration of the same-side kaon tagging algorithm using hadronic B0s decays in 2011 data. LHCb-CONF-2012-033242. R. Fleischer, R. Knegjens, G. Ricciardi, Exploring CP violation and mixing with the B0s,d J/( ) systems. Eur. Phys. J.
C 71, 1798 (2011). arXiv:1110.5490243. R. Fleischer, Exploring CP violation and penguin effects through
B0d D+D and B0s D+sDs. Eur. Phys. J. C 51, 849 (2007).
arXiv:0705.4421244. LHCb Collaboration, First observations and branching fraction measurements of B0s to double-charm nal states. LHCb-CONF-
2012-009245. R. Aaij et al. (LHCb Collaboration), Evidence for the decay
B0 J/ and measurement of the relative branching frac
tions of B0s meson decays to J/ and J/ . Nucl. Phys. B 867, 547 (2013). arXiv:1210.2631246. C.-W. Chiang et al., New physics in B0s J/: a general anal
ysis. J. High Energy Phys. 04, 031 (2010). arXiv:0910.2929 247. V. Abazov et al. (D0 Collaboration), Measurement of the semileptonic charge asymmetry using B0s DsX decays.
Phys. Rev. Lett. 110, 011801 (2013). arXiv:1207.1769248. LHCb Collaboration, Measurement of the avour-specic CP violating asymmetry assl in B0s decays. LHCb-CONF-2012-022 249. K. Hara et al. (Belle Collaboration), Evidence for B
with a semileptonic tagging method. Phys. Rev. D 82, 071101 (2010). arXiv:1006.4201250. J.P. Lees et al. (BaBar Collaboration), Evidence of B de
cays with hadronic B tags. arXiv:1207.0698251. I. Adachi et al. (Belle Collaboration), Measurement of B
with a hadronic tagging method using the full data sample of Belle. Phys. Rev. Lett. (2013). doi:http://dx.doi.org/10.1103/PhysRevLett.110.131801
Web End =10.1103/PhysRevLett.110. 131801. arXiv:1208.4678252. J. Charles et al. (CKMtter group), CP violation and the CKM matrix: assessing the impact of the asymmetric B factories. Eur. Phys. J. C 41, 1 (2005). http://arxiv.org/abs/arXiv:hep-ph/0406184
Web End =arXiv:hep-ph/0406184 , updated results and plots available at http://ckmfitter.in2p3.fr
Web End =http://ckmtter.in2p3.fr 253. R. Aaij et al. (LHCb Collaboration), Measurement of the B0
B0 oscillation frequency md with the decays B0 J/K0
and B0 D+. Phys. Lett. B (2013). doi:http://dx.doi.org/10.1016/j.physletb.2013.01.019
Web End =10.1016/j.physletb.
2013.01.019. arXiv:1210.6750254. R. Aaij et al. (LHCb Collaboration), Measurement of the time-dependent CP asymmetry in B0 J/K0S decays. Phys. Lett. B
(2013). doi:http://dx.doi.org/10.1016/j.physletb.2013.02.054
Web End =10.1016/j.physletb.2013.02.054 . arXiv:1211.6093 255. T. Gershon, d: a forgotten null test of the Standard Model.
J. Phys. G 38, 015007 (2011). arXiv:1007.5135256. A. Lenz et al., Constraints on new physics in B B mixing in
the light of recent LHCb data. Phys. Rev. D 86, 033008 (2012). arXiv:1203.0238257. A.J. Lenz, A simple relation for B0s mixing. Phys. Rev. D 84,
031501 (2011). arXiv:1106.3200258. Y. Grossman, The Bs width difference beyond the standard model. Phys. Lett. B 380, 99 (1996). http://arxiv.org/abs/arXiv:hep-ph/9603244
Web End =arXiv:hep-ph/9603244 259. A. Lenz et al., Anatomy of new physics in B B mixing. Phys.
Rev. D 83, 036004 (2011). arXiv:1008.1593260. A. Badin, F. Gabbiani, A.A. Petrov, Lifetime difference in Bs mixing: Standard Model and beyond. Phys. Lett. B 653, 230 (2007). arXiv:0707.0294261. B.A. Dobrescu, P.J. Fox, A. Martin, CP violation in Bs mixing from heavy Higgs boson exchange. Phys. Rev. Lett. 105, 041801 (2010). arXiv:1005.4238
262. Z. Ligeti, M. Papucci, G. Perez, J. Zupan, Implications of the dimuon CP asymmetry in Bd,s decays. Phys. Rev. Lett. 105, 131601 (2010). arXiv:1006.0432
263. K. Flood (BaBar Collaboration), New results in radiative electroweak penguin decays at BaBar. PoS ICHEP2010, 234 (2010)
264. Y. Bai, A.E. Nelson, CP violating contribution to in the Bs system from mixing with a hidden pseudoscalar. Phys. Rev. D 82, 114027 (2010). arXiv:1007.0596
265. S. Oh, J. Tandean, Anomalous CP-violation in Bs Bs mixing due to a light spin-one particle. Phys. Lett. B 697, 41 (2011).
arXiv:1008.2153266. M. Bona et al. (UTt Collaboration), The 2004 UTt Collaboration report on the status of the unitarity triangle in the standard model. J. High Energy Phys., 07, 028 (2005). http://arxiv.org/abs/arXiv:hep-ph/0501199
Web End =arXiv:hep-ph/ 0501199, updated results and plots available at: http://www.utfit.org/UTfit/
Web End =http://www.utt. http://www.utfit.org/UTfit/
Web End =org/UTt/ 267. E. Lunghi, A. Soni, Possible evidence for the breakdown of the
CKM-paradigm of CP-violation. Phys. Lett. B 697, 323 (2011). arXiv:1010.6069268. G. Eigen, G. Dubois-Felsmann, D.G. Hitlin, F.C. Porter, Global
CKM Fits with the Scan Method. arXiv:1301.5867269. M. Bona et al. (UTt Collaboration), An improved Standard
Model prediction of B(B ) and its implications for new
physics. Phys. Lett. B 687, 61 (2010). arXiv:0908.3470270. M. Bona et al. (UTt Collaboration), Model-independent constraints on F = 2 operators and the scale of new physics.
J. High Energy Phys. 03, 049 (2008). arXiv:0707.0636271. I.I. Bigi, A.I. Sanda, Notes on the observability of CP violations in B decays. Nucl. Phys. B 193, 85 (1981)272. H. Boos, J. Reuter, T. Mannel, Gold plated mode reexamined: sin(2) and B0 J/K0S in the Standard Model. Phys. Rev. D
70, 036006 (2004). http://arxiv.org/abs/arXiv:hep-ph/0403085
Web End =arXiv:hep-ph/0403085 273. H.-n. Li, S. Mishima, Penguin pollution in the B0 J/K0S de
cay. J. High Energy Phys. 03, 009 (2007). http://arxiv.org/abs/arXiv:hep-ph/0610120
Web End =arXiv:hep-ph/0610120 274. M. Gronau, J.L. Rosner, Doubly CKM-suppressed corrections to CP asymmetries in B0 J/K0. Phys. Lett. B 672, 349
(2009). arXiv:0812.4796275. R. Fleischer, Extracting from Bs(d) J/K0S and Bd(s)
D+d(s)Dd(s). Eur. Phys. J. C 10, 299 (1999). http://arxiv.org/abs/arXiv:hep-ph/9903455
Web End =arXiv:hep-ph/ 9903455276. M. Ciuchini, M. Pierini, L. Silvestrini, Effect of penguin operators in the B0 J/K0 CP asymmetry. Phys. Rev. Lett. 95,
221804 (2005). http://arxiv.org/abs/arXiv:hep-ph/0507290
Web End =arXiv:hep-ph/0507290 277. S. Faller, R. Fleischer, T. Mannel, Precision physics with B0s
J/ at the LHC: the quest for new physics. Phys. Rev. D 79, 014005 (2009). arXiv:0810.4248278. S. Faller, M. Jung, R. Fleischer, T. Mannel, The golden modes
B0 J/KS,L in the era of precision avour physics. Phys.
Rev. D 79, 014030 (2009). arXiv:0809.0842279. M. Jung, T. Mannel, General analysis of U-spin breaking in B decays. Phys. Rev. D 80, 116002 (2009). arXiv:0907.0117280. K. De Bruyn, R. Fleischer, P. Koppenburg, Extracting gamma and penguin topologies through CP violation in B0s J/K0S.
Eur. Phys. J. C 70, 1025 (2010). arXiv:1010.0089281. M. Ciuchini, M. Pierini, L. Silvestrini, Theoretical uncertainty in sin 2: an update, in Proceedings of CKM2010, the 6th International Workshop on the CKM Unitarity Triangle, University of Warwick, UK, 610 September (2010). arXiv:1102.0392282. T. Aaltonen et al. (CDF Collaboration), Observation of B0s
J/K0(892) and B0s J/K0S decays. Phys. Rev. D 83,
052012 (2011). arXiv:1102.1961283. R. Aaij et al. (LHCb Collaboration), Measurement of Bs
J/ K0 branching fraction and angular amplitudes. Phys. Rev.
D 86, 071102(R) (2012). arXiv:1208.0738284. B. Bhattacharya, A. Datta, D. London, Reducing penguin pollution. arXiv:1209.1413
Page 82 of 92 Eur. Phys. J. C (2013) 73:2373
285. M. Jung, Determining weak phases from B J/P decays.
Phys. Rev. D 86, 053008 (2012). arXiv:1206.2050286. R. Aaij et al. (LHCb Collaboration), Measurements of the branching fractions and CP asymmetries of B+ J/+ and
B+ (2S)+ decays. Phys. Rev. 85, 091105 (2012). arXiv:
1203.3592
287. R. Aaij et al. (LHCb Collaboration), Measurement of the B0s
J/K0S branching fraction. Phys. Lett. B 713, 172 (2012). arXiv:1205.0934288. R. Fleischer, A closer look at Bd,s Dfr decays and novel av
enues to determine . Nucl. Phys. B 659, 321 (2003). arXiv: http://arxiv.org/abs/arXiv:hep-ph/0301256
Web End =hep-ph/0301256 289. S. Nandi, D. London, B0s(B0s) D0CPK K: detecting and dis
criminating new physics in B0sB0s mixing. Phys. Rev. D 85, 114015 (2012). arXiv:1108.5769290. J. Charles et al., B0(t) DP P time-dependent Dalitz plots, CP
violating angles 2, 2 + , and discrete ambiguities. Phys. Lett.
B 425, 375 (1998). http://arxiv.org/abs/arXiv:hep-ph/9801363
Web End =arXiv:hep-ph/9801363 291. T. Latham, T. Gershon, A method to measure cos(2) using time-dependent Dalitz plot analysis of B0 DCP+. J. Phys. G
36, 025006 (2009). arXiv:0809.0872292. R. Fleischer, R. Knegjens, Effective lifetimes of Bs decays and their constraints on the B0s B0s mixing parameters. Eur. Phys. J.
C 71, 1789 (2011). arXiv:1109.5115293. A.S. Dighe, T. Hurth, C.S. Kim, T. Yoshikawa, Measurement of the lifetime difference of B0 mesons: possible and worthwhile?Nucl. Phys. B 624, 377 (2002). http://arxiv.org/abs/arXiv:hep-ph/0109088
Web End =arXiv:hep-ph/0109088 294. V.A. Kostelecky, R. Van Kooten, Bounding CPT violation in the neutral B system. Phys. Rev. D 54, 5585 (1996). http://arxiv.org/abs/arXiv:hep-ph/9607449
Web End =arXiv:hep-ph/ 9607449295. B. Kayser, Cascade mixing and the CP violating angle , in Proceedings of Moriond EW (1997). http://arxiv.org/abs/arXiv:hep-ph/9709382
Web End =arXiv:hep-ph/9709382 296. D.-S. Du, Z.-T. Wei, Test of CPT symmetry in cascade decays.
Eur. Phys. J. C 14, 479 (2000). http://arxiv.org/abs/arXiv:hep-ph/9904403
Web End =arXiv:hep-ph/9904403 297. A. Kundu, S. Nandi, S.K. Patra, A. Soni, Bs DsK as a
probe of CPT violation. Phys. Rev. D 87, 016005 (2013). arXiv: 1209.6063298. M. Gronau, J.L. Rosner, Triple product asymmetries in K,
D(s) and B(s) decays. Phys. Rev. D 84, 096013 (2011). arXiv: 1107.1232299. M. Beneke, Corrections to sin(2) from CP asymmetries in
B0 (0, 0, , , , )K0S decays. Phys. Lett. B 620, 143
(2005). http://arxiv.org/abs/arXiv:hep-ph/0505075
Web End =arXiv:hep-ph/0505075 300. H.-Y. Cheng, C.-K. Chua, A. Soni, Effects of nal-state interactions on mixing-induced CP violation in penguin-dominated B decays. Phys. Rev. D 72, 014006 (2005). http://arxiv.org/abs/arXiv:hep-ph/0502235
Web End =arXiv:hep-ph/0502235 301. S. Descotes-Genon, J. Matias, J. Virto, Exploring Bd,s KK
decays through avor symmetries and QCD-factorization. Phys.
Rev. Lett. 97, 061801 (2006). http://arxiv.org/abs/arXiv:hep-ph/0603239
Web End =arXiv:hep-ph/0603239 302. S. Descotes-Genon, J. Matias, J. Virto, Penguin-mediated
Bd,s V V decays and the B0sB0s mixing angle. Phys. Rev. D
76, 074005 (2007). arXiv:0705.0477303. R. Aaij et al. (LHCb Collaboration), First observation of the decay B0s K0K0. Phys. Lett. B 709, 50 (2012). arXiv:
1111.4183304. R. Aaij et al. (LHCb Collaboration), Measurement of the polarization amplitudes and triple product asymmetries in the B0s
decay. Phys. Lett. B 713, 369 (2012). arXiv:1204.2813305. T. Aaltonen et al. (CDF Collaboration), Measurement of polarization and search for CP-violation in B0s decays. Phys.
Rev. Lett. 107, 261802 (2011). arXiv:1107.4999306. M. Bartsch, G. Buchalla, C. Kraus, B VLVL decays at next-
to-leading order in QCD. arXiv:0810.0249307. R. Fleischer, Extracting CKM phases from angular distributions of Bd,s decays into admixtures of CP eigenstates. Phys. Rev. D 60, 073008 (1999). http://arxiv.org/abs/arXiv:hep-ph/9903540
Web End =arXiv:hep-ph/9903540
308. M. Ciuchini, M. Pierini, L. Silvestrini, B0s K()0 K()0 CP
asymmetries: golden channels for new physics searches. Phys. Rev. Lett. 100, 031802 (2008). http://arxiv.org/abs/arXiv:hep-ph/0703137
Web End =arXiv:hep-ph/0703137 309. A. Datta, D. London, Triple-product correlations in B V1V2
decays and new physics. Int. J. Mod. Phys. A 19, 2505 (2004). http://arxiv.org/abs/arXiv:hep-ph/0303159
Web End =arXiv:hep-ph/0303159 310. C. Aubin, C.-J.D. Lin, A. Soni, Possible lattice approach to
B D(K) matrix elements. Phys. Lett. B 710, 164 (2012).
arXiv:1111.4686311. M. Gronau, D. London, How to determine all the angles of the unitarity triangle from B0 DK0S and B0s D. Phys. Lett. B
253, 483 (1991)312. M. Gronau, D. Wyler, On determining a weak phase from charged B decay asymmetries. Phys. Lett. B 265, 172 (1991) 313. D. Atwood, I. Dunietz, A. Soni, Enhanced CP violation with B KD0 (D0) modes and extraction of the Cabibbo
KobayashiMaskawa angle . Phys. Rev. Lett. 78, 3257 (1997). http://arxiv.org/abs/arXiv:hep-ph/9612433
Web End =arXiv:hep-ph/9612433 314. D. Atwood, I. Dunietz, A. Soni, Improved methods for observing
CP violation in B KD and measuring the CKM phase .
Phys. Rev. D 63, 036005 (2001). http://arxiv.org/abs/arXiv:hep-ph/0008090
Web End =arXiv:hep-ph/0008090 315. A. Giri, Y. Grossman, A. Soffer, J. Zupan, Determining using
B DK with multibody D decays. Phys. Rev. D 68, 054018
(2003). http://arxiv.org/abs/arXiv:hep-ph/0303187
Web End =arXiv:hep-ph/0303187 316. Y. Grossman, Z. Ligeti, A. Soffer, Measuring gamma in B
K(KK)D decays. Phys. Rev. D 67, 071301 (2003). arXiv: http://arxiv.org/abs/arXiv:hep-ph/0210433
Web End =hep-ph/0210433 317. A. Bondar, T. Gershon, On 3 measurements using B
DK decays. Phys. Rev. D 70, 091503 (2004). http://arxiv.org/abs/arXiv:hep-ph/0409281
Web End =arXiv:hep-ph/ 0409281318. M. Gronau, Improving bounds on in B DK and B,0
DX,0s. Phys. Lett. B 557, 198 (2003). http://arxiv.org/abs/arXiv:hep-ph/0211282
Web End =arXiv:hep-ph/0211282 319. D.M. Asner et al. (CLEO Collaboration), Determination of the
D0 K+ relative strong phase using quantum-correlated
measurements in e+e D0 D0 at CLEO. Phys. Rev. D 78,
012001 (2008). arXiv:0802.2268320. D. Asner et al. (CLEO Collaboration), Updated measurement of the strong phase in D0 K+ decay using quantum corre
lations in e+e D0 D0 at CLEO. Phys. Rev. D 86, 112001
(2012). arXiv:1210.0939321. Y. Horii et al. (Belle Collaboration), Evidence for the suppressed decay B DK, D K+. Phys. Rev. Lett. 106, 231803
(2011). arXiv:1103.5951322. P. del Amo Sanchez et al. (BaBar Collaboration), Search for b u transitions in B DK and DK Decays. Phys.
Rev. D 82, 072006 (2010). arXiv:1006.4241323. T. Aaltonen et al. (CDF Collaboration), Measurements of branching fraction ratios and CP-asymmetries in suppressed B
D( K+)K and B D( K+) decays. Phys.
Rev. D 84, 091504 (2011). arXiv:1108.5765324. B. Aubert et al. (BaBar Collaboration), Measurement of the
CabibboKobayashiMaskawa angle in B D()K de
cays with a Dalitz analysis of D K0S+. Phys. Rev. Lett.
95, 121802 (2005). http://arxiv.org/abs/arXiv:hep-ex/0504039
Web End =arXiv:hep-ex/0504039 325. A. Bondar, A. Poluektov, Feasibility study of model-independent approach to 3 measurement using Dalitz plot analysis. Eur.
Phys. J. C 47, 347 (2006). http://arxiv.org/abs/arXiv:hep-ph/0510246
Web End =arXiv:hep-ph/0510246 326. A. Bondar, A. Poluektov, The use of quantum-correlated D0 decays for 3 measurement. Eur. Phys. J. C 55, 51 (2008).
arXiv:0801.0840327. J. Libby et al. (CLEO Collaboration), Model-independent determination of the strong-phase difference between D0 and
D0 K0S,Lh+h (h = , K) and its impact on the measure
ment of the CKM angle /3. Phys. Rev. D 82, 112006 (2010). arXiv:1010.2817
Eur. Phys. J. C (2013) 73:2373 Page 83 of 92
328. I. Dunietz, R.G. Sachs, Asymmetry between inclusive charmed and anticharmed modes in B0, B0 decay as a measure of CP
violation. Phys. Rev. D 37, 3186 (1988)329. R. Aleksan, I. Dunietz, B. Kayser, Determining the CP violating phase . Z. Phys. C 54, 653 (1992)330. R. Fleischer, New strategies to obtain insights into CP violation through B0s DsK, DsK, . . . and B0 D, Ds,
. . . decays. Nucl. Phys. B 671, 459 (2003). http://arxiv.org/abs/arXiv:hep-ph/0304027
Web End =arXiv:hep-ph/ 0304027331. B. Aubert et al. (BaBar Collaboration), Measurement of time-dependent CP-violating asymmetries and constraints on sin(2 + ) with partial reconstruction of B D decays.
Phys. Rev. D 71, 112003 (2005). http://arxiv.org/abs/arXiv:hep-ex/0504035
Web End =arXiv:hep-ex/0504035 332. B. Aubert et al. (BaBar Collaboration), Measurement of time-dependent CP asymmetries in B0 D() and B0
D decays. Phys. Rev. D 73, 111101 (2006). http://arxiv.org/abs/arXiv:hep-ex/0602049
Web End =arXiv:hep-ex/ 0602049333. F.J. Ronga et al. (Belle Collaboration), Measurements of CP violation in B0 D+ and B0 D+ decays. Phys. Rev.
D 73, 092003 (2006). http://arxiv.org/abs/arXiv:hep-ex/0604013
Web End =arXiv:hep-ex/0604013 334. S. Bahinipati et al. (Belle Collaboration), Measurements of time-dependent CP asymmetries in B D decays using a par
tial reconstruction technique. Phys. Rev. D 84, 021101 (2011). arXiv:1102.0888335. S. Nandi, U. Nierste, Resolving the sign ambiguity in s with
Bs DsK. Phys. Rev. D 77, 054010 (2008). arXiv:0801.0143
336. LHCb Collaboration, Measurement of the time-dependent CP-violation parameters in B0s DsK. LHCb-CONF-2012-029
337. Y. Grossman, A. Soffer, J. Zupan, The effect of D0D0 mixing on the measurement of in B DK decays. Phys. Rev. D 72,
031501 (2005). http://arxiv.org/abs/arXiv:hep-ph/0505270
Web End =arXiv:hep-ph/0505270 338. A. Bondar, A. Poluektov, V. Vorobiev, Charm mixing in a model-independent analysis of correlated D0D0 decays. Phys. Rev. D 82, 034033 (2010). arXiv:1004.2350339. Y. Grossman, A.L. Kagan, Z. Ligeti, Can the CP asymmetries in
B K0S and B K0L differ? Phys. Lett. B 538, 327 (2002).
http://arxiv.org/abs/arXiv:hep-ph/0204212
Web End =arXiv:hep-ph/0204212 340. LHCb Collaboration, Measurement of CP observables in B0
DK0 with D K+K. LHCb-CONF-2012-024
341. LHCb Collaboration, First observation of B D0K+
decays to CP even nal states. LHCb-CONF-2012-021342. LHCb Collaboration, Search for the suppressed ADS modes
B [K+]DK and B [K+]D.
LHCb-CONF-2012-030343. LHCb Collaboration, A measurement of from a combination of B+ Dh+ analyses. LHCb-CONF-2012-032
344. M. Adinol et al. Performance of the LHCb RICH detector at the
LHC. arXiv:1211.6759345. P. del Amo Sanchez et al. (BaBar Collaboration), Measurement of CP observables in B DCPK decays and constraints
on the CKM angle . Phys. Rev. D 82, 072004 (2010). arXiv: 1007.0504346. T. Aaltonen et al. (CDF Collaboration), Measurements of branching fraction ratios and CP asymmetries in B DCPK de
cays in hadron collisions. Phys. Rev. D 81, 031105 (2010). arXiv: 0911.0425347. T. Aaltonen et al. (CDF Collaboration), First observation of
B0s DsK and measurement of the ratio of branching frac
tions B( B0s DsK)/B( B0s D+s). Phys. Rev. Lett. 103,
191802 (2009). arXiv:0809.0080348. R. Louvot et al. (Belle Collaboration), Measurement of the decay
B0s Ds+ and evidence for B0s DsK in e+e annihila
tion at s = 10.87 GeV. Phys. Rev. Lett. 102, 021801 (2009).
arXiv:0809.2526349. R. Aaij et al. (LHCb Collaboration), Determination of fs/fd for 7 TeV pp collisions and measurement of the B0 DK+
branching fraction. Phys. Rev. Lett. 107, 211801 (2011). arXiv: 1106.4435350. M. Gronau, D. London, Isospin analysis of CP asymmetries in B decays. Phys. Rev. Lett. 65, 3381 (1990)351. J. Charles, Taming the penguin contributions in the B0d(t)
+ CP asymmetry: observables and minimal theoretical input. Phys. Rev. D 59, 054007 (1999). http://arxiv.org/abs/arXiv:hep-ph/9806468
Web End =arXiv:hep-ph/9806468 352. M. Bona et al. (UTt Collaboration), Improved determination of the CKM angle from B decays. Phys. Rev. D 76,
014015 (2007). http://arxiv.org/abs/arXiv:hep-ph/0701204
Web End =arXiv:hep-ph/0701204 353. R. Fleischer, New strategies to extract and from Bd
+ and Bs K+K. Phys. Lett. B 459, 306 (1999). arXiv:
http://arxiv.org/abs/arXiv:hep-ph/9903456
Web End =hep-ph/9903456 354. R. Fleischer, Bs,d , K, KK: status and prospects. Eur.
Phys. J. C 52, 267 (2007). arXiv:0705.1121355. R. Fleischer, R. Knegjens, In pursuit of new physics with B0s
K+K. Eur. Phys. J. C 71, 1532 (2011). arXiv:1011.1096356. LHCb Collaboration, Measurement of time-dependent CP violation in charmless two-body B decays. LHCb-CONF-2012-007 357. M. Ciuchini, E. Franco, S. Mishima, L. Silvestrini, Testing the
Standard Model and searching for new physics with Bd
and Bs KK decays. J. High Energy Phys. 10, 029 (2012).
arXiv:1205.4948358. I. Adachi et al. (Belle Collaboration), Measurement of the CP violation parameters in B0 + decays. arXiv:1302.0551
359. J.P. Lees et al. (BaBar Collaboration), Measurement of CP asymmetries and branching fractions in charmless two-body B-meson decays to pions and kaons. Phys. Rev. D (2013). doi:10.1103/ http://dx.doi.org/10.1103/PhysRevD.87.052009
Web End =PhysRevD.87.052009 . arXiv:1206.3525
360. H. Ishino et al. (Belle Collaboration), Observation of direct
CP-violation in B0 + decays and model-independent
constraints on the quark-mixing angle 2. Phys. Rev. Lett. 98, 211801 (2007). http://arxiv.org/abs/arXiv:hep-ex/0608035
Web End =arXiv:hep-ex/0608035 361. B. Aubert et al. (BaBar Collaboration), Improved measurements of the branching fractions for B0 + and B0 K+,
and a search for B0 K+K. Phys. Rev. D 75, 012008 (2007).
http://arxiv.org/abs/arXiv:hep-ex/0608003
Web End =arXiv:hep-ex/0608003 362. Y.-T. Duh et al. (Belle Collaboration), Measurements of branching fractions and direct CP asymmetries for B K, B
and B KK decays. arXiv:1210.1348
363. A. Bornheim et al. (CLEO Collaboration), Measurements of charmless hadronic two body B meson decays and the ratio
B(B DK)/B(B D). Phys. Rev. D 68, 052002 (2003).
http://arxiv.org/abs/arXiv:hep-ex/0302026
Web End =arXiv:hep-ex/0302026 364. T. Aaltonen et al. (CDF Collaboration), Measurements of direct
CP violating asymmetries in charmless decays of strange bottom mesons and bottom baryons. Phys. Rev. Lett. 106, 181802 (2011). arXiv:1103.5762365. Y. Chao et al. (Belle Collaboration), Observation of B0 00.
Phys. Rev. Lett. 94, 181803 (2005). http://arxiv.org/abs/arXiv:hep-ex/0408101
Web End =arXiv:hep-ex/0408101 366. B. Aubert et al. (BaBar Collaboration), Study of B0 00,
B 0, and B K0 decays, and isospin analysis of
B decays. Phys. Rev. D 76, 091102 (2007). arXiv:0707.
2798
367. C.-C. Peng et al. (Belle Collaboration), Search for B0s hh de
cays at the (5S) resonance. Phys. Rev. D 82, 072007 (2010). arXiv:1006.5115368. M. Gronau, D. Pirjol, T.-M. Yan, Model independent electroweak penguin amplitudes in B decays to two pseudoscalars. Phys. Rev. D 60, 034021 (1999). http://arxiv.org/abs/arXiv:hep-ph/9810482
Web End =arXiv:hep-ph/9810482 369. J. Zupan, Penguin pollution estimates relevant for the extraction of /2. Nucl. Phys. B, Proc. Suppl. 170, 33 (2007). arXiv: http://arxiv.org/abs/arXiv:hep-ph/0701004
Web End =hep-ph/0701004 370. S. Gardner, Towards a precision determination of in B
decays. Phys. Rev. D 72, 034015 (2005). http://arxiv.org/abs/arXiv:hep-ph/0505071
Web End =arXiv:hep-ph/0505071
Page 84 of 92 Eur. Phys. J. C (2013) 73:2373
371. F.J. Botella, D. London, J.P. Silva, Looking for I = 5/2 ampli
tude components in B and B experiments. Phys.
Rev. D 73, 071501 (2006). http://arxiv.org/abs/arXiv:hep-ph/0602060
Web End =arXiv:hep-ph/0602060 372. G. Duplancic, B. Melic, B, Bs K form factors: an update
of light-cone sum rule results. Phys. Rev. D 78, 054015 (2008). arXiv:0805.4170373. B. Bhattacharya, A. Datta, M. Imbeault, D. London, Measuring
s with Bs K0() K0()a reappraisal. Phys. Lett. B 717, 403
(2012). arXiv:1203.3435374. I. Bediaga et al., On a CP anisotropy measurement in the Dalitz plot. Phys. Rev. D 80, 096006 (2009). arXiv:0905.4233375. M. Williams, Observing CP violation in many-body decays.
Phys. Rev. D 84, 054015 (2011). arXiv:1105.5338376. LHCb Collaboration, Evidence for CP violation in B K
and B KKK decays. LHCb-CONF-2012-018
377. LHCb Collaboration, Evidence for CP violation in B KK
and B decays. LHCb-CONF-2012-028
378. M. Ciuchini, M. Pierini, L. Silvestrini, New bounds on the CabibboKobayashiMaskawa matrix from B K Dalitz
plot analyses. Phys. Rev. D 74, 051301 (2006). http://arxiv.org/abs/arXiv:hep-ph/0601233
Web End =arXiv:hep-ph/ 0601233379. M. Ciuchini, M. Pierini, L. Silvestrini, Hunting the CKM weak phase with time-integrated Dalitz analyses of B0s K de
cays. Phys. Lett. B 645, 201 (2007). http://arxiv.org/abs/arXiv:hep-ph/0602207
Web End =arXiv:hep-ph/0602207 380. M. Gronau, D. Pirjol, A. Soni, J. Zupan, Improved method for
CKM constraints in charmless three-body B and B0s decays.
Phys. Rev. D 75, 014002 (2007). http://arxiv.org/abs/arXiv:hep-ph/0608243
Web End =arXiv:hep-ph/0608243 381. I. Bediaga, G. Guerrer, J.M. de Miranda, Extracting the quark mixing phase from B K+, B0 K0S+, and
B0 K0S+. Phys. Rev. D 76, 073011 (2007). http://arxiv.org/abs/arXiv:hep-ph/0608268
Web End =arXiv:hep-ph/
0608268382. M. Gronau, D. Pirjol, A. Soni, J. Zupan, Constraint on rho
eta from B K. Phys. Rev. D 77, 057504 (2008). arXiv:
0712.3751383. M. Gronau, D. Pirjol, J. Zupan, CP asymmetries in B
K, K, K decays. Phys. Rev. D 81, 094011 (2010). arXiv: 1001.0702384. M. Gronau, D. Pirjol, J.L. Rosner, Calculating phases between B K amplitudes. Phys. Rev. D 81, 094026 (2010).
arXiv:1003.5090385. M. Imbeault, N.R.-L. Lorier, D. London, Measuring in B
K decays. Phys. Rev. D 84, 034041 (2011). arXiv:1011.4973 386. R. Sinha, N. Deshpande, S. Pakvasa, C. Sharma, Determination of weak amplitudes using Bose symmetry and Dalitz plots. Phys.Rev. Lett. 107, 271801 (2011). arXiv:1104.3938387. N.R.-L. Lorier, D. London, Measuring gamma with B K
and B KK K Decays. Phys. Rev. D 85, 016010 (2012).
arXiv:1109.0881388. LHCb Collaboration, Branching fraction measurements of B0d,s
decays to K0Shh nal states, including rst observation of B0s
KSK. LHCb-CONF-2012-023389. R. Aaij et al. (LHCb Collaboration), First observation of the decays B0 D+K+ and B D0K+. Phys. Rev.
Lett. 108, 161801 (2012). arXiv:1201.4402390. T. Gershon, On the measurement of the unitarity triangle angle
from B0 DK0 decays. Phys. Rev. D 79, 051301 (2009).
arXiv:0810.2706391. T. Gershon, M. Williams, Prospects for the measurement of the unitarity triangle angle from B0 DK+ decays. Phys.
Rev. D 80, 092002 (2009). arXiv:0909.1495392. T. Gershon, A. Poluektov, Double Dalitz plot analysis of the decay B0 DK+, D K0S+. Phys. Rev. D 81, 014025
(2010). arXiv:0910.5437393. M. Gronau, Y. Grossman, Z. Surujon, J. Zupan, Enhanced effects on extracting from untagged B0 and B0s decays. Phys. Lett. B 649, 61 (2007). http://arxiv.org/abs/arXiv:hep-ph/0702011
Web End =arXiv:hep-ph/0702011
394. S. Ricciardi, Measuring the CKM angle at LHCb using untagged B0s D decays. LHCb-PUB-2010-005
395. R. Aaij et al. (LHCb Collaboration), Observation of the decay
B0 D0K+K and evidence of B0s D0K+K. Phys. Rev.
Lett. 109, 131801 (2012). arXiv:1207.5991396. M. Masetti, CP violation in B+c decays. Phys. Lett. B 286, 160
(1992)397. R. Fleischer, D. Wyler, Exploring CP violation with B+c decays.
Phys. Rev. D 62, 057503 (2000). http://arxiv.org/abs/arXiv:hep-ph/0004010
Web End =arXiv:hep-ph/0004010 398. A.K. Giri, R. Mohanta, M.P. Khanna, Determination of the angle from nonleptonic B+c D+sD0 decays. Phys. Rev. D 65,
034016 (2002). http://arxiv.org/abs/arXiv:hep-ph/0104009
Web End =arXiv:hep-ph/0104009 399. A.K. Giri, B. Mawlong, R. Mohanta, Determining the CKM angle with B+c decays. Phys. Rev. D 75, 097304 (2007). arXiv: http://arxiv.org/abs/arXiv:hep-ph/0611212
Web End =hep-ph/0611212 400. A.K. Giri, R. Mohanta, M.P. Khanna, Possibility of extracting the weak phase from b D0 decays. Phys. Rev. D 65,
073029 (2002). http://arxiv.org/abs/arXiv:hep-ph/0112220
Web End =arXiv:hep-ph/0112220 401. LHCb Collaboration, Studies of beauty baryons decaying to
D0p and D0pK. LHCb-CONF-2011-036402. Y. Nir, N. Seiberg, Should squarks be degenerate? Phys. Lett. B
309, 337 (1993). http://arxiv.org/abs/arXiv:hep-ph/9304307
Web End =arXiv:hep-ph/9304307
403. M. Leurer, Y. Nir, N. Seiberg, Mass matrix models: the sequel.
Nucl. Phys. B 420, 468 (1994). http://arxiv.org/abs/arXiv:hep-ph/9310320
Web End =arXiv:hep-ph/9310320 404. A.F. Falk et al., D0D0 mass difference from a dispersion relation. Phys. Rev. D 69, 114021 (2004). http://arxiv.org/abs/arXiv:hep-ph/0402204
Web End =arXiv:hep-ph/0402204 405. E. Golowich, J. Hewett, S. Pakvasa, A.A. Petrov, Implications of
D0D0 mixing for new physics. Phys. Rev. D 76, 095009 (2007). arXiv:0705.3650406. L. Okun, B. Pontecorvo, V.I. Zakharov, On the possible violation of CP-invariance in the decays of charmed particles. Lett. Nuovo Cimento 13, 218 (1975)407. A. Pais, S. Treiman, CP violation in charmed particle decays.
Phys. Rev. D 12, 2744 (1975). Phys. Rev. D 16, 2390 (1977). Erratum408. I.I. Bigi, A. Sanda, CP violation in heavy avor decays: predictions and search strategies. Nucl. Phys. B 281, 41 (1987)409. B. Aubert et al. (BaBar Collaboration), Evidence for D0D0
Mixing. Phys. Rev. Lett. 98, 211802 (2007). http://arxiv.org/abs/arXiv:hep-ex/0703020
Web End =arXiv:hep-ex/ 0703020410. M. Staric et al. (Belle Collaboration), Evidence for D0D0 Mix
ing. Phys. Rev. Lett. 98, 211803 (2007). http://arxiv.org/abs/arXiv:hep-ex/0703036
Web End =arXiv:hep-ex/0703036 411. R. Aaij et al. (LHCb Collaboration), Observation of D0D0
oscillations. Phys. Rev. Lett. (2013). doi:http://dx.doi.org/10.1103/PhysRevLett.110.101802
Web End =10.1103/PhysRevLett. 110.101802. arXiv:1211.1230412. I.I. Bigi, H. Yamamoto, Interference between Cabibbo allowed and doubly forbidden transitions in D K0S, K0L + s decays.
Phys. Lett. B 349, 363 (1995). http://arxiv.org/abs/arXiv:hep-ph/9502238
Web End =arXiv:hep-ph/9502238 413. M. Gersabeck et al., On the interplay of direct and indirect CP violation in the charm sector. J. Phys. G 39, 045005 (2012). arXiv:1111.6515414. N. Neri, Recent results for D0D0 mixing and CP violation, and
HFAG averages, in Proceedings of Charm 2012, the 5th International Workshop on Charm Physics, Honolulu, Hawaii, US, May (2012). arXiv:1208.5877415. T. Peng (Belle Collaboration), D0D0 mixing results from Belle, talk given at ICHEP 2012, Melbourne, July 5th 2012, slides available online416. L.M. Zhang et al. (Belle Collaboration), Measurement of D0D0
mixing in D0 K0S+ decays. Phys. Rev. Lett. 99, 131803
(2007). arXiv:0704.1000417. P. del Amo Sanchez et al. (BaBar Collaboration), Measurement of D0D0 mixing parameters using D0 K0S+ and
D0 K0SK+K decays. Phys. Rev. Lett. 105, 081803 (2010).
arXiv:1004.5053
Eur. Phys. J. C (2013) 73:2373 Page 85 of 92
418. Y. Grossman, A.L. Kagan, Y. Nir, New physics and CP violation in singly Cabibbo suppressed D decays. Phys. Rev. D 75, 036008 (2007). http://arxiv.org/abs/arXiv:hep-ph/0609178
Web End =arXiv:hep-ph/0609178
419. B. Aubert et al. (BaBar Collaboration), Search for CP violation in the decays D0 KK+ and D0 +. Phys. Rev. Lett.
100, 061803 (2008). arXiv:0709.2715420. M. Staric et al. (Belle Collaboration), Search for a CP asymmetry in Cabibbo-suppressed D0 decays. Phys. Lett. B 670, 190 (2008). arXiv:0807.0148421. T. Aaltonen et al. (CDF Collaboration), Measurement of CP-violating asymmetries in D0 + and D0 K+K de
cays at CDF. Phys. Rev. D 85, 012009 (2012). arXiv:1111.5023 422. T. Aaltonen et al. (CDF Collaboration), Measurement of the difference of CP-violating asymmetries in D0 K+K and
D0 + decays at CDF. Phys. Rev. Lett. 109, 111801
(2012). arXiv:1207.2158423. B.R. Ko (Belle Collaboration), Direct CP violation in charm at
Belle, Talk given at ICHEP 2012, Melbourne, July 5th 2012, slides available online424. S. Bianco, F. Fabbri, D. Benson, I. Bigi, A Cicerone for the physics of charm. Riv. Nuovo Cimento 26(7), 1 (2003). http://arxiv.org/abs/arXiv:hep-ex/0309021
Web End =arXiv:hep-ex/0309021 425. A.L. Kagan, M.D. Sokoloff, Indirect CP violation and implications for D0D0 and B0sB0s mixing. Phys. Rev. D 80, 076008 (2009). arXiv:0907.3917426. LHCb Collaboration, Time integrated ratio of wrong-sign to right-sign D0 K decays in 2010 data at LHCb. LHCb-
CONF-2011-029427. R. Aaij et al. (LHCb Collaboration), Search for CP violation in D+ KK++ decays. Phys. Rev. D 84, 112008 (2011).
arXiv:1110.3970428. R. Aaij et al. (LHCb Collaboration), Measurement of the D+s
Ds production asymmetry in 7 TeV pp collisions. Phys. Lett. 713, 186 (2012). arXiv:1205.0897429. R. Aaij et al. (LHCb Collaboration), Measurement of the D
production asymmetry in 7 TeV pp collisions. Phys. Lett. B 718, 902909 (2013). arXiv:1210.4112430. P. del Amo Sanchez et al. (BaBar Collaboration), Search for CP violation using T -odd correlations in D0 K+K+ de
cays. Phys. Rev. D 81, 111103 (2010). arXiv:1003.3397431. LHCb Collaboration, Search for CP violation in D0
++ decays. LHCb-CONF-2012-019432. I. Bigi, Probing CP asymmetries in charm baryons decays.
arXiv:1206.4554433. E. Golowich, A.A. Petrov, Short distance analysis of D0D0
mixing. Phys. Lett. B 625, 53 (2005). http://arxiv.org/abs/arXiv:hep-ph/0506185
Web End =arXiv:hep-ph/0506185 434. M. Bobrowski, A. Lenz, J. Riedl, J. Rohrwild, How large can the
SM contribution to CP violation in D0D0 mixing be? J. High Energy Phys. 03, 009 (2010). arXiv:1002.4794435. H. Georgi, DD mixing in heavy quark effective eld theory.
Phys. Lett. B 297, 353 (1992). http://arxiv.org/abs/arXiv:hep-ph/9209291
Web End =arXiv:hep-ph/9209291 436. T. Ohl, G. Ricciardi, E.H. Simmons, DD mixing in heavy quark effective eld theory: the sequel. Nucl. Phys. B 403, 605 (1993). http://arxiv.org/abs/arXiv:hep-ph/9301212
Web End =arXiv:hep-ph/9301212 437. I.I. Bigi, N.G. Uraltsev, D0D0 oscillations as a probe of quark hadron duality. Nucl. Phys. B 592, 92 (2001). http://arxiv.org/abs/arXiv:hep-ph/0005089
Web End =arXiv:hep-ph/ 0005089438. E. Golowich, S. Pakvasa, A.A. Petrov, New physics contributions to the lifetime difference in D0D0 mixing. Phys. Rev. Lett. 98, 181801 (2007). http://arxiv.org/abs/arXiv:hep-ph/0610039
Web End =arXiv:hep-ph/0610039 439. S. Bergmann et al., Lessons from CLEO and FOCUS measurements of D0D0 mixing parameters. Phys. Lett. B 486, 418 (2000). http://arxiv.org/abs/arXiv:hep-ph/0005181
Web End =arXiv:hep-ph/0005181 440. O. Gedalia, Y. Grossman, Y. Nir, G. Perez, Lessons from recent measurements of D0D0 mixing. Phys. Rev. D 80, 055024 (2009). arXiv:0906.1879
441. G. Isidori, Y. Nir, G. Perez, Flavor physics constraints for physics beyond the Standard Model. Annu. Rev. Nucl. Part. Sci. 60, 355 (2010). arXiv:1002.0900
442. A.F. Falk, Y. Grossman, Z. Ligeti, A.A. Petrov, SU(3) breaking and D0D0 mixing. Phys. Rev. D 65, 054034 (2002). arXiv: http://arxiv.org/abs/arXiv:hep-ph/0110317
Web End =hep-ph/0110317
443. B. Chibisov, R.D. Dikeman, M.A. Shifman, N. Uraltsev, Operator product expansion, heavy quarks, QCD duality and its violations. Int. J. Mod. Phys. A 12, 2075 (1997). http://arxiv.org/abs/arXiv:hep-ph/9605465
Web End =arXiv:hep-ph/ 9605465
444. J.F. Donoghue, E. Golowich, B.R. Holstein, J. Trampetic, Dispersive effects in D0D0 mixing. Phys. Rev. D 33, 179 (1986)
445. L. Wolfenstein, D0D0 mixing. Phys. Lett. B 164, 170 (1985) 446. P. Colangelo, G. Nardulli, N. Paver, On D0D0 mixing in the
Standard Model. Phys. Lett. B 242, 71 (1990)447. T.A. Kaeding, D meson mixing in broken SU(3). Phys. Lett. B
357, 151 (1995). http://arxiv.org/abs/arXiv:hep-ph/9505393
Web End =arXiv:hep-ph/9505393 448. A.A. Anselm, Y.I. Azimov, CP violating effects in e+e annihilation. Phys. Lett. B 85, 72 (1979)
449. H.-Y. Cheng, C.-W. Chiang, Long-distance contributions to D0
D0 mixing parameters. Phys. Rev. D 81, 114020 (2010). arXiv: 1005.1106450. Y. Grossman, Y. Nir, G. Perez, Testing new indirect CP violation.
Phys. Rev. Lett. 103, 071602 (2009). arXiv:0904.0305451. A.L. Kagan, G. Perez, T. Volansky, J. Zupan, General minimal avor violation. Phys. Rev. D 80, 076002 (2009). arXiv:0903. 1794452. L. Randall, R. Sundrum, A large mass hierarchy from a small extra dimension. Phys. Rev. Lett. 83, 3370 (1999). http://arxiv.org/abs/arXiv:hep-ph/9905221
Web End =arXiv:hep-ph/ 9905221453. K. Blum, Y. Grossman, Y. Nir, G. Perez, Combining K0K0
mixing and D0D0 mixing to constrain the avor structure of new physics. Phys. Rev. Lett. 102, 211802 (2009). arXiv:0903. 2118454. O. Gedalia, J.F. Kamenik, Z. Ligeti, G. Perez, On the universality of CP violation in F = 1 processes. Phys. Lett. B 714, 55
(2012). arXiv:1202.5038455. Y. Nir, G. Raz, Quark squark alignment revisited. Phys. Rev. D
66, 035007 (2002). http://arxiv.org/abs/arXiv:hep-ph/0206064
Web End =arXiv:hep-ph/0206064 456. B. Aubert et al. (BaBar Collaboration), Measurement of D0D0
mixing using the ratio of lifetimes for the decays D0 K+,
KK+, and +. Phys. Rev. D 78, 011105 (2008). arXiv: 0712.2249457. M. Golden, B. Grinstein, Enhanced CP violations in hadronic charm decays. Phys. Lett. B 222, 501 (1989)458. D. Pirtskhalava, P. Uttayarat, CP violation and avor SU(3) breaking in D-meson decays. Phys. Lett. B 712, 81 (2012). arXiv:1112.5451459. B. Bhattacharya, M. Gronau, J.L. Rosner, CP asymmetries in singly-Cabibbo-suppressed D decays to two pseudoscalar mesons. Phys. Rev. D 85, 054014 (2012). arXiv:1201.2351460. T. Feldmann, S. Nandi, A. Soni, Repercussions of avour symmetry breaking on CP violation in D meson decays. J. High Energy Phys. 06, 007 (2012). arXiv:1202.3795461. J. Brod, Y. Grossman, A.L. Kagan, J. Zupan, A consistent picture for large penguins in D +, K+K. J. High Energy Phys.
10, 161 (2012). arXiv:1203.6659462. H.-Y. Cheng, C.-W. Chiang, SU(3) symmetry breaking and CP violation in D PP decays. Phys. Rev. D 86, 014014 (2012).
arXiv:1205.0580463. G. Hiller, M. Jung, S. Schacht, SU(3)-avor anatomy of nonleptonic charm decays. Phys. Rev. D 87, 014024 (2013). arXiv:1211.3734464. F. Buccella et al., Nonleptonic weak decays of charmed mesons.
Phys. Rev. D 51, 3478 (1995). http://arxiv.org/abs/arXiv:hep-ph/9411286
Web End =arXiv:hep-ph/9411286
Page 86 of 92 Eur. Phys. J. C (2013) 73:2373
465. H.-n. Li, C.-D. Lu, F.-S. Yu, Branching ratios and direct CP asymmetries in D P P decays. Phys. Rev. D 86, 036012
(2012). arXiv:1203.3120466. E. Franco, S. Mishima, L. Silvestrini, The Standard Model confronts CP violation in D0 + and D0 K+K. J. High
Energy Phys. 05, 140 (2012). arXiv:1203.3131467. L. Wolfenstein, CP violation in D0D0 mixing. Phys. Rev. Lett.
75, 2460 (1995). http://arxiv.org/abs/arXiv:hep-ph/9505285
Web End =arXiv:hep-ph/9505285 468. J. Brod, A.L. Kagan, J. Zupan, Size of direct CP violation in singly Cabibbo-suppressed D decays. Phys. Rev. D 86, 014023 (2012). arXiv:1111.5000469. G. Isidori, J.F. Kamenik, Z. Ligeti, G. Perez, Implications of the
LHCb evidence for charm CP violation. Phys. Lett. B 711, 46 (2012). arXiv:1111.4987470. O. Gedalia, L. Mannelli, G. Perez, Covariant description of avor violation in the LHC. Phys. Lett. B 693, 301 (2010). arXiv: 1002.0778471. O. Gedalia, L. Mannelli, G. Perez, Covariant description of avor conversion at the LHC era. J. High Energy Phys. 10, 046 (2010). arXiv:1003.3869472. G.F. Giudice, G. Isidori, P. Paradisi, Direct CP violation in charm and avor mixing beyond the SM. J. High Energy Phys. 04, 060 (2012). arXiv:1201.6204473. G. Hiller, Y. Hochberg, Y. Nir, Supersymmetric ACP. Phys.
Rev. D 85, 116008 (2012). arXiv:1204.1046474. W.D. Goldberger, M.B. Wise, Modulus stabilization with bulk elds. Phys. Rev. Lett. 83, 4922 (1999). http://arxiv.org/abs/arXiv:hep-ph/9907447
Web End =arXiv:hep-ph/9907447 475. S.J. Huber, Q. Sha, Fermion masses, mixings and proton decay in a RandallSundrum model. Phys. Lett. B 498, 256 (2001). http://arxiv.org/abs/arXiv:hep-ph/0010195
Web End =arXiv:hep-ph/0010195 476. T. Gherghetta, A. Pomarol, Bulk elds and supersymmetry in a slice of AdS. Nucl. Phys. B 586, 141 (2000). http://arxiv.org/abs/arXiv:hep-ph/0003129
Web End =arXiv:hep-ph/ 0003129477. C. Delaunay, J.F. Kamenik, G. Perez, L. Randall, Charming CP violation and dipole operators from RS avor anarchy. J. High Energy Phys. 01, 027 (2013). arXiv:1207.0474478. K. Agashe, A. Azatov, L. Zhu, Flavor-violation tests of the warped/composite Standard Model in the two-site approach.Phys. Rev. D 79, 056006 (2009). arXiv:0810.1016479. C. Csaki, G. Perez, Z. Surujon, A. Weiler, Flavor alignment via shining in Randall-Sundrum models. Phys. Rev. D 81, 075025 (2010). arXiv:0907.0474480. B. Keren-Zur et al., On partial compositeness and the CP asymmetry in charm decays. Nucl. Phys. B 867, 429 (2012). arXiv: 1205.5803481. S. Nandi, A. Soni, Constraining the mixing matrix for Standard
Model with four generations: time dependent and semi-leptonic CP asymmetries in B0d, B0s and D0. Phys. Rev. D 83, 114510 (2011). arXiv:1011.6091482. CDF Collaboration, Study of the top quark production asymmetry and its mass and rapidity dependence in the full run II Tevatron dataset. CDF Public Note 10807, 2012483. K. Blum, Y. Hochberg, Y. Nir, Scalar-mediated t t forward-
backward asymmetry. J. High Energy Phys. 10, 124 (2011). arXiv:1107.4350484. Y. Hochberg, Y. Nir, Relating direct CP violation in D decays and the forward-backward asymmetry in tt production. Phys.Rev. Lett. 108, 261601 (2012). arXiv:1112.5268485. G. Isidori, J.F. Kamenik, Shedding light on CP violation in the charm system via D V decays. Phys. Rev. Lett. 109, 171801
(2012). arXiv:1205.3164486. C. Greub, T. Hurth, M. Misiak, D. Wyler, The c u contri
bution to weak radiative charm decay. Phys. Lett. B 382, 415 (1996). http://arxiv.org/abs/arXiv:hep-ph/9603417
Web End =arXiv:hep-ph/9603417 487. Y. Grossman, A.L. Kagan, J. Zupan, Testing for new physics in singly Cabibbo suppressed D decays. Phys. Rev. D 85, 114036 (2012). arXiv:1204.3557
488. D. Atwood, A. Soni, Searching for the origin of CP violation in
Cabibbo suppressed D-meson decays. arXiv:1211.1026489. S. Gardner, U.-G. Meissner, Rescattering and chiral dynamics in B decay. Phys. Rev. D 65, 094004 (2002). arXiv:
http://arxiv.org/abs/arXiv:hep-ph/0112281
Web End =hep-ph/0112281 490. M. Gronau, J. Zupan, Isospin-breaking effects on extracted in B , , . Phys. Rev. D 71, 074017 (2005). arXiv:
http://arxiv.org/abs/arXiv:hep-ph/0502139
Web End =hep-ph/0502139 491. H. Ishino, M. Hazumi, M. Nakao, T. Yoshikawa, New measurements using external photon conversion at a high luminosity B factory. http://arxiv.org/abs/arXiv:hep-ex/0703039
Web End =arXiv:hep-ex/0703039 492. A.F. Falk, Z. Ligeti, Y. Nir, H. Quinn, Comment on extracting from B . Phys. Rev. D 69, 011502 (2004). arXiv:
http://arxiv.org/abs/arXiv:hep-ph/0310242
Web End =hep-ph/0310242 493. M. Gaspero, B. Meadows, K. Mishra, A. Soffer, Isospin analysis of D0 decay to three pions. Phys. Rev. D 78, 014015 (2008). arXiv:0805.4050494. G. Colangelo et al., Review of lattice results concerning low energy particle physics. Eur. Phys. J. C 71, 1695 (2011). arXiv: 1011.4408495. M. Lscher, Volume dependence of the energy spectrum in massive quantum eld theories II. Scattering states. Commun. Math. Phys. 105, 153 (1986)496. M. Lscher, Two particle states on a torus and their relation to the scattering matrix. Nucl. Phys. B 354, 531 (1991)497. L. Lellouch, M. Lscher, Weak transition matrix elements from nite volume correlation functions. Commun. Math. Phys. 219, 31 (2001). http://arxiv.org/abs/arXiv:hep-lat/0003023
Web End =arXiv:hep-lat/0003023 498. T. Blum et al., The K ()I=2 decay amplitude from lattice
QCD. Phys. Rev. Lett. 108, 141601 (2012). arXiv:1111.1699 499. T. Blum et al., K to decay amplitudes from lattice QCD.
Phys. Rev. D 84, 114503 (2011). arXiv:1106.2714500. M.T. Hansen, S.R. Sharpe, Multiple-channel generalization of
LellouchLuscher formula. Phys. Rev. D 86, 016007 (2012). arXiv:1204.0826501. N.H. Christ (RBC Collaboration, UKQCD Collaboration), Computing the long-distance contribution to second order weak amplitudes. PoS LATTICE 2010, 300 (2010)502. J. Yu, Long distance contribution to K0LK0S mass difference.
PoS LATTICE 2011, 297 (2011). arXiv:1111.6953503. CDF Collaboration, Search for quark substructure in the angular distribution of dijets produced in p p collisions at s =
1.96 TeV. CDF Public Note 9609, 2008504. V.M. Abazov et al. (D0 Collaboration), Measurement of dijet angular distributions at s = 1.96 TeV and searches for quark
compositeness and extra spatial dimensions. Phys. Rev. Lett. 103, 191803 (2009). arXiv:0906.4819505. L. Da Rold, C. Delaunay, C. Grojean, G. Perez, Up asymme-tries From exhilarated composite avor structures. J. High Energy Phys. (2013). doi:10.1007/JHEP02(2013)149. arXiv:1208. 1499506. ATLAS Collaboration, Search for new physics in dijet mass and angular distributions using 4.8 fb1 of pp collisions at s =
7 TeV collected by the ATLAS detector. ATLAS-CONF-2012-038, 2012507. S. Chatrchyan et al. (CMS Collaboration), Search for quark compositeness in dijet angular distributions from pp collisions at s = 7 TeV. J. High Energy Phys. 05, 055 (2012). arXiv:1202.
5535508. L.M. Zhang et al. (Belle Collaboration), Improved constraints on
D0D0 mixing in D0 K+ decays at Belle. Phys. Rev. Lett.
96, 151801 (2006). http://arxiv.org/abs/arXiv:hep-ex/0601029
Web End =arXiv:hep-ex/0601029 509. B. Aubert et al. (BaBar Collaboration), Search for D0D0 mix
ing using semileptonic decay modes. Phys. Rev. D 70, 091102 (2004). http://arxiv.org/abs/arXiv:hep-ex/0408066
Web End =arXiv:hep-ex/0408066
Eur. Phys. J. C (2013) 73:2373 Page 87 of 92
510. B. Aubert et al. (BaBar Collaboration), Search for D0D0 mix
ing using doubly avor tagged semileptonic decay modes. Phys.
Rev. D 76, 014018 (2007). arXiv:0705.0704511. B. Aubert et al. (BaBar Collaboration), Measurement of D0
D0 mixing from a time-dependent amplitude analysis of D0
K+0 decays. Phys. Rev. Lett. 103, 211801 (2009). arXiv: 0807.4544512. V. Kartvelishvili, A. Likhoded, S. Slabospitsky, D meson and meson production in hadronic interactions. Sov. J. Nucl. Phys. 28, 678 (1978)513. R. Baier, R. Rckl, Hadronic production of J/ and : trans-verse momentum distribution. Phys. Lett. B 102, 364 (1981) 514. F. Abe et al. (CDF Collaboration), Inclusive J/, (2S) and b quark production in pp collisions at s = 1.8 TeV. Phys. Rev.
Lett. 69, 3704 (1992)515. E. Braaten, S. Fleming, Color octet fragmentation and the -surplus at the Fermilab Tevatron. Phys. Rev. Lett. 74, 3327 (1995). http://arxiv.org/abs/arXiv:hep-ph/9411365
Web End =arXiv:hep-ph/9411365 516. J. Campbell, F. Maltoni, F. Tramontano, QCD corrections to
J/ and production at hadron colliders. Phys. Rev. Lett. 98, 252002 (2007). http://arxiv.org/abs/arXiv:hep-ph/0703113
Web End =arXiv:hep-ph/0703113 517. B. Gong, J.-X. Wang, Next-to-leading-order QCD corrections to
J/ polarization at Tevatron and Large Hadron Collider energies. Phys. Rev. Lett. 100, 232001 (2008). arXiv:0802.3727 518. P. Artoisenet et al., production at Fermilab Tevatron and LHC energies. Phys. Rev. Lett. 101, 152001 (2008). arXiv:0806.3282 519. J.P. Lansberg, On the mechanisms of heavy-quarkonium hadroproduction. Eur. Phys. J. C 61, 693 (2009). arXiv:0811. 4005520. N. Brambilla et al., Heavy quarkonium: progress, puzzles, and opportunities. Eur. Phys. J. C 71, 1534 (2011). arXiv:1010.5827 521. R. Aaij et al. (LHCb Collaboration), Measurement of J/ production in pp collisions at s = 7 TeV. Eur. Phys. J. C 71, 1645
(2011). arXiv:1103.0423522. R. Aaij et al. (LHCb Collaboration), Measurement of the cross-section ratio (c2)/(c1) for prompt c production at s =
7 TeV. Phys. Lett. B 714, 215 (2012). arXiv:1202.1080523. R. Aaij et al. (LHCb Collaboration), Measurement of the ratio of prompt c to J/ production in pp collisions at s = 7 TeV.
Phys. Lett. B 718, 431 (2012). arXiv:1204.1462524. R. Aaij et al. (LHCb Collaboration), Measurement of production in pp collisions at s = 7 TeV. Eur. Phys. J. C 72, 2025
(2012). arXiv:1202.6579525. R. Aaij et al. (LHCb Collaboration), Measurement of (2S) meson production in pp collisions at s = 7 TeV. Eur. Phys. J. C
72, 2100 (2012). arXiv:1204.1258526. S.J. Brodsky, J.-P. Lansberg, Heavy-quarkonium production in high energy protonproton collisions at RHIC. Phys. Rev. D 81, 051502 (2010). arXiv:0908.0754527. C.H. Kom, A. Kulesza, W.J. Stirling, Pair production of J/ as a probe of double parton scattering at LHCb. Phys. Rev. Lett. 107, 082002 (2011). arXiv:1105.4186528. S.P. Baranov, A.M. Snigirev, N.P. Zotov, Double heavy meson production through double parton scattering in hadronic collisions. Phys. Lett. B 705, 116 (2011). arXiv:1105.6276529. A. Novoselov, Double parton scattering as a source of quarkonia pairs in LHCb. arXiv:1106.2184530. S. Brodsky, P. Hoyer, C. Peterson, N. Sakai, The intrinsic charm of the proton. Phys. Lett. B 93, 451 (1980)531. R. Aaij et al. (LHCb Collaboration), Observation of J/ pair production in pp collisions at s = 7 TeV. Phys. Lett. B 707, 52
(2012). arXiv:1109.0963532. V.G. Kartvelishvili, S.M. Esakiya, On hadron induced production of J/ meson pairs. Yad. Fiz. 38, 722 (1983)533. B. Humpert, P. Mery, production at collider energies.Z. Phys. C 20, 83 (1983)
534. A.V. Berezhnoy, A.K. Likhoded, A.V. Luchinsky, A.A.
Novoselov, Production of J/ meson pairs and 4c-tetraquark at the LHC. Phys. Rev. D 84, 094023 (2011). arXiv:1101.5881 535. M. Luszczak, R. Maciula, A. Szczurek, Production of two c c
pairs in double-parton scattering. Phys. Rev. D 85, 094034 (2011). arXiv:1111.3255536. F. Abe et al. (CDF Collaboration), Double parton scattering in
pp collisions at s = 1.8 TeV. Phys. Rev. D 56, 3811 (1997)
537. V.V. Braguta, A.K. Likhoded, A.V. Luchinsky, Double charmonium production in exclusive bottomonia decays. Phys. Rev. D 80, 094008 (2009). arXiv:0902.0459 [hep-ph]
538. Y. Jia, Which hadronic decay modes are good for b searching: double J/ or something else? Phys. Rev. D 78, 054003 (2008). http://arxiv.org/abs/arXiv:hep-ph/0611130v2
Web End =arXiv:hep-ph/0611130v2
539. S. Barsuk, J. He, E. Kou, B. Viaud, Investigating charmonium production at LHC with the p p nal state. Phys. Rev. D 86,
034011 (2012). arXiv:1202.2273540. J.J. Aubert et al. (E598 Collaboration), Experimental observation of a heavy particle J. Phys. Rev. Lett. 33, 1404 (1974)541. J.E. Augustin et al. (SLAC-SP-017 Collaboration), Discovery of a narrow resonance in e+e annihilation. Phys. Rev. Lett. 33, 1406 (1974)
542. S.W. Herb et al., Observation of a dimuon resonance at 9.5 GeV in 400 GeV proton-nucleus collisions. Phys. Rev. Lett. 39, 252 (1977)
543. S.K. Choi et al. (Belle Collaboration), Observation of a narrow charmonium state in exclusive B+ K+J/ decays.
Phys. Rev. Lett. 91, 262001 (2003). http://arxiv.org/abs/arXiv:hep-ex/0309032
Web End =arXiv:hep-ex/0309032 544. B. Aubert et al. (BaBar Collaboration), A study of B
X(3872)K, with X(3872) J/+. Phys. Rev. D 77,
111101 (2008). arXiv:0803.2838545. D. Acosta et al. (CDF Collaboration), Observation of the narrow state X(3872) J/+ in pp collisions at s = 1.96 TeV.
Phys. Rev. Lett. 93, 072001 (2004). http://arxiv.org/abs/arXiv:hep-ex/0312021
Web End =arXiv:hep-ex/0312021 546. V.M. Abazov et al. (D0 Collaboration), Observation and properties of the X(3872) decaying to J/+ in p p collisions
at s = 1.96 TeV. Phys. Rev. Lett. 93, 162002 (2004). arXiv:
http://arxiv.org/abs/arXiv:hep-ex/0405004
Web End =hep-ex/0405004 547. S.K. Choi et al. (Belle Collaboration), Observation of a resonance-like structure in the mass distribution in exclusive B K decays. Phys. Rev. Lett. 100, 142001 (2008).
arXiv:0708.1790548. R. Mizuk et al. (Belle Collaboration), Observation of two resonance-like structures in the +c1 mass distribution in exclusive B0 K+c1 decays. Phys. Rev. D 78, 072004
(2008). arXiv:0806.4098549. R. Mizuk et al. (Belle Collaboration), Dalitz analysis of B
K+ decays and the Z(4430)+. Phys. Rev. D 80, 031104 (2009). arXiv:0905.2869550. B. Aubert et al. (BaBar Collaboration), Search for the Z(4430)
at BaBar. Phys. Rev. D 79, 112001 (2009). arXiv:0811.0564 551. J. Lees et al. (BaBar Collaboration), Search for the Z1(4050)+ and Z2(4250)+ states in B0 c1K+ and B+
c1K0S+. Phys. Rev. D 85, 052003 (2012). arXiv:1111.5919 552. E.S. Swanson, The new heavy mesons: a status report. Phys. Rep.
429, 243 (2006). http://arxiv.org/abs/arXiv:hep-ph/0601110
Web End =arXiv:hep-ph/0601110 553. N.V. Drenska, R. Faccini, A.D. Polosa, Exotic hadrons with hidden charm and strangeness. Phys. Rev. D 79, 077502 (2009). arXiv:0902.2803554. M. Voloshin, Charmonium. Prog. Part. Nucl. Phys. 61, 455
(2008). arXiv:0711.4556555. S. Godfrey, S.L. Olsen, The exotic XY Z charmonium-like mesons. Annu. Rev. Nucl. Part. Sci. 58, 51 (2008). arXiv:0801. 3867556. M. Nielsen, F.S. Navarra, S.H. Lee, New charmonium states in
QCD sum rules: a concise review. Phys. Rep. 497, 41 (2010). arXiv:0911.1958
Page 88 of 92 Eur. Phys. J. C (2013) 73:2373
557. N. Drenska et al., New hadronic spectroscopy. Riv. Nuovo Cimento 033, 633 (2010). arXiv:1006.2741
558. S. Eidelman et al., Developments in heavy quarkonium spectroscopy. arXiv:1205.4189
559. A. Bondar et al. (Belle Collaboration), Observation of two charged bottomonium-like resonances in (5S) decays. Phys.Rev. Lett. 108, 122001 (2012). arXiv:1110.2251
560. I. Adachi et al. (Belle Collaboration), Evidence for a Z0b(10610) in Dalitz analysis of (5S) (nS)00. arXiv:1207.4345
561. I. Adachi et al. (Belle Collaboration), Study of three-body
(10860) decays. arXiv:1209.6450562. R. Aaij et al. (LHCb Collaboration), Observation of X(3872) production in pp collisions at s = 7 TeV. Eur. Phys. J. C 72,
1972 (2011). arXiv:1112.5310563. E.J. Eichten, K. Lane, C. Quigg, Charmonium levels near threshold and the narrow state X(3872) +J/. Phys. Rev. D
69, 094019 (2004). http://arxiv.org/abs/arXiv:hep-ph/0401210
Web End =arXiv:hep-ph/0401210 564. R. Balest et al. (CLEO Collaboration), Inclusive decays of B mesons to charmonium. Phys. Rev. D 52, 2661 (1995)565. B. Aubert et al. (BaBar Collaboration), Study of inclusive production of charmonium mesons in B decay. Phys. Rev. D 67, 032002 (2003). http://arxiv.org/abs/arXiv:hep-ex/0207097
Web End =arXiv:hep-ex/0207097 566. C.-H.V. Chang, W.-S. Hou, Probing for the charm content of B and mesons. Phys. Rev. D 64, 071501 (2001). http://arxiv.org/abs/arXiv:hep-ph/0101162
Web End =arXiv:hep-ph/ 0101162567. S.J. Brodsky, F.S. Navarra, Looking for exotic multi-quark states in nonleptonic B decays. Phys. Lett. B 411, 152 (1997). http://arxiv.org/abs/arXiv:hep-ph/9704348
Web End =arXiv:hep-ph/9704348 568. T.J. Burns et al., Momentum distribution of J/ in B decays.
Phys. Rev. D 83, 114029 (2011). arXiv:1104.1781569. G. Eilam, M. Ladisa, Y.-D. Yang, Study of B0 J/D() and
cD() in perturbative QCD. Phys. Rev. D 65, 037504 (2002). http://arxiv.org/abs/arXiv:hep-ph/0107043
Web End =arXiv:hep-ph/0107043 570. B. Aubert et al. (BaBar Collaboration), Evidence for B+
J/p and search for B0 J/p p. Phys. Rev. Lett. 90,
231801 (2003). http://arxiv.org/abs/arXiv:hep-ex/0303036
Web End =arXiv:hep-ex/0303036 571. Q.L. Xie et al. (Belle Collaboration), Observation of B
J/p and searches for B J/0p and B0 J/pp
decays. Phys. Rev. D 72, 051105 (2005). http://arxiv.org/abs/arXiv:hep-ex/0508011
Web End =arXiv:hep-ex/0508011 572. R. Aaij et al. (LHCb Collaboration), First observation of the decay B+c J/++. Phys. Rev. Lett. 108, 251802 (2012).
arXiv:1204.0079573. G. Altarelli, M. Mangano et al., Workshop on Standard Model physics (and more) at the LHC, CERN Yellow Report 2000-004, 2000574. R. Aaij et al. (LHCb Collaboration), Measurement of relative branching fractions of B decays to (2S) and J/ mesons. Eur.Phys. J. C 72, 2118 (2012). arXiv:1205.0918575. Y.-N. Gao et al., Experimental prospects of the B+c studies of the
LHCb experiment. Chin. Phys. Lett. 27, 061302 (2010)576. I.P. Gouz et al., Prospects for the Bc studies at LHCb. Phys. At.
Nucl. 67, 1559 (2004). http://arxiv.org/abs/arXiv:hep-ph/0211432
Web End =arXiv:hep-ph/0211432 577. S. Godfrey, Spectroscopy of Bc mesons in the relativized quark model. Phys. Rev. D 70, 054017 (2004). http://arxiv.org/abs/arXiv:hep-ph/0406228
Web End =arXiv:hep-ph/0406228 578. S.S. Gershtein, V.V. Kiselev, A.K. Likhoded, A.V. Tkabladze,
B+c spectroscopy. Phys. Rev. D 51, 3613 (1995). http://arxiv.org/abs/arXiv:hep-ph/9406339
Web End =arXiv:hep-ph/ 9406339579. R. Dowdall, C. Davies, T. Hammant, R. Horgan, Precise heavy-light meson masses and hyperne splittings from lattice QCD including charm quarks in the sea. Phys. Rev. D 86, 094510 (2012). arXiv:1207.5149580. LHCb Collaboration, Measurement of the masses of the b and
b. LHCb-CONF-2011-060581. N. Uraltsev, On the problem of boosting nonleptonic b baryon decays. Phys. Lett. B 376, 303 (1996). http://arxiv.org/abs/arXiv:hep-ph/9602324
Web End =arXiv:hep-ph/9602324 582. M. Voloshin, Relations between inclusive decay rates of heavy baryons. Phys. Rep. 320, 275 (1999). http://arxiv.org/abs/arXiv:hep-ph/9901445
Web End =arXiv:hep-ph/9901445
583. R. Aaij et al. (LHCb Collaboration), Observation of excited b baryons. Phys. Rev. Lett. 109, 172003 (2012). arXiv:1205.3452
584. C.-H. Chang, J.-P. Ma, C.-F. Qiao, X.-G. Wu, Hadronic production of the doubly charmed baryon cc with intrinsic charm.
J. Phys. G 34, 845 (2007). http://arxiv.org/abs/arXiv:hep-ph/0610205
Web End =arXiv:hep-ph/0610205 585. J.-W. Zhang et al., Hadronic production of the doubly heavy baryon bc at the LHC. Phys. Rev. D 83, 034026 (2011).
arXiv:1101.1130586. R. McNulty, LHCb: tools to incorporate LHCb data in ts, Working group on electroweak precision measurements at the LHC, 2011587. ALEPH Collaboration, DELPHI Collaboration, L3 Collaboration, OPAL Collaboration, SLD Collaboration, LEP Electroweak Working Group, The SLD Electroweak and Heavy Flavour Groups, Precision electroweak measurements on the Z resonance. Phys. Rep. 427, 257 (2006). http://arxiv.org/abs/arXiv:hep-ex/0509008
Web End =arXiv:hep-ex/0509008 588. R. Aaij et al. (LHCb Collaboration), Inclusive W and Z production in the forward region at s = 7 TeV. J. High Energy Phys.
06, 058 (2012). arXiv:1204.1620589. J. Rojo, NNPDF2.3 and inclusion of the LHC data, PDF4LHC meeting, 2012590. LHCb Collaboration, Inclusive low mass DrellYan production in the forward region at s = 7 TeV. LHCb-CONF-2012-013
591. N. Besson et al., Re-evaluation of the LHC potential for the measurement of mW . Eur. Phys. J. C 57, 627 (2008). arXiv:0805.
2093592. T. Aaltonen et al. (CDF Collaboration), Evidence for a mass dependent forwardbackward asymmetry in top quark pair production. Phys. Rev. D 83, 112003 (2011). arXiv:1101.0034593. V.M. Abazov et al. (D0 Collaboration), Forward-backward asymmetry in top quarkantiquark production. Phys. Rev. D 84, 112005 (2011). arXiv:1107.4995594. Y. Takeuchi et al. (CDF Collaboration), CDF Note 10398595. T. Schwarz et al. (CDF Collaboration), CDF Note 10584596. S. Leone (CDF Collaboration), Top quark production at the Tevatron, Talk given at Moriond EW, March 9th 2012, proceedings available online597. A.L. Kagan, J.F. Kamenik, G. Perez, S. Stone, Top LHCb physics. Phys. Rev. Lett. 107, 082003 (2011). arXiv:1103.3747 598. K.M. Zurek, TASI 2009 lectures: searching for unexpected physics at the LHC, arXiv:1001.2563599. M.J. Strassler, K.M. Zurek, Echoes of a hidden valley at hadron colliders. Phys. Lett. B 651, 374 (2007). http://arxiv.org/abs/arXiv:hep-ph/0604261
Web End =arXiv:hep-ph/0604261 600. L.M. Carpenter, D.E. Kaplan, E.-J. Rhee, Six-quark decays of the Higgs boson in supersymmetry with R-parity violation. Phys. Rev. Lett. 99, 211801 (2007). http://arxiv.org/abs/arXiv:hep-ph/0607204
Web End =arXiv:hep-ph/0607204 601. M.J. Strassler, K.M. Zurek, Discovering the Higgs through highly-displaced vertices. Phys. Lett. B 661, 263 (2008). arXiv: http://arxiv.org/abs/arXiv:hep-ph/0605193
Web End =hep-ph/0605193 602. P. Fileviez Perez, S. Spinner, M.K. Trenkel, Lightest supersym-metric particle stability and new Higgs signals at the LHC. Phys. Rev. D 84, 095028 (2011). arXiv:1103.5504603. F. de Campos, O.J.P. boli, M.B. Magro, D. Restrepo, Searching supersymmetry at the LHCb with displaced vertices. Phys. Rev. D 79, 055008 (2009). arXiv:0809.0007604. G. Brooijmans et al. (New Physics Working Group), New physics at the LHC. A Les Houches report: physics at TeV colliders 2009new physics working group. arXiv:1005.1229605. LHCb Collaboration, Search for (Higgs-like) bosons decaying into long-lived exotic particles. LHCb-CONF-2012-014606. T. Aaltonen et al. (CDF Collaboration), Search for exclusive
production in hadron-hadron collisions. Phys. Rev. Lett. 99, 242002 (2007). arXiv:0707.2374607. T. Aaltonen et al. (CDF Collaboration), Observation of exclusive dijet production at the Fermilab Tevatron p p collider. Phys. Rev.
D 77, 052004 (2008). arXiv:0712.0604
Eur. Phys. J. C (2013) 73:2373 Page 89 of 92
608. V.M. Abazov et al. (D0 Collaboration), High mass exclusive diffractive dijet production in p p collisions at s = 1.96 TeV.
Phys. Lett. B 705, 193 (2011). arXiv:1009.2444609. T. Aaltonen et al. (CDF Collaboration), Observation of exclusive charmonium production and + in pp colli
sions at s = 1.96 TeV. Phys. Rev. Lett. 102, 242001 (2009).
arXiv:0902.1271610. LHCb Collaboration, Central exclusive dimuon production at
s = 7 TeV. LHCb-CONF-2011-022
611. http://projects.hepforge.org/superchic
Web End =http://projects.hepforge.org/superchic 612. J.W. Lms, R. Orava, Central diffraction at the LHCb. J. Instrum. 4, P11019 (2009). arXiv:0907.3847613. M.G. Albrow et al. (FP420 Collaboration), The FP420 R&D project: Higgs and new physics with forward protons at the LHC.J. Instrum. 4, T10001 (2009). arXiv:0806.0302614. L.A. Harland-Lang, V.A. Khoze, M.G. Ryskin, W.J. Stirling,
Standard candle central exclusive processes at the Tevatron and LHC. Eur. Phys. J. C 69, 179 (2010). arXiv:1005.0695615. S. Heinemeyer et al., BSM Higgs physics in the exclusive forward proton mode at the LHC. Eur. Phys. J. C 71, 1649 (2011). arXiv:1012.5007
616. R. Aaij et al. (LHCb Collaboration), Observation of double charm production involving open charm in pp collisions at s =
7 TeV. J. High Energy Phys. 06, 141 (2012). arXiv:1205.0975 617. LHCb Collaboration, Measurement of jet production in
Z0/ + events at LHCb in s = 7 TeV pp collisions.
LHCb-CONF-2012-016618. LHCb Collaboration, The LHCb upgrade. LHCb-PUB-2012-
010619. M. Bona et al. (SuperB Collaboration), SuperB: a high-luminosity asymmetric e+e super avor factory. Conceptual design report. arXiv:0709.0451620. T. Browder et al., On the physics case of a super avour factory.J. High Energy Phys. 02, 110 (2008). arXiv:0710.3799621. T.E. Browder et al., New physics at a super avor factory. Rev.
Mod. Phys. 81, 1887 (2009). arXiv:0802.3201622. T. Aushev et al., Physics at super B factory. arXiv:1002.5012 623. M. Ciuchini, A. Stocchi, Physics opportunities at the next generation of precision avor physics experiments. Annu. Rev. Nucl. Part. Sci. 61, 491 (2011). arXiv:1110.3920
The LHCb Collaboration
R. Aaij74, C. Abellan Beteta69,n, A. Adametz47, B. Adeva70, M. Adinol79, C. Adrover42, A. Affolder85, Z. Ajaltouni41,J. Albrecht71, F. Alessio71, M. Alexander84, S. Ali74, G. Alkhazov63, P. Alvarez Cartelle70, A.A. Alves Jr58, S. Amato38,Y. Amhis72, L. Anderlini53,f, J. Anderson73, R. Andreassen93,t, M. Anelli54, R.B. Appleby87, O. Aquines Gutierrez46,F. Archilli54,71, A. Artamonov68, M. Artuso89, E. Aslanides42, G. Auriemma58,m, S. Bachmann47, J.J. Back81, C. Baesso90,r,W. Baldini52, H. Band74, R.J. Barlow87, C. Barschel71, S. Barsuk43, W. Barter80, A. Bates84, Th. Bauer74, A. Bay72, J. Beddow84, I. Bediaga37, C. Beigbeder-Beau43, S. Belogurov64, K. Belous68, I. Belyaev64, E. Ben-Haim44, M. Benayoun44,G. Bencivenni54, S. Benson83, J. Benton79, A. Berezhnoy65, F. Bernard72, R. Bernet73, M.-O. Bettler80, M. van Beuzekom74,V. van Beveren74, A. Bien47, S. Bifani48, T. Bird87, A. Bizzeti53,h, P.M. Bjrnstad87, T. Blake71, F. Blanc72, C. Blanks86,J. Blouw47, S. Blusk89, A. Bobrov67, V. Bocci58, B. Bochin63, H. Boer Rookhuizen74, G. Bogdanova65, E. Bonaccorsi71,A. Bondar67, N. Bondar63, W. Bonivento51, S. Borghi87,84, A. Borgia89, T.J.V. Bowcock85, E. Bowen73, C. Bozzi52, T. Bram-bach45, J. van den Brand75, L. Brarda71, J. Bressieux72, D. Brett87, M. Britsch46, T. Britton89, N.H. Brook79, H. Brown85,A. Bchler-Germann73, I. Burducea62, A. Bursche73, J. Buytaert71, T. Cacrs43, J.-P. Cachemiche42, S. Cadeddu51, O. Callot43, M. Calvi56,j, M. Calvo Gomez69,n, A. Camboni69, P. Campana54,71, A. Carbone50,c, G. Carboni57,k, R. Cardinale55,i,A. Cardini51, H. Carranza-Mejia83, L. Carson86, K. Carvalho Akiba38, A. Casajus Ramo69, G. Casse85, M. Cattaneo71, Ch. Cauet45, L. Ceelie74, B. Chadaj71, H. Chanal41, M. Charles88, D. Charlet43, Ph. Charpentier71, M. Chebbi71, P. Chen39,72,N. Chiapolini73, M. Chrzaszcz59, P. Ciambrone54, K. Ciba71, X. Cid Vidal70, G. Ciezarek86, P.E.L. Clarke83, M. Clemencic71, H.V. Cliff80, J. Closier71, C. Coca62, V. Coco74, J. Cogan42, E. Cogneras41, P. Collins71, A. Comerma-Montells69,A. Contu51,88, A. Cook79, M. Coombes79, B. Corajod71, G. Corti71, B. Couturier71, G.A. Cowan72, D. Craik81, S. Cunliffe86,R. Currie83, C. DAmbrosio71, I. DAntone50, P. David44, P.N.Y. David74, I. De Bonis40, K. De Bruyn74, S. De Capua87,M. De Cian73, P. De Groen74, J.M. De Miranda37, L. De Paula38, P. De Simone54, D. Decamp40, M. Deckenhoff45, G. Decreuse71, H. Degaudenzi72,71, L. Del Buono44, C. Deplano51, D. Derkach50, O. Deschamps41, F. Dettori75, A. Di Canto47,J. Dickens80, H. Dijkstra71, P. Diniz Batista37, M. Dogaru62, F. Domingo Bonal69,n, M. Domke45, S. Donleavy85, F. Dordei47,A. Dosil Surez70, D. Dossett81, A. Dovbnya76, C. Drancourt40, O. Duarte43, R. Dumps71, F. Dupertuis72, P.-Y. Duval42,R. Dzhelyadin68, A. Dziurda59, A. Dzyuba63, S. Easo82,71, U. Egede86, V. Egorychev64, S. Eidelman67, D. van Eijk74,S. Eisenhardt83, R. Ekelhof45, L. Eklund84, I. El Rifai41, Ch. Elsasser73, D. Elsby78, F. Evangelisti52, A. Falabella50,e,C. Frber47, G. Fardell83, C. Farinelli74, S. Farry48, P.J.W. Faulkner78, V. Fave72, G. Felici54, V. Fernandez Albor70, F. Ferreira Rodrigues37, M. Ferro-Luzzi71, S. Filippov66, C. Fitzpatrick71, C. Fhr46, M. Fontana46, F. Fontanelli55,i, R. Forty71,C. Fournier71, O. Francisco38, M. Frank71, C. Frei71, R. Frei72, M. Frosini53,f, H. Fuchs46, S. Furcas56, A. Gallas Torreira70,D. Galli50,c, M. Gandelman38, P. Gandini88, Y. Gao39, J. Garofoli89, P. Garosi87, J. Garra Tico80, L. Garrido69, D. Gascon69, C. Gaspar71, R. Gauld88, E. Gersabeck47, M. Gersabeck87, T. Gershon81,71, S. Gets63, Ph. Ghez40, A. Giachero56,V. Gibson80, V.V. Gligorov71, C. Gbel90,r, V. Golovtsov63, D. Golubkov64, A. Golutvin86,64,71, A. Gomes38, G. Gong39,
Page 90 of 92 Eur. Phys. J. C (2013) 73:2373
H. Gong39, H. Gordon88, C. Gotti56, M. Grabalosa Gndara69, R. Graciani Diaz69, L.A. Granado Cardoso71, E. Graugs69,G. Graziani53, A. Grecu62, E. Greening88, S. Gregson80, V. Gromov74, O. Grnberg91,s, B. Gui89, E. Gushchin66, Yu. Guz68,Z. Guzik61, T. Gys71, F. Hachon42, C. Hadjivasiliou89, G. Haefeli72, C. Haen71, S.C. Haines80, S. Hall86, T. Hampson79, S. Hansmann-Menzemer47, N. Harnew88, S.T. Harnew79, J. Harrison87, P.F. Harrison81, T. Hartmann91,s, J. He43,B. van der Heijden74, V. Heijne74, K. Hennessy85, P. Henrard41, J.A. Hernando Morata70, E. van Herwijnen71, E. Hicks85,D. Hill88, M. Hoballah41, W. Hofmann46, C. Hombach87, P. Hopchev40, W. Hulsbergen74, P. Hunt88, T. Huse85, N. Hussain88,D. Hutchcroft85, D. Hynds84, V. Iakovenko77, P. Ilten48, J. Imong79, R. Jacobsson71, A. Jaeger47, O. Jamet71, E. Jans74,F. Jansen74, L. Jansen74, P. Jansweijer74, P. Jaton72, F. Jing39, M. John88, D. Johnson88, C.R. Jones80, B. Jost71, M. Kaballo45,S. Kandybei76, M. Karacson71, O. Karavichev66, T.M. Karbach71, A. Kashchuk63, T. Kechadi48, I.R. Kenyon78, U. Kerzel71,T. Ketel75, A. Keune72, B. Khanji56, T. Kihm46, R. Kluit74, O. Kochebina43, V. Komarov72,65, R.F. Koopman75, P. Koppenburg74, M. Korolev65, J. Kos75, A. Kozlinskiy74, L. Kravchuk66, K. Kreplin47, M. Kreps81, R. Kristic71, G. Krocker47,P. Krokovny67, F. Kruse45, M. Kucharczyk56,59,j, Y. Kudenko66, V. Kudryavtsev67, T. Kvaratskheliya64,71, V.N. La Thi72,D. Lacarrere71, G. Lafferty87, A. Lai51, D. Lambert83, R.W. Lambert75, E. Lanciotti71, L. Landi52,e, G. Lanfranchi54,71,C. Langenbruch71, S. Laptev66, T. Latham81, I. Lax50, C. Lazzeroni78, R. Le Gac42, J. van Leerdam74, J.-P. Lees40,R. Lefvre41, A. Leat65,71, J. Lefranois43, O. Leroy42, T. Lesiak59, Y. Li39, L. Li Gioi41, A. Likhoded68, M. Liles85,R. Lindner71, C. Linn47, B. Liu39, G. Liu71, J. von Loeben56, J.H. Lopes38, E. Lopez Asamar69, N. Lopez-March72,H. Lu39, J. Luisier72, H. Luo83, A. Mac Raighne84, F. Machefert43, I.V. Machikhiliyan40,64, F. Maciuc62, O. Maev63,71,M. Maino56, S. Malde88, G. Manca51,d, G. Mancinelli42, N. Mangiafave80, U. Marconi50, R. Mrki72, J. Marks47, G. Martellotti58, A. Martens44, A. Martn Snchez43, M. Martinelli74, D. Martinez Santos70, D. Martins Tostes38, A. Massafferri37,R. Matev71, Z. Mathe71, C. Matteuzzi56, M. Matveev63, E. Maurice42, J. Mauricio69, A. Mazurov52,66,71,e, J. McCarthy78,R. McNulty48, B. Meadows93,t, M. Meissner47, H. Mejia83, V. Mendez-Munoz69,o, M. Merk74, D.A. Milanes49, M.-N. Minard40, J. Molina Rodriguez90,r, S. Monteil41, D. Moran87, P. Morawski59, R. Mountain89, I. Mous74, F. Muheim83, F. Mul75,K. Mller73, B. Munneke74, R. Muresan62, B. Muryn60, B. Muster72, P. Naik79, T. Nakada72, R. Nandakumar82, I. Nasteva37,A. Nawrot61, M. Needham83, N. Neufeld71, A.D. Nguyen72, T.D. Nguyen72, C. Nguyen-Mau72,p, M. Nicol43, V. Niess41,N. Nikitin65, T. Nikodem47, Y. Nikolaiko77, S. Nisar92,t, A. Nomerotski88,71, A. Novoselov68, A. Oblakowska-Mucha60,V. Obraztsov68, S. Oggero74, S. Ogilvy84, O. Okhrimenko77, R. Oldeman51,71,d, M. Orlandea62, A. Ostankov68, J.M. Otalora Goicochea38, M. van Overbeek74, P. Owen86, B.K. Pal89, A. Palano49,b, M. Palutan54, J. Panman71, A. Papanestis82,M. Pappagallo84, C. Parkes87, C.J. Parkinson86, G. Passaleva53, G.D. Patel85, M. Patel86, G.N. Patrick82, C. Patrignani55,i,C. Pavel-Nicorescu62, A. Pazos Alvarez70, A. Pellegrino74, G. Penso58,l, M. Pepe Altarelli71, S. Perazzini50,c, D.L. Perego56,j,E. Perez Trigo70, A. Prez-Calero Yzquierdo69, P. Perret41, M. Perrin-Terrin42, G. Pessina56, K. Petridis86, A. Petrolini55,i,O. van Petten74, A. Phan89, E. Picatoste Olloqui69, D. Piedigrossi71, B. Pietrzyk40, T. Pila81, D. Pinci58, S. Playfer83, M. Plo Casasus70, F. Polci44, G. Polok59, A. Poluektov81,67, E. Polycarpo38, D. Popov46, B. Popovici62, C. Potterat69, A. Powell88,J. Prisciandaro72, M. Pugatch77, V. Pugatch77, A. Puig Navarro72, W. Qian40, J.H. Rademacker79, B. Rakotomiaramanana72, M.S. Rangel38, I. Raniuk76, N. Rauschmayr71, G. Raven75, S. Redford88, M.M. Reid81, A.C. dos Reis37, F. Rethore42,S. Ricciardi82, A. Richards86, K. Rinnert85, V. Rives Molina69, D.A. Roa Romero41, P. Robbe43, E. Rodrigues87,84, P. Rodriguez Perez70, E. Roeland74, G.J. Rogers80, S. Roiser71, V. Romanovsky68, A. Romero Vidal70, K. de Roo74, J. Rouvinet72,L. Roy71, K. Rudloff45, T. Ruf71, H. Ruiz69, G. Sabatino58,k, J.J. Saborido Silva70, N. Sagidova63, P. Sail84, B. Saitta51,d,C. Salzmann73, B. Sanmartin Sedes70, R. Santacesaria58, C. Santamarina Rios70, E. Santovetti57,k, S. Saornil Gamarra73,M. Sapunov42, A. Saputi54, A. Sarti54,l, C. Satriano58,m, A. Satta57, T. Savidge86, M. Savrie52,e, P. Schaack86, M. Schiller75,A. Schimmel74, H. Schindler71, S. Schleich45, M. Schlupp45, M. Schmelling46, B. Schmidt71, O. Schneider72, T. Schneider71, A. Schopper71, H. Schuijlenburg74, M.-H. Schune43, R. Schwemmer71, B. Sciascia54, A. Sciubba54,l, M. Seco70,A. Semennikov64, K. Senderowska60, I. Sepp86, N. Serra73, J. Serrano42, P. Seyfert47, B. Shao39, M. Shapkin68, I. Shapoval76,71, P. Shatalov64, Y. Shcheglov63, T. Shears85,71, L. Shekhtman67, O. Shevchenko76, V. Shevchenko64, A. Shires86,S. Sigurdsson80, R. Silva Coutinho81, T. Skwarnicki89, M.W. Slater78, T. Sluijk74, N.A. Smith85, E. Smith88,82, M. Smith87,K. Sobczak41, M.D. Sokoloff93,t, F.J.P. Soler84, F. Soomro54,71, D. Souza79, B. Souza De Paula38, B. Spaan45, A. Sparkes83,P. Spradlin84, S. Squerzanti52, F. Stagni71, S. Stahl47, O. Steinkamp73, O. Stenyakin68, S. Stoica62, S. Stone89, B. Storaci74,M. Straticiuc62, U. Straumann73, V.K. Subbiah71, S. Swientek45, M. Szczekowski61, P. Szczypka72,71, T. Szumlak60,S. TJampens40, M. Teklishyn43, E. Teodorescu62, F. Teubert71, C. Thomas88, E. Thomas71, A. Tikhonov66, J. van Tilburg47,V. Tisserand40, M. Tobin73, V. Tocut43, S. Tolk75, D. Tonelli71, S. Topp-Joergensen88, N. Torr88, E. Tourneer40,86,S. Tourneur72, M.T. Tran72, M. Tresch73, A. Tsaregorodtsev42, P. Tsopelas74, N. Tuning74, M. Ubeda Garcia71, A. Ukleja61,O. Ullaland71, D. Urner87, U. Uwer47, V. Vagnoni50, G. Valenti50, R. Vazquez Gomez69, P. Vazquez Regueiro70, S. Vecchi52, J.J. Velthuis79, M. Veltri53,g, G. Veneziano72, M. Vesterinen71, B. Viaud43, D. Vieira38, X. Vilasis-Cardona69,n, W. Vink74,S. Volkov63, V. Volkov65, A. Vollhardt73, D. Volyanskyy46, D. Voong79, A. Vorobyev63, V. Vorobyev67, C. Vo91,s,
Eur. Phys. J. C (2013) 73:2373 Page 91 of 92
H. Voss46, G. Vouters40, R. Waldi91,s, R. Wallace48, S. Wandernoth47, J. Wang89, D.R. Ward80, K. Warda45, N.K. Watson78, A.D. Webber87, D. Websdale86, P. Wenerke74, M. Whitehead81, J. Wicht71, D. Wiedner47, L. Wiggers74, G. Wilkinson88, M.P. Williams81,82, M. Williams86,q, F.F. Wilson82, J. Wishahi45, M. Witek59, W. Witzeling71, S.A. Wotton80, S. Wright80,S. Wu39, K. Wyllie71, Y. Xie83,71, Z. Xing89, T. Xue39, Z. Yang39, R. Young83, X. Yuan39, O. Yushchenko68, M. Zangoli50,F. Zappon74, M. Zavertyaev46,a, M. Zeng39, F. Zhang39, L. Zhang89, W.C. Zhang48, Y. Zhang39, A. Zhelezov47, L. Zhong39,E. Zverev65, A. Zvyagin71, A. Zwart74
37Centro Brasileiro de Pesquisas Fsicas (CBPF), Rio de Janeiro, Brazil
38Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
39Center for High Energy Physics, Tsinghua University, Beijing, China
40LAPP, Universit de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
41Clermont Universit, Universit Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
42CPPM, Aix-Marseille Universit, CNRS/IN2P3, Marseille, France
43LAL, Universit Paris-Sud, CNRS/IN2P3, Orsay, France
44LPNHE, Universit Pierre et Marie Curie, Universit Paris Diderot, CNRS/IN2P3, Paris, France
45Fakultt Physik, Technische Universitt Dortmund, Dortmund, Germany
46Max-Planck-Institut fr Kernphysik (MPIK), Heidelberg, Germany
47Physikalisches Institut, Ruprecht-Karls-Universitt Heidelberg, Heidelberg, Germany
48School of Physics, University College Dublin, Dublin, Ireland
49Sezione INFN di Bari, Bari, Italy
50Sezione INFN di Bologna, Bologna, Italy
51Sezione INFN di Cagliari, Cagliari, Italy
52Sezione INFN di Ferrara, Ferrara, Italy
53Sezione INFN di Firenze, Firenze, Italy
54Laboratori Nazionali dellINFN di Frascati, Frascati, Italy
55Sezione INFN di Genova, Genova, Italy
56Sezione INFN di Milano Bicocca, Milano, Italy
57Sezione INFN di Roma Tor Vergata, Roma, Italy
58Sezione INFN di Roma La Sapienza, Roma, Italy
59Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krakw, Poland
60AGH University of Science and Technology, Krakw, Poland
61National Center for Nuclear Research (NCBJ), Warsaw, Poland
62Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
63Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
64Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
65Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
66Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia
67Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia
68Institute for High Energy Physics (IHEP), Protvino, Russia
69Universitat de Barcelona, Barcelona, Spain
70Universidad de Santiago de Compostela, Santiago de Compostela, Spain
71European Organization for Nuclear Research (CERN), Geneva, Switzerland
72Ecole Polytechnique Fdrale de Lausanne (EPFL), Lausanne, Switzerland
73Physik-Institut, Universitt Zrich, Zrich, Switzerland
74Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
75Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands
76NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
77Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
78University of Birmingham, Birmingham, United Kingdom
79H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
80Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
81Department of Physics, University of Warwick, Coventry, United Kingdom
82STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
83School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
Page 92 of 92 Eur. Phys. J. C (2013) 73:2373
84School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
85Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
86Imperial College London, London, United Kingdom
87School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
88Department of Physics, University of Oxford, Oxford, United Kingdom
89Syracuse University, Syracuse, NY, United States
90Pontifcia Universidade Catlica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil
91Institut fr Physik, Universitt Rostock, Rostock, Germany
92Institute of Information Technology, COMSATS, Lahore, Pakistan
93University of Cincinnati, Cincinnati, OH, United States
aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia
bUniversit di Bari, Bari, Italy
cUniversit di Bologna, Bologna, Italy
dUniversit di Cagliari, Cagliari, Italy
eUniversit di Ferrara, Ferrara, Italy
fUniversit di Firenze, Firenze, Italy
gUniversit di Urbino, Urbino, Italy
hUniversit di Modena e Reggio Emilia, Modena, Italy
iUniversit di Genova, Genova, Italy
jUniversit di Milano Bicocca, Milano, Italy
kUniversit di Roma Tor Vergata, Roma, Italy
lUniversit di Roma La Sapienza, Roma, Italy
mUniversit della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
oPort dInformaci Cientca (PIC), Barcelona, Spain
pHanoi University of Science, Hanoi, Viet Nam
qMassachusetts Institute of Technology, Cambridge, MA, United States
rAssociated to Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
sAssociated to Physikalisches Institut, Ruprecht-Karls-Universitt Heidelberg, Heidelberg, Germany
tAssociated to Syracuse University, Syracuse, NY, United States
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer
Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013
Abstract
(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)
During 2011 the LHCb experiment at CERN collected 1.0 fb^sup -1^ of ... pp collisions. Due to the large heavy quark production cross-sections, these data provide unprecedented samples of heavy flavoured hadrons. The first results from LHCb have made a significant impact on the flavour physics landscape and have definitively proved the concept of a dedicated experiment in the forward region at a hadron collider. This document discusses the implications of these first measurements on classes of extensions to the Standard Model, bearing in mind the interplay with the results of searches for on-shell production of new particles at ATLAS and CMS. The physics potential of an upgrade to the LHCb detector, which would allow an order of magnitude more data to be collected, is emphasised.
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer