The NMSSM with F-theory unified boundary conditions

Abstract

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

We study the phenomenological viability of a constrained NMSSM with parameters subject to unified boundary conditions from F-theory GUTs. We find that very simple assumptions about modulus dominance SUSY breaking in F-theory unification lead to a predictive set of boundary conditions, consistent with all phenomenological constraints. The second lightest scalar Higgs H ^sub 2^ can get a mass ... GeV and has properties similar to the SM Higgs. On the other hand the lightest scalar H ^sub 1^, with a dominant singlet component, would have barely escaped detection at LEP and could be observable at LHC as a peak in H ^sub 1^ [arrow right] γγ at around 100 GeV. The LSP is mostly singlino and is consistent with WMAP constraints due to coannihilation with the lightest stau, whose mass is in the range 100 - 250 GeV. Such light staus may lead to very characteristic signatures at LHC and be directly searched at linear colliders. In these models tan [beta] is large, of order 50, still the branching ratio for B ^sub s^ [arrow right] [mu] ^sup +^ [mu] ^sup -^ is consistent with the LHCb bounds and in many cases is also even smaller than the SM prediction. Gluinos and squarks have masses in the 2-3 TeV region and may be accessible at the LHC at 14TeV. No large enhancement of the H ^sub 2^ [arrow right] γγ rate over that of the SM Higgs is expected.

Published for SISSA by Springer

Received: January 17, 2013

Accepted: January 27, 2013 Published: February 14, 2013

L. Aparicio,a P.G. Cmara,b,c D.G. Cerdeo,d L.E. Ibezd and I. Valenzuelad

aInternational Centre for Theoretical Physics (ICTP),

Strada Costiera 11, I-34014 Trieste, Italy

bDepartament dEstructura i Constituents de la Matria and Institut de Cincies del Cosmos, Universitat de Barcelona, Mart i Franqus 1, 08028 Barcelona, Spain

cDepartament de Fsica Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain

dDepartamento de Fsica Terica and Instituto de Fsica Terica UAM/CSIC, Universidad Autnoma de Madrid, Cantoblanco, 28049 Madrid, Spain

E-mail: mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected] , [email protected], [email protected]

Abstract: We study the phenomenological viability of a constrained NMSSM with parameters subject to unied boundary conditions from F-theory GUTs. We nd that very simple assumptions about modulus dominance SUSY breaking in F-theory unication lead to a predictive set of boundary conditions, consistent with all phenomenological constraints. The second lightest scalar Higgs H2 can get a mass mH2 125 GeV and has properties

similar to the SM Higgs. On the other hand the lightest scalar H1, with a dominant singlet component, would have barely escaped detection at LEP and could be observable at LHC as a peak in H1 at around 100 GeV. The LSP is mostly singlino and is consistent

with WMAP constraints due to coannihilation with the lightest stau, whose mass is in the range 100 250 GeV. Such light staus may lead to very characteristic signatures at LHC

and be directly searched at linear colliders. In these models tan is large, of order 50, still the branching ratio for Bs + is consistent with the LHCb bounds and in many

cases is also even smaller than the SM prediction. Gluinos and squarks have masses in the 2 3 TeV region and may be accessible at the LHC at 14 TeV. No large enhancement of

the H2 rate over that of the SM Higgs is expected.

Keywords: Supersymmetry Phenomenology, Strings and branes phenomenology

ArXiv ePrint: 1212.4808

c

The NMSSM with F-theory unied boundary conditions

JHEP02(2013)084

SISSA 2013 doi:http://dx.doi.org/10.1007/JHEP02(2013)084

Web End =10.1007/JHEP02(2013)084

Contents

1 Introduction 1

2 The NMSSM and F-theory unication 52.1 The couplings and 82.2 T -modulus dominance and unied soft-terms 9

3 Higgs masses, dark matter and other constraints 103.1 Scanning over modulus dominated NMSSM vacua 113.2 The Higgs sector at two loops 143.3 Neutralino dark matter 163.4 Constraints on rare decays and the muon anomalous magnetic moment 18

4 Consistency with F-theory unication 204.1 M, H and tan 214.2 The singlet sector: A , A and 22

5 Supersymmetric spectrum and signatures 25

6 Discussion 26

A The Higgs sector at one loop 28

1 Introduction

The starting into operation of LHC is already testing many avenues beyond the Standard Model (SM). In particular, the discovery of a boson with mass around 125 GeV [1, 2] and properties compatible with those of the SM Higgs is signicantly constraining many of these ideas beyond the SM. In this regard one may argue that such value for a Higgs mass goes in the direction of low energy SUSY, since supersymmetric models predict a lightest Higgs with mass mh [lessorsimilar] 130 GeV. On the other hand, the observed mass is close to the maximum expected in low energy SUSY theories, implying a certain degree of ne-tuning in the SUSY-breaking parameters which must be relatively large. This is also consistent with the no observation as yet of any supersymmetric particle at LHC.

The simplest testing ground for low energy SUSY is the Minimal Supersymmetric Standard Model (MSSM) which does not involve any new particle beyond the SUSY partners required by supersymmetry. Still the MSSM has an unattractive ingredient in its bilinear Higgs superpotential term, the -term. Although supersymmetric, this mass term has to be (for no good reason) of order of the SUSY-breaking soft terms to get consistent electro-weak (EW) symmetry breaking and low energy SUSY spectrum. Perhaps the most

1

JHEP02(2013)084

economical solution to this problem is the scale invariant Next to Minimal Supersymmetric Standard Model (NMSSM) [3, 4] in which a singlet S is added to the MSSM spectrum and the -term is replaced in the superpotential by new couplings,

WNMSSM = WYuk + SHuHd + 3 S3 . (1.1)

There are no mass parameters in the superpotential and the role of the -parameter is now played by hSi which upon minimization of the scalar potential gets naturally of the same

order than the SUSY-breaking soft parameters.

The SUSY-breaking soft terms involving the singlet S and the Higgs chiral elds have the general form

V Ssoft = m2Hu|Hu|2 + m2Hd|Hd|2 + m2S|S|2 + [parenleftbigg]

A SHuHd +

As in the case of the MSSM, the most general NMSSM model has plenty of free parameters. On the other hand, in the presence of some underlying unication structure at a high energy scale, one expects the number of parameters to be reduced to a few. In the case of the MSSM, the constrained MSSM (CMSSM) has universal parameters m, M, A, and B, where m is the universal scalar mass, M the universal gaugino mass, A the universal trilinear parameter of the standard Yukawa couplings and B the universal bilinear coupling, all of them dened at the unication scale. Indeed, there are models based on String Theory that lead to such universal selection of parameters or extensions of it (for instance with non-universal Higgs masses), see e.g. [5] and references therein. Similarly, a constrained version of the NMSSM is usually dened in terms of the ve universal parameters

m , M , , , A = A = A . (1.3)

In practice, however, one usually takes as free parameters m, M, A, tan and (plus the sign of the e ective -term). The values of mS and are xed upon minimization and hence mS in general does not unify with the rest of the scalars of the theory. The theory is therefore not constrained in the same sense as it is in the CMSSM [6, 7]. One may argue that the singlet may be a bit special and is perhaps not surprising that mS is not unied with the rest of the scalar masses. But then it would be inconsistent to unify the trilinear A-terms. In particular, A and A should be unrelated to the Yukawa trilinear coupling A. Thus, the least one can say is that the partially constrained versions of the NMSSM considered up to now are slightly inconsistent, unless one allows A and A as free parameters, with the resulting reduction of predictivity. This is one of the main issues that we address in this paper, namely we try to understand and constraint the structure of the NMSSM parameters at a more fundamental level.

The NMSSM has received recently a lot of attention after the evidence and subsequent discovery of the 125 GeV boson at LHC [822]. There are two main reasons for that. On the one hand, in a general NMSSM model the mass of the Higgs particle receives extra contributions from the SHuHd superpotential term,

m2h m2Z cos2 2 + 2v2sin2 2 + (m2h), (1.4)

2

3 A S3 + h.c.[parenrightbigg]

JHEP02(2013)084

(1.2)

where v = 174 GeV is the Higgs vev, mZ is the mass of the Z boson and (m2h) denote the loop corrections to the Higgs mass. In the MSSM these loop corrections account for the increasing of the Higgs mass from 90 to 125 GeV, requiring large soft terms, stop mixing and ne-tuning. In the NMSSM, however, the second term in eq. (1.4) gives an additional contribution to the mass for relatively large ([greaterorsimilar] 0.5) and small tan . This allows to get a fairly heavy Higgs boson while reducing the ne-tuning. The second reason for this recent interest on the NMSSM is the fact that for some regions of the parameter space one may get an enhanced Higgs decay rate to two photons, as suggested by the ATLAS and CMS results as of July 2012 [1, 2].

As we have already mentioned above, our investigation is however not led by these two interests but rather by the attempt to dene a fundamentally-motivated constrained NMSSM and to check it against the present experimental data, including a 125 GeV Higgs. Concretely, as in the CMSSM, a unied gauge symmetry like SU(5) naturally induces universal gaugino masses and also unies many of the sfermion masses. Further assumptions about the origin of SUSY-breaking may lead to an increased degree of unication of the SUSY-breaking soft terms. That is for instance the case of modulus dominance SUSY-breaking in F-theory SU(5) GUTs (for reviews see ref. [2327]) that we consider here. In refs. [28, 29] boundary conditions of the general form1

m2 = 12|M|2 , A =

32M , (1.5)

were phenomenologically analysed in the context of the MSSM. These conditions appear naturally in F-theory SU(5) schemes in which one assumes that the auxiliary eld of the local Kahler modulus T is the dominant source of SUSY-breaking, see [28]. In the above references it was found that these boundary conditions are consistent with all low energy constraints, including a Higgs eld with mass around 125 GeV and appropriate dark matter relic density. The scheme is very predictive, implying tan 41 and a relatively heavy

spectrum with M 1.4 TeV, leading to squarks and gluinos of order 3 TeV. Such heavy

spectrum is required after imposing the recent bounds on the branching ratio BR(Bs +) from LHCb [30] and CMS [31]. Actually, the most recent results for this decay [32, 33] corner very much the parameter space of this very constrained MSSM model.

On the light of the above NMSSM discussion, it is thus natural to explore whether the F-theory SU(5) unication idea exploited in [28] for the MSSM may be extended to the case of the scale invariant NMSSM. In this paper we nd that the boundary conditions (1.5) are indeed consistent with all the current phenomenological constraints, including a 125 GeV Higgs boson. A large value of tan 50 is again selected and a very small parameter is

required. Small values of naively correspond to an e ective MSSM limit. Still, the presence of the singlet S leads to quite di erent physics as compared to the MSSM case. First, the lightest supersymmetric particle is mostly singlino and correct dark matter abundance is obtained due to coannihilation with the lightest stau, which is the NLSP, with masses in the range 100 250 GeV. Secondly, in addition to the SM-like Higgs with mass around

125 GeV, there is a lighter neutral scalar with mass around 100 GeV which would have

1Gauge uxes may slightly distort these boundary condition as we will see later [28].

3

JHEP02(2013)084

barely escaped detection at LEP and that should be detectable at LHC. Thirdly, due to an interference e ect, the branching ratio BR(Bs +) is easily consistent with the recent

LHCb data and may be even smaller than the SM prediction. Finally, the squark/gluino spectrum is typically lighter than in the MSSM, with masses as low as 2 TeV, easily accessible at LHC at 13 TeV. All in all, we nd that these are highly constrained and predictive scenarios which pass all the current experimental constraints with a scale of SUSY-breaking that can be as low as M 850 GeV.

Another particularly attractive aspect of our theoretical approach is the additional information obtained about the singlet sector. In the context of modulus dominated SUSY-breaking within local F-theory SU(5) unication, the singlet sector is less determined. Still, in the simplest scenarios we expect additional constraints that, to rst approximation, are of the form

A M , A m2S 0 . (1.6)

Due to the approximate nature of these constraints, we do not impose them in our analysis. However and remarkably, we nd that almost all the region of the parameter space that the current low energy data selects is also consistent with the relationships (1.6) at the unication scale. This is particularly remarkable for the linear relationship A M, see gure 10 in section 4. Moreover, the geometric structure of the F-theory unication predicts small values for the couplings and , in agreement with the phenomenological requirements. Thus, at least at the semi-quantitative level, combining eqs. (1.5) and (1.6), the present NMSSM scheme essentially depends on only three free parameters, namely M, and , that are reduced (approximately) to two parameters M and once we impose correct EW symmetry breaking. Of course, this is only semi-quantitative since eqs. (1.6) are only approximate and eqs. (1.5) and (1.6) may have small corrections from gauge uxes in the extra dimensions. However, it explains the very constrained structure of possible benchmarks in this scheme, as displayed in table 1 in section 5.

Finally, let us mention that in this constrained version of the NMSSM we do not nd an enhanced Higgs decay rate to compared to the SM, but rather a slight reduction. Whereas our numerical analysis takes into account all the known two loop radiative corrections to the Higgs sector of the NMSSM [34], in this region of the parameter space these corrections are very large. Since some of the two loop corrections to the Higgs sector in the NMSSM have not yet been computed and are thus not taken into account by our numerical analysis, we expect relatively large uncertainties in our numerical estimations for the masses and decay rates of the Higgs sector. Nevertheless, a strong enhancement in this rate, as suggested by the preliminary ATLAS and CMS recent results [1, 2], appears to be clearly disfavoured in this scenario.

The structure of this paper is as follows. In section 2 we describe the F-theory unication structure in the context of NMSSM models with Kahler modulus domination. In section 3 we run the SUSY-breaking soft parameters from the unication scale down to the EW scale according to the renormalization group equations and perform a computerized scan over the complete parameter space of these models. We also comment on the main phenomenological constraints that shape the allowed regions of the parameter space.

4

JHEP02(2013)084

The main constraints arise from the Higgs sector, the dark matter relic density and rare decays such as Bs +. In section 4 we analyze the consistency of the regions of the

parameter space that pass all the current phenomenological constraints, with the F-theory unication structure discussed in section 2. In section 5 we give some benchmarks and discuss their possible signatures at LHC and other future experiments. Finally, we end with some last comments in section 6. All the above analysis takes into account the known two loop radiative corrections to the Higgs sector of the NMSSM. In appendix A we repeat the analysis of the Higgs sector but keeping only account of the one loop radiative corrections to this sector, showing still qualitatively good agreement with the results in the main part of the text.

2 The NMSSM and F-theory unication

F-theory SU(5) unication [3538] has been recently the subject of intense research both from the phenomenological and string compactication points of view [2327, 39]. These theories provide an ultraviolet completion within string theory to more traditional SU(5) GUTs, while involving new mechanisms to address some of the problems of eld theory GUTs. The symmetry breaking from SU(5) down to the SM is induced by the generic presence of hypercharge uxes in the compact dimensions. The presence of these uxes can also give rise to doublet-triplet splitting for appropriate ux choices. Furthermore the observed departure of Yukawa couplings for D-quarks and charged leptons from unication may also be accounted for [40, 41]. The reader not interested in the formal details of this class of model may safely jump to section 3.

F-theory may be considered as a non-perturbative generalization of type IIB orientifold compactications. Ten-dimensional type IIB string theory contains a complex scalar dilaton eld = e + iC0, where controls the perturbative loop expansion and C0 is the Ramond-Ramond scalar. The theory is invariant under a SL(2, Z) symmetry generated by the transformations 1/ and + i. F-theory provides a geometrization of

this symmetry by adding two (auxiliary) extra dimensions with T 2 toroidal geometry and identifying the complex structure of this T 2 with the complex dilaton . The resulting geometric construction is 12-dimensional and N = 1 4d vacua can be obtained by compactifying the theory on a complex Calabi-Yau (CY) 4-fold X4. Such 4-fold is required to be an eliptic bration over a 6-dimensional base B3, so that locally X4 T 2 B3.

Codimension-4 singularities of the bration correspond to 7-branes wrapping 4-cycles of the base B3. In F-theory SU(5) GUTs one set of such 7-branes, wrapping a 4-cycle S, yield

an SU(5) gauge symmetry. Moreover, for suitable topologies of B3, it is possible decouple the local dynamics associated to the SU(5) branes living on the 4-fold S from the global

aspects of the B3 compact space.

Chiral matter appears at the complex 1-dimensional pairwise intersections of 7-branes, corresponding to an enhanced degree of the singularity (see gure 1). In F-theory language the locus of the intersection is usually called matter curve. In minimal SU(5) GUTs the gauge symmetry is locally enhanced to SU(6) or SO(10) at the matter curves. Indeed,

5

JHEP02(2013)084

Figure 1. General structure of a local F-theory SU(5) GUT. The GUT group lives on 7-branes whose 4 extra dimensions beyond Minkowski wrap a 4-cycle S inside a complex 3-fold B3, on which the 6 extra dimensions of String Theory are compactied. Gauge bosons live in the bulk of

S whereas quarks, leptons, and Higgsses are localized in complex curves inside S. These matter

curves (denoted as 10, 5, 5H and 5H in the gure) correspond to the intersection of the 7-branes wrapping S with other U(1) 7-branes, as depicted in the gure of the right hand side. There is one

matter curve for each SU(5) representation. At the intersection of matter curves with Higgs curves 5H and 5H, Yukawa couplings develop (gure taken from ref. [39]).

recalling the adjoint branchings

SU(6) SU(5) U(1) (2.1)

35 240 + 10 + [51 + c.c.]

SO(10) SU(5) U(1) (2.2)

45 240 + 10 + [104 + c.c.]

we observe that in the matter curve associated to a 5 (or a 5) representation of SU(5) the gauge symmetry is enhanced to SU(6), whereas in the one related to a 10 of SU(5) the gauge symmetry is enhanced to SO(10). In order to get chiral fermions there must be non-vanishing uxes along the U(1) and U(1) symmetries.

In addition to the above matter curves, a third matter curve with an enhanced SU(6) symmetry is required to obtain Higgs 5-plets. Yukawa couplings appear at the point-like intersection of the Higgs matter curve with the fermion matter curves, as illustrated in gure 1. At the intersection point the symmetry is further enhanced to SO(12) in the case of 10

5H down Yukawa couplings and to E6 in the case of 10 10 5H up

Yukawa couplings.

In order to make contact with SM physics, the SU(5) gauge symmetry must be broken down to SU(3) SU(2) U(1). In these constructions there are no massless adjoints to

make that breaking and discrete Wilson lines are also not available. Nevertheless, one can still achieve such breaking by means of an additional ux FY along the hypercharge

6

5

JHEP02(2013)084

Figure 2. General structure of a local F-theory SU(5) GUT with NMSSM couplings. The matter curves where the Higgs multiplets live intersect with a transverse curve where the singlet S lives. At the triple intersection point the gauge symmetry is enhanced to SU(7).

generator in SU(5), leading to the same symmetry breaking e ect as an adjoint Higgssing. Interestingly enough, this hypercharge ux is also a source for doublet-triplet splitting of the Higgs multiplets 5H + 5H.

Besides the above points of SO(12) and E6 enhancement, F-theory SU(5) GUTs may also contain points at which the gauge symmetry is enhanced to SU(7). These correspond to 5

5 1 intersections between two 5-plet curves and a singlet curve, as can be derived

from the adjoint branching

SU(7) SU(5) U(1)2 (2.3)

48 24 + 1(0,0) + 1(0,0) + [5(0,1) + 1(1,1) +

5(1,0) + c.c. ]

The bosons associated to the extra U(1)s are in general anomalous and become massive in the usual way.2

The simplest models of this class contain one extra singlet S coupling to the Higgs multiplets and at low energies are equivalent to the scale invariant NMSSM. In what follows we consider that specic setup. The structure of the superpotential is thus given by

WNMSSM = WYuk + SHuHd +

3 S3 . (2.4) with WYuk the standard superpotential Yukawa couplings. To get this structure the matter curves associated to the two Higgs 5-plets Hu and Hd must intersect with a transverse

2F-theory models with hypercharge ux GUT group breaking and SU(5) singlets charged under U(1) Peccei-Quinn like gauge symmetries have been argued to require the presence of exotics in the spectrum [42 45]. Here we assume models with no exotics or with very massive ones. Other constructions, such as those where the singlets are not charged under the extra U(1)s (for instance, if they come from closed and/or open string moduli in the microscopic theory) also t well within this context.

7

JHEP02(2013)084

singlet S curve, see gure 2. At the point of intersection the symmetry is enhanced from SU(6) to SU(7). Identifying the singlet in the brackets of eq. (2.3) with S we see that indeed it may couple to the two Higgs multiplets while respecting the U(1) symmetries.

In an F-theory construction as above there is a Kahler modulus Tb whose real part tb describes the size of the 6-dimensional manifold B3. In addition, the volume of the 4-cycle

S where the SU(5) degrees of freedom live is controlled by a local modulus T with real part

t. Finally, the U(1)s live in other 4-cycles di erent than S whose volumes are controlled by

Kahler moduli that we will denote collectively as TS, with real part tS. In a local setting one assumes t, tS tb, so that to leading approximation we can safely ignore the details of

B3 in order to study the dynamics of the SU(5) branes.3 One can describe this structure by a Swiss cheese type Kahler potential of the simplied form [4750]

K = 2log

t3/2b t3/2 t3/2S[parenrightBig]

where we are working in Planck units. Following [51] (see also [5]), we can make use of scaling arguments in order to extract the leading moduli dependence of the Kahler metrics of the matter elds. For a matter eld X living on a divisor SX the Kahler metric admits

an expansion for tX tb of the form

KX = t(1X)Xtb (2.6)

where X is the so-called modular weight of the eld with respect to the local modulus tX. For matter elds localized on a matter curve the mentioned scaling arguments yield X = 1/2. In our case we have respectively for the SU(5) matter multiplets and the singlet S

K5,10 = t1/2

tb , KS =

4/3g1/3s , t = 1G 24 (2.8)

where G 1/24 is the gauge coupling at the unication scale, Ms = ()1/2 is the

string scale and gs = hei the string coupling constant. For Ms 1016 GeV one has

tb 115 g1/3s t for gs 0.01, consistently with our requirement t tb.2.1 The couplings and

Due to the above hierarchy of volumes, physical Yukawa couplings (namely, those that correspond to normalized kinetic terms) may di er substantially from the holomorphic

3The existence of a manifold B3 admitting such a local limit is however not always guaranteed (see e.g. [46]).

8

JHEP02(2013)084

(2.5)

t1/2Stb (2.7)

In particular, note that the Kahler metric of S is independent of t. This fact will be relevant for the structure of soft terms discussed below.

The values of tb and t are related to known physical quantities. In particular in the perturbative regime one obtains (see e.g. [5])

tb = 14 [parenleftbigg]

Mp

Ms

Yukawas appearing in the superpotential. Physical Yukawa couplings hphys are related to

the holomorphic ones h0 by the standard N = 1 supergravity expression

hijkphys = hijk0(KiKjKk)1/2eK/2 (2.9)

where Ki are the (diagonal) Kahler metrics of the elds involved in the coupling and we do not sum over i, j and k. In particular, for the NMSSM specic Yukawa couplings in eq. (2.4) we obtain

phys = 0 t1/2 t1/4S 0

phys = 0 t3/4S .

where we have made use of eqs. (2.5) and (2.7). For tS t 24 we thus get a sup

pression factor in relating the holomorphic couplings 0 and 0 to the physical ones, with phys, phys 9 102 0, 0. We will show in section 3 that appropriate EW symmetry breaking in these models together with the current experimental constraints require small physical couplings phys and phys. This is indeed consistent with the above suppression

coming from the Kahler metrics, as typically |0|, |0| 1. On the contrary, large values

for these couplings as required e.g. in refs. [810, 1216, 1820, 22] do not seem viable within our context.

We have already mentioned in the previous subsection the possible origin of the cubic coupling in eq. (2.4) from the intersection of three matter curves on a point of enhanced SU(7) symmetry. If that is the case, the cubic coupling in eq. (2.4) should arise from instanton corrections that violate the (typically anomalous) U(1)s, under which S is charged (see e.g. [52]). In particular, the absence of a quadratic S2 coupling suggests the presence of a Z3 gauged symmetry remnant of a gauged U(1)X symmetry [53]. One thus expects

to be a small parameter.4

2.2 T -modulus dominance and unied soft-terms

A natural source of supersymmetry breaking in type IIB string theory compactications, or more generally in F-theory, is the presence of certain classes of closed string antisymmetric uxes (G4 uxes in F-theory). As described in [5458], from the point of view of the 4-dimensional e ective supergravity, the supersymmetry breaking uxes are encoded in non-zero vevs of the F-auxiliary elds of the Kahler moduli. In this work we assume a hierarchy of vevs Ftb Ft FtS as it will lead to a very constrained set of soft-terms.

Such hierarchies of auxiliary elds easily arise in large volume models (see [4750]). Thus, following [28] and making use of eqs. (2.5) and (2.7) we can compute explicitly the structure of soft terms at the unication scale for the MSSM sector of the theory, yielding results as

4Cubic self-couplings could also arise if S were in fact a linear combination of three di erent singlets within an extended gauge symmetry E7 or E8 in F-theory. Even in this case a small coupling is expected due to the geometric suppression discussed above.

9

1/2G

t1/4S

, (2.10)

JHEP02(2013)084

in [28], namely

2 (3 H) .

where M are universal gaugino masses, A are trilinear couplings (which appear multiplied by the SM Yukawa couplings in the Lagrangian) and mH, m5 and m10 are universal masses for the scalar elds in the three SM matter curves. The parameter H corresponds to a correction describing the e ect of gauge uxes on the Higgs matter curve, see [28] for details. This parameter should be small, of order H 1/2G 0.2 or smaller.

In addition to the above MSSM-like soft terms, there are also soft terms that involve the singlet S. The structure of such soft terms is however more subtle since, unlike the SM elds and gauge bosons, S is not localized on the 4-cycle S and therefore may be subject

to extra sources of supersymmetry breaking. The statements that one can make for the soft terms involving S are thus more model dependent. In the simplest case, with no other sources of supersymmetry breaking for S other than Ftb and Ft, making use of the Kahler metric for S, eq. (2.7), yields at the unication scale

A = M (1 H) , A = m2S = 0 , (2.12) where A and A are the coe cients of the trilinear scalar couplings (SHuHd) and S3 in the Lagrangian.5

In the next section we analyze the phenomenological implications of the boundary conditions (2.11) that depend on the two parameters M and H, and we leave , , A , A

and mS as free parameters. However, as described in detail in section 4, the regions of the parameter space that are consistent with correct EW symmetry breaking, a Higgs mass in the vicinity of 125 GeV and other phenomenological constraints tend to select solutions that are also consistent with the constraints (2.12)! This is remarkable since in no place such second stronger unication conditions were imposed.

3 Higgs masses, dark matter and other constraints

In order to analyze the phenomenological prospects of the NMSSM models with F-theory unication boundary conditions discussed above, in this section we run the soft terms eqs. (2.11) from the unication scale down to the EW scale according to the renormalization group equations, and impose radiative EW symmetry breaking in the standard way as well as the main phenomenological constraints. The strongest phenomenological constraints

5By a slight abuse of notation, we make use of the same letter to denote the multiplet (appearing in the superpotential) and its scalar component (appearing in the Lagragian).

10

M = Ft

m2H = |M|2

2

M|2

2 ,

A =

M

t , (2.11)

,

1 3 2H

[parenrightbigg]

m25,10 = |

JHEP02(2013)084

that shape the structure of our solutions come from the Higgs sector, the dark matter relic density and the branching ratio BR(Bs +), as we discuss below.

3.1 Scanning over modulus dominated NMSSM vacua

Without imposing the extra conditions (2.12), NMSSM models with F-theory unication boundary conditions consist of seven parameters, namely the values of M, H, , , A ,

A and mS at the GUT scale. One combination of these parameters is however xed by requiring the correct pole mass for the Z boson, mZ = 91.187 GeV [59]. Equivalently, we can take the six independent parameters to be given by the values of M, H, A and A

at the unication scale, at the supersymmetry breaking scale and tan at the scale mZ.

We perform a large scan over this parameter space by means of a modied version of the computer program NMSSMTools [6062] v3.2.0, where we have implemented the boundary conditions eqs. (2.11) at the unication scale. We take the latest combined result from Tevatron for the top quark pole mass, mt = 173.2 GeV [63].

The output of NMSSMTools consists of the supersymmetric mass spectrum computed at the scale Q2 = m~q3m~u3, with ~q3 and3 the third generation squarks; as well as the main couplings and reduced cross sections at the supersymmetry breaking scale, taking into account the known two-loop radiative corrections to the NMSSM Higgs sector [34]. Moreover, it imposes the main experimental constraints from LEP, Tevatron, LHC and WMAP, that we have updated with the most recent CMS results for the observed 95% condence level upper limit on the reduced cross sections for the Higgs decays H + [64],

H W +W + [65], H ZZ ++ [66] and V H V b

b [67], based on

17 fb1 of integrated luminosity at s = 7 8 TeV, the ATLAS and CMS recent results

for H [68, 69], based on near 11 fb1 of integrated luminosity at s = 7 8 TeV,

and the ATLAS result for the MSSM decay H+ + [70], based on 4.6 fb1 of inte

grated luminosity at s = 7 TeV. We have also included the recent LHCb result measuring BR(Bs +) = 3.2+1.51.2 109 at 95% condence level [33]. Regarding the relic den

sity of neutralino dark matter, NMSSMTools calls the computer program micrOMEGAs [7173] v2.2 in order to estimate it and compares with the amount of cold dark matter observed by the WMAP satellite, 0.1008 h2 0.1232 at the 2 condence level [74]. We do not

impose a priori any constraint on the muon anomalous magnetic moment (g 2) but will

comment on the numerical results for this quantity below.

Despite the large amount of constraints, we nd solutions with correct EW symmetry breaking that pass all the current theoretical and phenomenological constraints and have a moderately low scale of supersymmetry breaking, M [greaterorsimilar] 850 GeV. All these vacua have large tan and small , typically with tan [greaterorsimilar] 46 and [lessorsimilar] 0.01 (see gure 3 below and gure 8 in section 4.1). The input parameters for a representative sample of benchmark points are shown in table 1, where we also include GUT and mGUTS . The resulting values of the

NMSSM parameters at the SUSY scale are indicated in table 2. Having such large values of tan introduces important uncertainties in the computation of the masses for the Higgs sector, as threshold corrections to down Yukawa couplings become large in this regime (see e.g. [75, 76] for similar considerations in the context of the MSSM). Moreover, in this region of the parameter space also two-loop radiative corrections to the neutral scalar and

11

JHEP02(2013)084

Point

P1 858.2 47.5 0.035 5.2 103 4.1 104 -895.4 -319.2 105.9 P2 888.0 49.0 0.0092 6.5 103 3.8 104 -922.9 -195.6 50.0

P3 981.4 49.5 0.021 6.7 103 4.1 104 -1015.7 -262.2 82.9 P4 1009.9 52.9 0.195 6.4 103 3.7 104 -1045.7 -252.7 78.5

P5 1036.0 51.5 0.135 6.3 103 3.9 104 -1070.3 -303.1 99.9 P6 1180.5 53.3 0.030 5.5 103 2.5 104 -1204.2 -198.2 50.6

P7 1218.5 56.8 0.30 5.7 103 2.8 104 -1257.9 -281.6 91.9 P8 1271.0 55.1 0.182 5.1 103 1.9 104 -1290.0 -160.5 22.7

Table 1. F-theory unication/modulus dominance boundary conditions for a representative of benchmark points satisfying all the experimental constraints. Masses are given in GeV.

Point

SUSY

SUSY

ASUSY

P1 4.8 103 4.1 104 -107.0 -319.1 105.8 1243 P2 5.9 103 3.8 104 -84.3 -195.5 49.9 1280

P3 6.1 103 4.1 104 -97.2 -262.2 82.8 1401 P4 5.7 103 3.7 104 -98.9 -252.6 78.4 1447

P5 5.7 103 4.0 104 -107.3 -303 99.9 1478 P6 4.9 103 2.5 104 -91.0 -198.2 50.5 1662

P7 4.9 103 2.8 104 -107.3 -281.5 91.9 1723 P8 4.5 103 1.9 104 -86.0 -160.5 22.5 1780

Table 2. Boundary conditions at SUSY scale. Masses are given in GeV.

pseudoscalar masses are large and particularly sensitive to the value of mt. Whereas most of these radiative corrections have been computed [34] and are actually taken into account by NMSSMTools, some of them remain yet unknown. The reader should hence bear in mind that some of our numerical estimations (mostly those concerning the masses of the neutral scalar and pseudoscalar sectors) may contain relatively large uncertainties.6 Nevertheless, we nd that the qualitative conclusions of our analysis are solid, and do not change if the analysis is done for instance at the one loop level (see appendix A).

6A similar statement is obtained from comparison with the results obtained by means of the SARAH-Spheno [7779] NMSSM implementation presented in [80] that includes the two-loop radiative corrections of [34].

12

M

tan

H

GUT

GUT

AGUT

AGUT

mGUTS

ASUSY

mSUSYS

e

JHEP02(2013)084

JHEP02(2013)084

Figure 3. Distribution of NMSSM vacua over the plane (, ) with F-theory boundary conditions at the unication scale given by eqs. (2.11) and unconstrained values of A , A and . Dark blue and red points both pass all the current experimental and theoretical constraints. Dark blue points, however, have a deciency of neutralino relic density and therefore require some additional source of dark matter.

On the other hand, having small values of is consistent with the F-theory considerations discussed in section 2.1, and drives these solutions near the e ective MSSM limit of the NMSSM. In spite of the apparent similitude with the MSSM, there are however important di erences, coming from the fact that for such small values of the lightest scalar and pseudoscalar Higgsses and the lightest neutralino are largely dominated by their singlet and singlino components, respectively. This has important consequences for the neutralino relic density and the Higgs couplings, as we discuss below.

Whereas we have scanned for arbitrary signs and values of A , A and , we have only found phenomenologically viable vacua for the sign choice A < 0, A 0 and 0. We

will discuss further this point in section 4.2. In what follows we focus in that region. We have represented in gure 3 the values of and at the scale of supersymmetry breaking for the set of NMSSM vacua considered in this paper. As we observe, for > 0 we recover positive values of and generally one order of magnitude smaller, <

/10. This is a consequence of the minimization conditions of the scalar potential and is consistent with what happens in the constrained NMSSM [6].

13

JHEP02(2013)084

Figure 4. Distribution of the light Higgs masses (mH1, mH2) for NMSSM vacua with F-theory unication boundary conditions (2.11) and unconstrained values of A , A and . Dark blue and red points both pass all the current experimental and theoretical constraints. Dark blue points, however, have a deciency of neutralino relic density and therefore require some additional source of dark matter.

3.2 The Higgs sector at two loops

In the NMSSM the Higgs sector consists of three neutral scalars, Hi, i = 1, 2, 3, two neutral

pseudoscalars, Ak, k = 1, 2, and one charged scalar, H+. Scanning over modulus dominated NMSSM vacua as described in the previous subsection, reveals that the boundary conditions (2.11) do not allow for mH1 [greaterorsimilar] 120 GeV in any region of the parameter space.

The only possibility is hence that H2 plays the role of the SM-like Higgs boson, with mH2 > mH1, and H1 is fairly decoupled from the SM sector such that it escaped detection at LEP. This leads naturally to small values of since in that case H1 is mostly singlet (see gure 3) and it couples very weakly to the SM elds. Thus, one of the main predictions of NMSSM models with F-theory unied boundary conditions (2.11) is the presence of an extra light Higgs that is fairly decoupled from the SM elds. Such possibility has also been recently considered in [20].

To be more precise, we represent in gure 4 the distribution of masses (mH1, mH2) for

the two lightest Higgs bosons. The strongest constraints in this plane come from the LHC

upper limits on the reduced cross section of the Higgs decay H [68, 69] and from the

analogous LEP results for H b

b [81]. The former puts a lower bound mH2 [greaterorsimilar] 122 GeV on the mass of the SM-like Higgs, whereas the latter constrains vacua where the lightest

14

Higgs H1 couples too strongly to the SM fermions. Since in these models the scalar singlet component is distributed among H1 and H2, and large masses mH2 require a non-negligible singlet component for H2, the cross section bbZ(e+e H1Z) increases with the mass

of H2 and therefore LEP bounds e ectively constrain mH2 from above, see gure 4. This upper bound on mH2 is in particular (slightly) stronger than the one derived from the recent LHC results. Vacua that are consistent with both LHC and LEP bounds thus have approximately mH1 = 100 15 GeV and mH2 = 124 2 GeV, with the signal of H1 tting

in the 2 excess observed at LEP [81].

It is also interesting to compare the predicted reduced cross sections of the SM-like Higgs boson H2 with the recently observed Higgs signal at the LHC, particularly in the

H channel, as it is starting to being measured with increasing precision. In gure 5

we represent the reduced signal cross section in the gg H2 channel

R 2(gg)

(gg H2)

SM(gg H)

(3.1)

against the mass of H2. As we have already mentioned, the singlet component of H2 is not negligible for the above allowed range of masses. This leads to a mild suppression of the couplings of the SM-like Higgs H2 to the other SM elds, and in particular to the top quark and the W bosons that dominate the one loop SM contribution to (gg H). Moreover,

the stau is not light enough to enhance the di-photon production by running in the loops. Hence, as it can be observed in gure 5, there is no enhancement in (gg H2) with

respect to the SM but rather a mild suppression, with R 2(gg H2) 0.70.9. Although

this is still in reasonable agreement with the latest LHC results [68, 69], an experimental conrmation of a large enhancement in R 2(gg H2) could disfavour the present class of

models.7 For the same above reasons, similar considerations apply to the other reduced cross sections of H2, leading also to mild suppressions with respect to the SM. Concretely, we observe RW+W2(gg H2) RZZ2(gg H2) R+2(VBF H2) 0.7 0.8.

We now briey comment on the remaining part of the Higgs spectrum. Apart from H1 and H2 discussed above, the pseudoscalar A1 is also relatively light in these models, with mA1 [lessorsimilar] 350 GeV, see gure 6. However, it is highly dominated by its singlet component (its doublet composition is insignicant, of the order of 108 %) and therefore very

decoupled from the SM fermions. In this limit the pseudoscalar mass can be written as m2A1 3vsA . On the contrary, H3, A2 and H+ have much larger masses and are nearly

degenerated, with mH3 mA2 mH

+ [greaterorsimilar] 1 TeV. They are therefore much harder to detect

at the LHC.

Finally, we may wonder about the robustness of the above Higgs spectrum. As we have already mentioned, in this region of the parameter space of the NMSSM there are relatively large uncertainties coming from some of the two loop corrections to the NMSSM Higgs sector that have not yet been computed. In this regard and for completeness, in

7Nevertheless, as noted in appendix A, mild enhancements in the di-photon rate with respect to the SM are allowed by keeping the computation of the Higgs masses at the one loop level. In this regard it would be interesting to understand the e ect of the complete set of two loop corrections to the NMSSM Higgs sector on the di-photon rate.

15

JHEP02(2013)084

JHEP02(2013)084

Figure 5. Distribution of the the reduced signal cross section in the H2 channel, R 2(gg

H2) versus the mass for the SM-like Higgs H2 in NMSSM vacua with F-theory unication boundary conditions (2.11) and unconstrained values of A , A and . Dark blue and red points both pass all the current experimental and theoretical constraints. Dark blue points, however, have a deciency of neutralino relic density and therefore require some additional source of dark matter.

appendix A we perform the same analysis of this subsection but keeping only one loop radiative corrections to the Higgs sector into account. Such analysis reveals that the above qualitative results for the Higgs sector also hold at the one loop level, although the range of masses is broadened considerably and small enhancements to the di-photon rate with respect to the SM appear also to be possible.

3.3 Neutralino dark matter

The lightest neutralino, ~

01, can be a viable dark matter candidate in the NMSSM with interesting phenomenological properties [82]. It di ers from the MSSM in that it now contains a singlino component, which alters its couplings to the SM particles. The neutralino is also very sensitive to the structure of the Higgs sector, since it determines its annihilation cross section in the Early Universe (and thus the theoretical predictions for its relic density) and plays an important role in the computation of the scattering cross section of quarks.

In our construction, the neutralino turns out to be an almost pure singlino in all the allowed regions of the parameter space. This is due to the very small values of , which are

16

JHEP02(2013)084

Figure 6. Distribution of the SM-like Higgs and the lightest pseudoscalar masses (mH2, mA1) for

NMSSM vacua with F-theory unication boundary conditions (2.11) and unconstrained values of A , A and . Dark blue and red points both pass all the current experimental and theoretical constraints. Dark blue points, however, have a deciency of neutralino relic density and therefore require some additional source of dark matter.

at least one order of magnitude smaller than as we already showed in gure 3. This leads to a hierarchical structure in the neutralino mass matrix, vs M1,2 < vs, which implies that the gaugino and Higgsino components of the lightest neutralino are almost negligible (to less than approximately a 0.1%). This also implies that the neutralino mass can be small in these scenarios without violating any experimental limit. To a good approximation we can write m~~01 2vs, and in principle, neutralinos as light as 50 GeV are possible, but

when the recent experimental constraints are applied on other observables (mostly the Higgs decays discussed above), we are left with the range 100 GeV <

240 GeV.

We have represented in gure 7 the mass of the lightest neutralino m~~01 against the stau mass m~, for vacua that pass all current experimental constraints except that of the relic density observed by WMAP. A singlino-like neutralino has reduced couplings to the SM particles and thus generally displays a small annihilation cross-section in the Early Universe. As a consequence, the relic density is too large in most of the parameter space, and typically exceeds the WMAP range 0.1008 < h2 < 0.1232 (at the 2 level). The relic density can be lowered through coannihilation e ects when the stau mass is very close to that of the neutralino. In fact, we observe that the allowed regions of the parameter space have m~ m~~

01 10 GeV. This leads to a very interesting prediction of this scenario,

17

m~~01 <

JHEP02(2013)084

, m~) for NMSSM vacua with F-theory unication boundary conditions (2.11) and unconstrained values of A , A and , for points that pass all current experimental constraints except that of the relic density, that is encode in the legend of colors.

namely that the stau mass is in the range 110 GeV <

Figure 7. Distribution of neutralino and stau masses (m~~0

1

250 GeV. Notice that unlike the scenarios discussed in ref. [29], the stau-neutralino mass di erence is never small enough to allow for long-lived staus.

Dark matter can be detected directly through its scattering o nuclei in a detector. The interaction of neutralinos with quarks has contributions from s-channel squark exchange and t-channel Higgs exchange diagrams. Since the neutralino is a pure singlino state, its coupling to squarks is completely negligible. A pure singlino only couples to the singlet part of the Higgs, but this coupling CSS = 22 vanishes in the limit 0 and is

tiny in our vacua. This results in a extremely small neutralino-nucleon scattering cross-section. In particular, the theoretical predictions for the spin-independent contribution is below SI~~0

1p 1013 pb, several orders of magnitude below the predicted sensitivity of the

projected 1 ton scale detectors. The same happens with the spin-dependent component.

3.4 Constraints on rare decays and the muon anomalous magnetic moment

Rare decays constitute excellent probes for new physics beyond the SM. In particular, the e ect of avour-changing neutral currents in b-physics signals is extremely interesting in supersymmetric models, since it can be sizeable at large tan , and rather sensitive to the

18

m~ <

Higgs sector. For example, supersymmetric contributions to the branching ratios of the rare processes Bs + or b s can easily exceed the experimental measurements of

these quantities and generally lead to stringent constraints on the parameter space. This is particularly important in the NMSSM due to the presence of new scalar and pseudoscalar Higgsses which induce new contributions to these observables.

Let us start by addressing the branching ratio BR(Bs +). This observable can

be written in terms of the Wilson coe cients which appear the e ective Hamiltonian that describes the transition b s as follows,

BR(Bs +) [bracketleftBigg][parenleftBigg]

1

4m2

m2B

[parenrightBigg]

C2S +

CP + 2m m2BCA

[bracketrightBigg]

2 . (3.2)

In the SM calculation of this quantity [83] only CA is relevant, since CS and CP are suppressed by the small Yukawas. However, in supersymmetric theories, there are penguin contributions involving the neutral scalar and pseudoscalar Higgs bosons to CS and CP which can be sizeable, both in the MSSM [84] and the NMSSM [8587]. In the MSSM one nds BR(Bs +) (tan6 /m4A), and therefore in the large tan regime super-

symmetric contributions easily exceed the recent LHCb measurement BR(Bs +)= 3.2+1.51.2 109 [33], especially for light pseudoscalars. In the NMSSM the Wilson coe -

cient CP receives contributions from both pseudoscalar Higgses, but it is only their doublet component that contributes.

As we have already commented in section 3.2, the viable points resulting from our scan display a relatively light pseudoscalar, mA1 [lessorsimilar] 350 GeV, which is a pure singlet. Therefore, it does not contribute to the Wilson coe cient CP , and only the heavy pseudoscalar A2 has to be taken into account. The latter is rather heavy (in our scan its mass varies in the range from 1 to 1.4 TeV) and as a consequence the resulting value of CP is also small. In fact, it is of the same order as the SM contribution (2m/m2B) CA but with opposite sign. This implies that not only BR(Bs +) can be small, in agreement with the experimental

data, but even a cancellation between CP and CA that leads to a smaller value than the SM prediction is possible (see [76] for a similar e ect in the context of the MSSM). This last possibility, in fact, happens in parts of our parameter space for M >

JHEP02(2013)084

1200 GeV, where

values as low as BR(Bs +) 1.8 109 can be obtained. As we will see in the next

section (see gure 8), for not too large values of tan this actually favours a light spectrum.

We will now briey turn our attention to the branching ratio BR(b s). In the past

years this has been one of the strongest constraints on supersymmetric models, mainly because of the additional contributions from loops of charged Higgs bosons. There are also specic contributions from the extended Higgs and neutralino sectors of the NMSSM, although these start at the two loop level [85, 86]. Whereas imposing the experimental result BR(b s) = (3.52 0.23 0.09) 104 generally leads to constraints on the

NMSSM parameter space [88], our scan reveals that these bounds are now superseded by those on BR(Bs +) discussed above. Therefore, the current experimental bounds

on BR(b s) do not have a large impact in the space of parameters of these models.

Let us nally address the supersymmetric contribution to the muon anomalous magnetic moment, aSUSY. The observed discrepancy between the experimental value [89] and

19

Point

BR(Bs +)

BR(b s)

aSUSY

R H1(gg)

R H2(gg)

RV VH1 (gg)

RV VH2 (gg)

P1 3.17 109 2.88 104 8.32 1010 0.250 0.775 0.242 0.742 P2 3.40 109 2.89 104 8.05 1010 0.263 0.798 0.243 0.739

P3 2.62 109 2.95 104 6.66 1010 0.280 0.766 0.262 0.722 P4 3.77 109 2.97 104 6.73 1010 0.288 0.767 0.267 0.715

P5 2.86 109 2.98 104 6.22 1010 0.280 0.761 0.264 0.721 P6 2.38 109 3.03 104 5.00 1010 0.302 0.774 0.275 0.708

P7 3.31 109 3.04 104 4.99 1010 0.248 0.813 0.228 0.754 P8 2.35 109 3.05 104 4.48 1010 0.297 0.804 0.264 0.718

Table 3. Low energy observables and reduced cross-sections for di erent Higgs signals calculated for the set of benchmark points.

the Standard Model predictions using e+e data, favours positive contributions from new physics. These can be constrained to be in the range 10.1 1010 < aSUSY < 42.1 1010 at the 2 condence level [90] where theoretical and experimental errors are combined in quadrature (see also refs. [91, 92] that lead to a similar range). However, if tau data is used this discrepancy is smaller 2.9 1010 < aSUSY < 36.1 1010 [92]. The theoreti

cal predictions for this observable generally increase for light supersymmetric masses and large tan . Although in this scenario the masses of the rst and second family sleptons are relatively high, we are in the regime of large tan . The predicted aSUSY turns out to be within the 3 range of the e+e data and well within the 2 range of the discrepancy predicted by tau data.

To illustrate this discussion, we display the specic values of these low energy observables for our choice of representative benchmark points in table 3.

4 Consistency with F-theory unication

In the previous section we have discussed the main phenomenological constraints that shape the parameter space of NMSSM vacua with F-theory unication boundary conditions eqs. (2.11). We now describe the overall structure of the allowed regions and further comment on their consistency with an underlying F-theory unication structure, including also the extra conditions (2.12).

Indeed, as we have already mentioned, leaving the singlet sector unconstrained, NMSSM vacua with F-theory unication boundary conditions are completely specied by six parameters that encode the relevant information of the local F-theory background. In our scan these are given by the values of M, H, A and A at the unication scale, at the supersymmetry breaking scale and tan at the scale mZ. However, in specic F-theory

20

JHEP02(2013)084

JHEP02(2013)084

Figure 8. Distribution of NMSSM vacua over the plane (M, tan ) with F-theory boundary conditions at the unication scale given by eqs. (2.11) and unconstrained values of A , A and . Points pass all the current experimental and theoretical constraints. Dark blue points, however, have a deciency of neutralino relic density and therefore require some additional source of dark matter.

GUTs the singlet sector will also satisfy a set of boundary conditions at the unication scale which, under the simplifying assumptions of section 2, are given by eqs. (2.12). Hence, the number of independent parameters in specic models can be reduced from six to three (for instance, the values of M, H and at the unication scale), as we discuss below.

4.1 M, H and tan

Let us rst address the e ect of the phenomenological constraints on the region of the parameter space spanned by M, H and tan . We have represented in gure 8 the distribution of phenomenologically viable NMSSM vacua with F-theory unication boundary conditions (2.11), over the relevant region of the plane (M, tan ). As we have advanced in previous sections, vacua satisfying all the current phenomenological constraints sit in the region of large tan , with tan [greaterorsimilar] 46. In this region the contribution of the heaviest pseudoscalar A2 to the branching ratio BR(Bs +) is such that it leads to important

cancellations with the SM contribution, giving rise to comparable or even reduced values with respect to the SM (see section 3.4). For regions of the parameter space where the above cancellation is maximal the branching ratio BR(Bs +) in particular becomes

too small, below the recent 95 % condence level lower limit measured by the LHCb collaboration [33]. For moderately large values of tan , this disfavours a band in the plane

21

(M, tan ) with approximately 1200 GeV [lessorsimilar] M [lessorsimilar] 1800 GeV, see gure 8. Nevertheless, the reader should bear in mind that all points in this band have BR(Bs +) [greaterorsimilar] 1.8109, and therefore many of them are actually within the theoretical uncertainties from QCD [84].

Regarding the scale of supersymmetry breaking, we observe in the same gure that the lower bound on M compatible with all the current experimental constraints is M

850 GeV. Below that scale, the cross section for the SM-like Higgs decay H2 + becomes larger than the most recent experimental upper limits set by the CMS and ATLAS collaborations [64, 93]. On the other hand, since the LSP is a singlino-like neutralino, its mass m~~01 2s [lessorsimilar] 240 GeV is independent of M and vacua with the correct neutralino

relic density are possible for arbitrarily large values of M, contrary to what occurs in the modulus dominated MSSM [28, 29]. Nevertheless, the amount of ne-tuning required in order to have a light stau with mass in the region of co-annihilation increases considerably for large values of M.8

Similarly, we have represented in gure 9 the distribution of phenomenologically viable vacua on the plane (H, tan ). In this case, the LHCb upper limit on BR(Bs +)

forces H to take small values, H [lessorsimilar] 0.4, with most of the points below 0.2. Remarkably, this is consistent with our treatment of the e ect of magnetic uxes on the Kahler metrics for the Higgs as small perturbations, see section 2.

Having looked at the e ect of the phenomenological constraints on M, H and tan , let us now move on to the discussion of the singlet sector.

4.2 The singlet sector: A , A and

As already mentioned in section 2, the singlet S is not localized in the local 4-cycle S and

therefore its interactions depend on the details of the background along the bulk of the compactication, making this sector very model-dependent. Nevertheless, in simple models where the only source of supersymmetry breaking for S is given by the F-terms Ft and Ftb we expect A , A and mS to satisfy a set of boundary conditions at the unication scale which, to rst approximation, are given by eqs. (2.12).

It is highly remarkable to see how the above type of relations are also strongly favoured by the current experimental input. Indeed, although we have scanned over unconstrained values and sign choices of A , A and , requiring a SM-like Higgs in the window 122

128 GeV and a neutralino relic density below the WMAP bound h2 < 0.1232 uniquely selects the sign choice A < 0, A 0 and 0, consistently with the F-theoretic

boundary conditions for the singlet sector, eqs. (2.12). Moreover, it is possible to check that the current experimental constraints imply also a strong correlation between the values of A and M at the unication scale, similar to that of eqs. (2.12). Indeed, in gure 10 we have represented the distribution of NMSSM vacua on the plane (M, A ) with boundary conditions (2.11) and unconstrained values of A , A and . The linear correlation between A and M for vacua that pass all the current phenomenological constraints is clearly visible in this gure. Finally, in all these vacua A and mS take relatively small values at the

8Moreover, for large values of M the value of tan becomes too large for the computation of down-type Yukawa couplings to be reliable.

22

JHEP02(2013)084

JHEP02(2013)084

Figure 9. Distribution of NMSSM vacua over the plane (H, tan ) with F-theory boundary conditions at the unication scale given by eqs. (2.11) and unconstrained values of A , A and . Points pass all the current experimental and theoretical constraints. Dark blue points, however, have a deciency of neutralino relic density and therefore require some additional source of dark matter. The upper yellow and pink regions in this plot are only indicative: whereas all points inside this regions are excluded because the branching ratio BR(Bs +), mH2 and/or h2, there

are also points outside this regions that are also excluded by these observables.

unication scale, with 0.015 [lessorsimilar] (mS/m5,10)2 [lessorsimilar] 0.035 and (A /A) [lessorsimilar] 0.3 (see table 1 in

section 5), also in fairly good agreement with the F-theoretic expectation A mS 0 in eqs. (2.12).

In order to make a more quantitative estimation of the compatibility between the phenomenological constraints and the F-theoretic relations for the singlet sector, we can consider a slightly more general Kahler metric for S than that of eq. (2.7), depending also on the Kahler modulus of S,

KS = t1/2S t1ttb (4.1)

Making use of this metric, the boundary conditions (2.12) generalize to

A = M(2 t H) (4.2)

A = 3M(1 t) m2S = |M|2(1 t)

23

JHEP02(2013)084

Figure 10. Distribution of NMSSM vacua over the plane (M, A ) with F-theory boundary conditions at the unication scale given by eqs. (2.11) and unconstrained values of A , A and . Points pass all the current experimental and theoretical constraints. Dark blue points, however, have a deciency of neutralino relic density and therefore require some additional source of dark matter. For convenience, in this plot we have not imposed the lower bound BR(Bs +) > 2.0 109.

where the simple F-theory unication conditions for the singlet sector, eqs. (2.12), are recovered for t = 1. Making use of these equations we can estimate the modular weight t in three di erent ways (one from each equation) for each vacuum in our scan with boundary conditions (2.11) and unconstrained values of A , A and . If the vacuum is consistent with the F-theoretic boundary conditions, the three estimations of t should agree with each other and with t 1. We have represented in gure 11 (left) the maximum value

of the three estimations against the mass of the SM-like Higgs H2 for vacua that pass all the current experimental constraints. We observe in this gure that the latter strongly favour the F-theory value t = 1. Similarly, in gure 11 (right) we have represented the maximum percentage of mismatch between the three di erent estimations of t, showing that for a large fraction of the phenomenologically viable vacua the mismatch between the three eqs. (4.2) is lower than 10%.

Hence, whereas in the scan over modulus dominated vacua that we have performed in section 3.1 we have taken six independent parameters, it turns out that many of the vacua that satisfy all the current experimental bounds can be actually described to a large extend in terms of just three parameters, namely M, H and , satisfying the boundary conditions (2.11) together with the additional boundary conditions (2.12) for the singlet sector.

24

JHEP02(2013)084

Figure 11. (Left): Modular weight t estimated from eqs. (4.2) against the mass of the SM-like Higgs, for NMSSM vacua with F-theory boundary conditions at the unication scale given by eqs. (2.11) and unconstrained values of A , A and . (Right): Percentage of mismatch between the three eqs. (4.2) against M. For convenience, in this plot we have not imposed the lower bound BR(Bs +) > 2.0 109. In both gures all the points pass all the current experimental and

theoretical constraints. Dark blue points, however, have a deciency of neutralino relic density and therefore require some additional source of dark matter.

5 Supersymmetric spectrum and signatures

The model is extremely predictive. After imposing all the experimental constraints on the parameter space we are left with a very characteristic supersymmetric spectrum. In table 4 we indicate the masses of the various supersymmetric particles and Higgs bosons for a series of representative benchmark points.

Regarding the Higgs sector, this model provides a very interesting scenario, with two light scalar Higgses. In this sense it seems similar to the proposal of ref. [20] where the lightest Higgses had masses of 98 and 125 GeV. Notice however that the solution that we nd belongs to a completely di erent region of the NMSSM parameter space. The most important di erences are the large value of tan in our scenario and the very small values of both and . Also e >

1 TeV, thus being much larger than in ref. [20]. This leads to a di erent phenomenology (as already emphasized in section 3.2, most notably, in our case we predict no enhancement of Higgs decay H2 ). Notice also that this scenario does

not contain exotic channels for Higgs decay of the two lightest CP-even states, since the pseudoscalar is heavier than H1 and H2. In any case, we can be certain that this scenario can be tested through the branching fractions of these two lightest states. In particular, the lightest Higgs could lead to a peak in the H1 channel around 100 GeV that would

be observable at the LHC. Regarding the lightest pesudoscalar, it is singlet like and its production rate is extremely suppressed. The heavier pseudoscalar and the third CP-even Higgs state are doublet like, but very heavy and thus very di cult to produce.

The coloured section is in the 1.5 to 3 TeV range. Squarks are lighter than the gluino and, interestingly, the lightest stop can be as light as m~t1 1200 GeV in the regions

with smaller gaugino masses. As already emphasized the next-to-lightest supersymmetric particle is the lightest stau, whose mass di erence with the neutralino is of the order of

25

10 GeV for the whole range of viable gaugino masses. The nature of the neutralino and chargino sector is easily understood from the resulting hierarchy vs M1 < M2 < vs.

As already stated in section 3.3, the lightest neutralino is pure singlino. The second neutralino state is bino-like and relatively light (m~~02 300500 GeV). The third neutralino

state and the lightest chargino are wino-like and with a mass in the range m~~03,~

~1

6001000 GeV. Finally the heavier neutralino states and the heavier chargino are Higgsino-

like states with masses approximately equal to e = vs.

This kind of spectrum is very similar to what is obtained in the Constrained NMSSM [6] and both share the same search strategies. In particular, the branching ratios of the lightest chargino and the second and third neutralino states into the stau NLSP are sizable, thus potentially leading to signicant rates of tau-rich nal states [94, 95]. Let us be more specic about this. Left-handed squarks can decay into the lightest chargino with a branching fraction of approximately 65% and into the third neutralino with 33%, whereas right-handed squarks decay mostly into the second neutralino with a branching fraction of approximately 99%. Regarding the stops, the lightest stop undergoes the following decays ~t1 ~

02t (60%), ~t1 ~

03t (12%), ~t1 ~

1t (25%). So either if they are directly produced of obtained in gluino decays, the resulting production of ~

1 and ~

02,3 is copious. The second and third neutralino states decay in turn into the lightest stau with a branching ratio of approximately 100%. Obviously the stau NLSP can only decay into the lightest neutralino, producing another tau in the nal state which is softer than the previous one (as the mass-di erence of the stau and neutralino is approximately 10 GeV) thus leading to ~

02,3 ~

1 + ~

01. The lightest chargino decays into a stau and the corresponding neutrino thus giving rise to only one nal state tau ~

1 ~

1 ~

01. The signal

expected from this kind of scenarios is therefore the presence of multitau signals, originated from the two chains of cascade decays, associated to the emission of hard central jets and missing energy [94].

Notice nally that the upper bound set by BR(Bs +) implies that the whole

spectrum is lighter than approximately 3 TeV. This is well within the reach of LHC at14 TeV for searches involving multijets plus missing energy.

6 Discussion

The most elegant solution to the -problem in the MSSM is perhaps its extension to the scale invariant NMSSM model. In the MSSM, the existence of unifying underlying symmetries suggest the existence of unied boundary conditions leading to simple structures like that of the constrained MSSM, the CMSSM, with only a few free parameters, i.e. m, M, A, and B. In contrast, unlike the MSSM case, there is some ambiguity in the denition of what a constrained version of the NMSSM, the CNMSSM, could be.

In this paper we have analyzed in detail a constrained version of the NMSSM model with boundary conditions obtained from the assumption of modulus dominated SUSY breaking in F-theory SU(5) unication models. Such theories provide for an ultraviolet completion for more traditional SU(5) GUTs and provide for new solutions for problems like doublet-triplet splitting and D-quark to lepton mass ratios. One obtains a simple and very

26

JHEP02(2013)084

Point ~QR,L ~t1,2 ~b1,2 ~LR,L ~

1,2 ~

0i ~

+i mHi mAi mH+

P1

1921

1758 1827

1263 1558

1481 1583

684 827

230 719

213367; 696 1238; 1243

696 1244

103 122.4 1016

321 1016

1019

P2

1983

1814 1886

1302 1601

1521 1626

708

855

175 735

164381; 721 1274; 1279

721 1279

98.1 123.4 1036

220 1036

1040

P3

2716

1989

2069

1434 1749

1673 1778

782 944

199 807

189423; 800 1394; 1400

800 1400

96.9 124.8 1131

273 1131

1134

JHEP02(2013)084

P4

2236

2042 2125

1499 1802

1718 1827

804

971

197 831

186436; 824 1440; 1444

824 1445

97.4 124.3 1095

266 1094

1098

P5

2289

2091 2175

1527 1841

1762 1868

825

996

216 851

205447; 845 1471; 1475

845 1476

97.4 124.7 1148

306 1148

1151

P6

2585

2358 2455

1728

2064

1986

2095

939 1133

178 955

167513; 967 1653; 1657

967 1657

98.5 124.4 1274

223 1274

1277

P7

2663

2428 2528

1809

2134

2046 2161

970 1169

204 990

193530; 999 1712; 1716

999 1716

93.9 123.4 1227

287 1227

1230

P8

2769

2525 2629

1862

2207

2127 2238

1011 1219

164 1023

153554; 1043 1770; 1774

1043 1774

97.9 123.7 1330

192 1329

1332

Table 4. Supersymmetric spectrum and Higgs masses for the set of benchmark points. All the masses are given in GeV.

predictive structure of SUSY breaking soft terms summarized in eqs. (2.11). Additional approximate boundary conditions eq. (1.6) may also be derived for soft terms involving the NMSSM singlet S. Furthermore, the geometrical structure of F-theory unication implies that the NMSSM couplings and are small with , 0.1. In spite of all these very

constrained parameter values, we nd that the obtained very constrained NMSSM model is consistent with correct EW symmetry breaking, a 125 GeV Higgs and appropriate relic dark matter. The model passes also B-decay constraints as well as LEP and LHC limits.

Independently of its underlying string theory motivation, the structure of soft terms (2.11) and (1.6) provides for a denition of a constrained NMSSM model consistent with all presently available data. The resulting NMSSM model is very predictive and the low-energy spectrum very constrained, as it is visible from table (4). The second lightest Higgs scalar H2 can get a mass mH2 125 GeV whereas the lightest scalar H1, with a domi-

27

nant singlet component, barely escaped detection at LEP and could be observable at LHC as a peak in H1 at around 100 GeV. The LSP is mostly singlino and may provide

for the correct relict density thanks to coannihilation with the lightest stau, which is the NLSP with a mass in the range 100-250 GeV. Such stau NLSP leads to signals at LHC involving multi-tau events with missing energy. In this model the value of tan is very large, tan 50, still the branching ratio for Bs + is below recent LHCb and

CMS bounds and in many cases is smaller than the SM prediction, due to an interference e ect. Gluinos and squarks have masses in the 2 3 TeV range with a stop with a mass

as low as 1.2 TeV, all within reach of LHC(14). On the other hand no large enhancement of the H2 over that of the SM is expected. It is exciting to think that, if indeed the

signatures above are observed at LHC, it will be evidence not only for SUSY but for an underlying F-theory unied structure.

Acknowledgments

We thank U. Ellwanger, F. Marchesano and E. Palti for useful discussions. We are grateful to F. Staub for providing us with the modied SARAH-Spheno NMSSM implementation of [80]. This work has been partially supported by the grants FPA 2009-09017, FPA 2009-07908, FPA2009-08958, FPA 2010-20807, FPA2012-34694, Consolider-CPAN (CSD2007-00042) and MultiDark (CSD2009-00064) from the Spanish MICINN, HEPHACOS-S2009/ESP1473 from the C.A. de Madrid, AGAUR 2009-SGR-168 from the Generalitat de Catalunya and the contract UNILHC PITN-GA-2009-237920 of the European Commission. The IFT authors also thank the spanish MINECO Centro de excelencia Severo Ochoa Program under grant SEV-2012-0249. D.G.C. is supported by the MICINN Ramn y Cajal programme through the grant RYC-2009-05096.

A The Higgs sector at one loop

For completeness, in this appendix we repeat the analysis of section 3.2 taking only into account one loop radiative corrections, as well as the two loop contributions to the bottom and top Yukawa couplings to leading logarithmic approximation. Namely, in this appendix we do not consider two loop radiative corrections to the Higgs sector. As we summarize below, the results however agree qualitatively with the ones in section 3.2, showing the robustness of our conclusions.

In the models that we consider in this paper two loop radiative corrections tend to lower Higgs masses in as much as 25 GeV. Thus, at one loop we nd in general higher masses than those in section 3.2. In spite of this, the mass of the lightest Higgs, H1, is still not large enough to t the LHC Higgs signal at any region of the parameter space, so that the role of the SM-like Higgs boson has again to be played by H2. In gure 12 we represent the distribution of masses (mH1, mH2) for the two lightest Higgs bosons computed at one loop. One di erence with respect to the two loop analysis performed in section 3.2 is that the LHC bound on W+W(gg H) now becomes also relevant, excluding solutions in the

region mH1 [greaterorsimilar] 110 GeV, mH2 [greaterorsimilar] 129 GeV. Moreover, the LEP bound on bbZ(e+e HZ)

and the LHC bound on (gg H) become softer, leading to the range of masses

28

JHEP02(2013)084

Figure 12. Distribution of the light Higgs masses (mH1, mH2) for NMSSM vacua with F-theory unication boundary conditions (2.11) and unconstrained values of A , A and , computed at one loop.

Figure 13. Distribution of the the reduced signal cross section in the H2 channel, R 2(gg

H2), versus the mass for the SM-like Higgs H2 computed at one loop in NMSSM vacua with F-theory unication boundary conditions (2.11) and unconstrained values of A , A and .

29

JHEP02(2013)084

50 GeV [lessorsimilar] mH1 [lessorsimilar] 120 GeV and 123 GeV [lessorsimilar] mH2 [lessorsimilar] 129 GeV. The upper limit mA1 [lessorsimilar] 350 GeV on the mass of the lightest pseudoscalar, on the other hand, still holds.

Regarding the reduced cross sections of the SM-like Higgs boson H2, we nd that the contribution from stau loops to the diphoton rate production become relevant in some cases, allowing for small enhancements with respect to the SM, as it can be seen in gure 13. More precisely, we observe from that gure that the reduced signal cross section R 2(gg H2)

lays in the range 0.61.4.

References

[1] CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, http://dx.doi.org/10.1016/j.physletb.2012.08.021

Web End =Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1207.7235

Web End =INSPIRE ].

[2] ATLAS collaboration, Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, http://dx.doi.org/10.1016/j.physletb.2012.08.020

Web End =Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1207.7214

Web End =INSPIRE ].

[3] M. Maniatis, The next-to-minimal supersymmetric extension of the standard model reviewed, http://dx.doi.org/10.1142/S0217751X10049827

Web End =Int. J. Mod. Phys. A 25 (2010) 3505 [arXiv:0906.0777] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0906.0777

Web End =INSPIRE ].

[4] U. Ellwanger, C. Hugonie and A.M. Teixeira, The next-to-minimal supersymmetric standard model, http://dx.doi.org/10.1016/j.physrep.2010.07.001

Web End =Phys. Rept. 496 (2010) 1 [arXiv:0910.1785] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0910.1785

Web End =INSPIRE ].

[5] L.E. Ibez and A. Uranga, String theory and partiicle physics: an introduction to string phenomenology, Cambridge Univiersity Press, Camrbidge U.K. (2012).

[6] A. Djouadi, U. Ellwanger and A. Teixeira, Phenomenology of the constrained NMSSM, http://dx.doi.org/10.1088/1126-6708/2009/04/031

Web End =JHEP 04 (2009) 031 [arXiv:0811.2699] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0811.2699

Web End =INSPIRE ].

[7] A. Djouadi, U. Ellwanger and A.M. Teixeira, The constrained next-to-minimal supersymmetric standard model, http://dx.doi.org/10.1103/PhysRevLett.101.101802

Web End =Phys. Rev. Lett. 101 (2008) 101802 [arXiv:0803.0253] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0803.0253

Web End =INSPIRE ].

[8] U. Ellwanger, Higgs bosons in the next-to-minimal supersymmetric standard model at the LHC, http://dx.doi.org/10.1140/epjc/s10052-011-1782-3

Web End =Eur. Phys. J. C 71 (2011) 1782 [arXiv:1108.0157] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1108.0157

Web End =INSPIRE ].

[9] L.J. Hall, D. Pinner and J.T. Ruderman, A natural SUSY Higgs near 126 GeV, http://dx.doi.org/10.1007/JHEP04(2012)131

Web End =JHEP 04 (2012) 131 [arXiv:1112.2703] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1112.2703

Web End =INSPIRE ].

[10] U. Ellwanger, A Higgs boson near 125 GeV with enhanced di-photon signal in the NMSSM, http://dx.doi.org/10.1007/JHEP03(2012)044

Web End =JHEP 03 (2012) 044 [arXiv:1112.3548] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1112.3548

Web End =INSPIRE ].

[11] J.F. Gunion, Y. Jiang and S. Kraml, The constrained NMSSM and Higgs near 125 GeV, http://dx.doi.org/10.1016/j.physletb.2012.03.027

Web End =Phys. Lett. B 710 (2012) 454 [arXiv:1201.0982] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1201.0982

Web End =INSPIRE ].

[12] A. Arvanitaki and G. Villadoro, A non standard model Higgs at the LHC as a sign of naturalness, http://dx.doi.org/10.1007/JHEP02(2012)144

Web End =JHEP 02 (2012) 144 [arXiv:1112.4835] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1112.4835

Web End =INSPIRE ].

[13] S. King, M. Muhlleitner and R. Nevzorov, NMSSM Higgs benchmarks near 125 GeV, http://dx.doi.org/10.1016/j.nuclphysb.2012.02.010

Web End =Nucl. Phys. B 860 (2012) 207 [arXiv:1201.2671] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1201.2671

Web End =INSPIRE ].

[14] Z. Kang, J. Li and T. Li, On naturalness of the MSSM and NMSSM, http://dx.doi.org/10.1007/JHEP11(2012)024

Web End =JHEP 11 (2012) 024 [arXiv:1201.5305] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1201.5305

Web End =INSPIRE ].

[15] J.-J. Cao, Z.-X. Heng, J.M. Yang, Y.-M. Zhang and J.-Y. Zhu, A SM-like Higgs near 125 GeV in low energy SUSY: a comparative study for MSSM and NMSSM,http://dx.doi.org/10.1007/JHEP03(2012)086

Web End =JHEP 03 (2012) 086 [arXiv:1202.5821] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1202.5821

Web End =INSPIRE ].

30

JHEP02(2013)084

[16] U. Ellwanger and C. Hugonie, Higgs bosons near 125 GeV in the NMSSM with constraints at the GUT scale, http://dx.doi.org/10.1155/2012/625389

Web End =Adv. High Energy Phys. 2012 (2012) 625389 [arXiv:1203.5048] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1203.5048

Web End =INSPIRE ].

[17] R. Benbrik et al., Confronting the MSSM and the NMSSM with the discovery of a signal in the two photon channel at the LHC, http://dx.doi.org/10.1140/epjc/s10052-012-2171-2

Web End =Eur. Phys. J. C 72 (2012) 2171 [arXiv:1207.1096] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1207.1096

Web End =INSPIRE ].

[18] J.F. Gunion, Y. Jiang and S. Kraml, Could two NMSSM Higgs bosons be present near 125 GeV?, http://dx.doi.org/10.1103/PhysRevD.86.071702

Web End =Phys. Rev. D 86 (2012) 071702 [arXiv:1207.1545] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1207.1545

Web End =INSPIRE ].

[19] J. Cao, Z. Heng, J.M. Yang and J. Zhu, Status of low energy SUSY models confronted with the LHC 125 GeV Higgs data, http://dx.doi.org/10.1007/JHEP10(2012)079

Web End =JHEP 10 (2012) 079 [arXiv:1207.3698] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1207.3698

Web End =INSPIRE ].

[20] G. Blanger et al., Higgs bosons at 98 and 125 GeV at LEP and the LHC, http://dx.doi.org/10.1007/JHEP01(2013)069

Web End =JHEP 01 (2013) 069 [arXiv:1210.1976] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1210.1976

Web End =INSPIRE ].

[21] K. Kowalska et al., The constrained NMSSM with a 125 GeV Higgs boson A global analysis, arXiv:1211.1693 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1211.1693

Web End =INSPIRE ].

[22] S.F. King, M. Muhlleitner, R. Nevzorov and K. Walz, Natural NMSSM Higgs bosons, arXiv:1211.5074 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1211.5074

Web End =INSPIRE ].

[23] J.J. Heckman, Particle physics implications of F-theory,

http://dx.doi.org/10.1146/annurev.nucl.012809.104532

Web End =Ann. Rev. Nucl. Part. Sci. 60 (2010) 237 [arXiv:1001.0577] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1001.0577

Web End =INSPIRE ].

[24] T. Weigand, Lectures on F-theory compactications and model building, http://dx.doi.org/10.1088/0264-9381/27/21/214004

Web End =Class. Quant. Grav. 27 (2010) 214004 [arXiv:1009.3497] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1009.3497

Web End =INSPIRE ].

[25] L.E. Ibez, From strings to the LHC: Les Houches lectures on string phenomenology, arXiv:1204.5296 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1204.5296

Web End =INSPIRE ].

[26] G.K. Leontaris, Aspects of F-theory GUTs, http://pos.sissa.it/cgi-bin/reader/contribution.cgi?id=PoS(CORFU2011)095

Web End =PoS(CORFU2011)095 [arXiv:1203.6277] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1203.6277

Web End =INSPIRE ].

[27] A. Maharana and E. Palti, Models of particle physics from type IIB string theory and F-theory: a review, arXiv:1212.0555 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1212.0555

Web End =INSPIRE ].

[28] L. Aparicio, D. Cerdeno and L. Ibez, Modulus-dominated SUSY-breaking soft terms in F-theory and their test at LHC, http://dx.doi.org/10.1088/1126-6708/2008/07/099

Web End =JHEP 07 (2008) 099 [arXiv:0805.2943] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0805.2943

Web End =INSPIRE ].

[29] L. Aparicio, D. Cerdeno and L. Ibez, A 119125 GeV Higgs from a string derived slice of the CMSSM, http://dx.doi.org/10.1007/JHEP04(2012)126

Web End =JHEP 04 (2012) 126 [arXiv:1202.0822] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1202.0822

Web End =INSPIRE ].

[30] LHCb collaboration, Strong constraints on the rare decays Bs + and B0 +,

http://dx.doi.org/10.1103/PhysRevLett.108.231801

Web End =Phys. Rev. Lett. 108 (2012) 231801 [arXiv:1203.4493] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1203.4493

Web End =INSPIRE ].

[31] CMS collaboration, Search for Bs + and B0 + decays in CMS,

http://dx.doi.org/10.1051/epjconf/20122812038

Web End =EPJ Web Conf. 28 (2012) 12038 [arXiv:1201.4257] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1201.4257

Web End =INSPIRE ].

[32] ATLAS collaboration, Search for the rare decays B at the LHC with the ATLAS, CMS

and LHCb experiments, http://cds.cern.ch/record/1456262

Web End =ATLAS-CONF-2012-061 (2012).

[33] LHCb collaboration, First evidence for the decay Bs +, Phys. Rev. Lett. 110 (2013)

021801 [arXiv:1211.2674] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1211.2674

Web End =INSPIRE ].

[34] G. Degrassi and P. Slavich, On the radiative corrections to the neutral Higgs boson masses in the NMSSM, http://dx.doi.org/10.1016/j.nuclphysb.2009.09.018

Web End =Nucl. Phys. B 825 (2010) 119 [arXiv:0907.4682] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0907.4682

Web End =INSPIRE ].

[35] R. Donagi and M. Wijnholt, Model building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0802.2969

Web End =INSPIRE ].

[36] C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory I, http://dx.doi.org/10.1088/1126-6708/2009/01/058

Web End =JHEP 01 (2009) 058 [arXiv:0802.3391] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0802.3391

Web End =INSPIRE ].

31

JHEP02(2013)084

[37] C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory II: experimental predictions, http://dx.doi.org/10.1088/1126-6708/2009/01/059

Web End =JHEP 01 (2009) 059 [arXiv:0806.0102] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0806.0102

Web End =INSPIRE ].

[38] R. Donagi and M. Wijnholt, Breaking GUT groups in F-theory, Adv. Theor. Math. Phys. 15 (2011) 1523 [arXiv:0808.2223] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0808.2223

Web End =INSPIRE ].

[39] L. Aparicio, Some phenomenological aspects of Type IIB/F-theory string compactications, arXiv:1210.0339 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1210.0339

Web End =INSPIRE ].

[40] A. Font, L.E. Ibez, F. Marchesano and D. Regalado, Non-perturbative e ects and Yukawa hierarchies in F-theory SU(5) Unication, arXiv:1211.6529 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1211.6529

Web End =INSPIRE ].

[41] L. Aparicio, A. Font, L.E. Ibez and F. Marchesano, Flux and instanton e ects in local F-theory models and hierarchical fermion masses, http://dx.doi.org/10.1007/JHEP08(2011)152

Web End =JHEP 08 (2011) 152 [arXiv:1104.2609] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1104.2609

Web End =INSPIRE ].

[42] J. Marsano, N. Saulina and S. Schafer-Nameki, Compact F-theory GUTs with U(1) (PQ), http://dx.doi.org/10.1007/JHEP04(2010)095

Web End =JHEP 04 (2010) 095 [arXiv:0912.0272] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0912.0272

Web End =INSPIRE ].

[43] E. Dudas and E. Palti, On hypercharge ux and exotics in F-theory GUTs, http://dx.doi.org/10.1007/JHEP09(2010)013

Web End =JHEP 09 (2010) 013 [arXiv:1007.1297] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1007.1297

Web End =INSPIRE ].

[44] J. Marsano, Hypercharge ux, exotics and anomaly cancellation in F-theory GUTs, http://dx.doi.org/10.1103/PhysRevLett.106.081601

Web End =Phys. Rev. Lett. 106 (2011) 081601 [arXiv:1011.2212] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1011.2212

Web End =INSPIRE ].

[45] E. Palti, A note on hypercharge ux, anomalies and U(1)s in F-theory GUTs, arXiv:1209.4421 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1209.4421

Web End =INSPIRE ].

[46] C. Ldeling, H.P. Nilles and C.C. Stephan, The potential fate of local model building, http://dx.doi.org/10.1103/PhysRevD.83.086008

Web End =Phys. Rev. D 83 (2011) 086008 [arXiv:1101.3346] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1101.3346

Web End =INSPIRE ].

[47] V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau ux compactications, http://dx.doi.org/10.1088/1126-6708/2005/03/007

Web End =JHEP 03 (2005) 007 [http://arxiv.org/abs/hep-th/0502058

Web End =hep-th/0502058 ] [http://inspirehep.net/search?p=find+EPRINT+hep-th/0502058

Web End =INSPIRE ].

[48] J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume ux compactications: Moduli spectrum and D3/D7 soft supersymmetry breaking, http://dx.doi.org/10.1088/1126-6708/2005/08/007

Web End =JHEP 08 (2005) 007 [http://arxiv.org/abs/hep-th/0505076

Web End =hep-th/0505076 ] [http://inspirehep.net/search?p=find+EPRINT+hep-th/0505076

Web End =INSPIRE ].

[49] M. Cicoli, J.P. Conlon and F. Quevedo, General analysis of LARGE volume scenarios with string loop moduli stabilisation, http://dx.doi.org/10.1088/1126-6708/2008/10/105

Web End =JHEP 10 (2008) 105 [arXiv:0805.1029] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0805.1029

Web End =INSPIRE ].

[50] M. Cicoli, C. Burgess and F. Quevedo, Anisotropic modulus stabilisation: strings at LHC scales with micron-sized extra dimensions, http://dx.doi.org/10.1007/JHEP10(2011)119

Web End =JHEP 10 (2011) 119 [arXiv:1105.2107] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1105.2107

Web End =INSPIRE ].

[51] J.P. Conlon, D. Cremades and F. Quevedo, Kahler potentials of chiral matter elds for Calabi-Yau string compactications, http://dx.doi.org/10.1088/1126-6708/2007/01/022

Web End =JHEP 01 (2007) 022 [http://arxiv.org/abs/hep-th/0609180

Web End =hep-th/0609180 ] [http://inspirehep.net/search?p=find+EPRINT+hep-th/0609180

Web End =INSPIRE ].

[52] M. Cveti, J. Halverson and P. Langacker, Singlet extensions of the MSSM in the quiver landscape, http://dx.doi.org/10.1007/JHEP09(2010)076

Web End =JHEP 09 (2010) 076 [arXiv:1006.3341] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1006.3341

Web End =INSPIRE ].

[53] M. Berasaluce-Gonzalez, L.E. Ibez, P. Soler and A.M. Uranga, Discrete gauge symmetries in D-brane models, http://dx.doi.org/10.1007/JHEP12(2011)113

Web End =JHEP 12 (2011) 113 [arXiv:1106.4169] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1106.4169

Web End =INSPIRE ].

[54] P.G. Camara, L. Ibez and A. Uranga, Flux induced SUSY breaking soft terms, http://dx.doi.org/10.1016/j.nuclphysb.2004.04.013

Web End =Nucl. Phys. B 689 (2004) 195 [http://arxiv.org/abs/hep-th/0311241

Web End =hep-th/0311241 ] [http://inspirehep.net/search?p=find+EPRINT+hep-th/0311241

Web End =INSPIRE ].

[55] D. Lst, S. Re ert and S. Stieberger, Flux-induced soft supersymmetry breaking in chiral type IIB orientifolds with D3/D7-branes, http://dx.doi.org/10.1016/j.nuclphysb.2004.11.030

Web End =Nucl. Phys. B 706 (2005) 3 [http://arxiv.org/abs/hep-th/0406092

Web End =hep-th/0406092 ] [http://inspirehep.net/search?p=find+EPRINT+hep-th/0406092

Web End =INSPIRE ].

32

JHEP02(2013)084

[56] P.G. Camara, L. Ibez and A. Uranga, Flux-induced SUSY-breaking soft terms on D7-D3 brane systems, http://dx.doi.org/10.1016/j.nuclphysb.2004.11.035

Web End =Nucl. Phys. B 708 (2005) 268 [http://arxiv.org/abs/hep-th/0408036

Web End =hep-th/0408036 ] [http://inspirehep.net/search?p=find+EPRINT+hep-th/0408036

Web End =INSPIRE ].

[57] D. Lst, S. Re ert and S. Stieberger, MSSM with soft SUSY breaking terms from D7-branes with uxes, http://dx.doi.org/10.1016/j.nuclphysb.2005.08.009

Web End =Nucl. Phys. B 727 (2005) 264 [http://arxiv.org/abs/hep-th/0410074

Web End =hep-th/0410074 ] [http://inspirehep.net/search?p=find+EPRINT+hep-th/0410074

Web End =INSPIRE ].

[58] M. Graa, T.W. Grimm, H. Jockers and J. Louis, Soft supersymmetry breaking in Calabi-Yau orientifolds with D-branes and uxes, http://dx.doi.org/10.1016/j.nuclphysb.2004.04.021

Web End =Nucl. Phys. B 690 (2004) 21 [http://arxiv.org/abs/hep-th/0312232

Web End =hep-th/0312232 ] [http://inspirehep.net/search?p=find+EPRINT+hep-th/0312232

Web End =INSPIRE ].

[59] Particle Data Group collaboration, J. Beringer et al., Review of particle physics, http://dx.doi.org/10.1103/PhysRevD.86.010001

Web End =Phys. Rev. D 86 (2012) 010001 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D86,010001

Web End =INSPIRE ].

[60] U. Ellwanger, J.F. Gunion and C. Hugonie, NMHDECAY: a Fortran code for the Higgs masses, couplings and decay widths in the NMSSM, http://dx.doi.org/10.1088/1126-6708/2005/02/066

Web End =JHEP 02 (2005) 066 [http://arxiv.org/abs/hep-ph/0406215

Web End =hep-ph/0406215 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0406215

Web End =INSPIRE ].

[61] U. Ellwanger and C. Hugonie, NMHDECAY 2.0: an Updated program for sparticle masses, Higgs masses, couplings and decay widths in the NMSSM,http://dx.doi.org/10.1016/j.cpc.2006.04.004

Web End =Comput. Phys. Commun. 175 (2006) 290 [http://arxiv.org/abs/hep-ph/0508022

Web End =hep-ph/0508022 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0508022

Web End =INSPIRE ].

[62] U. Ellwanger and C. Hugonie, NMSPEC: A Fortran code for the sparticle and Higgs masses in the NMSSM with GUT scale boundary conditions,http://dx.doi.org/10.1016/j.cpc.2007.05.001

Web End =Comput. Phys. Commun. 177 (2007) 399 [http://arxiv.org/abs/hep-ph/0612134

Web End =hep-ph/0612134 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0612134

Web End =INSPIRE ].

[63] CDF, D0 collaboration, T. Aaltonen et al., Combination of the top-quark mass measurements from the Tevatron collider, http://dx.doi.org/10.1103/PhysRevD.86.092003

Web End =Phys. Rev. D 86 (2012) 092003 [arXiv:1207.1069] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1207.1069

Web End =INSPIRE ].

[64] CMS collaboration, Search for the standard model Higgs boson decaying to pairs, http://cds.cern.ch/record/1493615

Web End =CMS-PAS-HIG-12-043 (2012).

[65] CMS collaboration, Evidence for a particle decaying to W +W in the fully leptonic nal state in a standard model Higgs boson search in pp collisions at the LHC, http://cds.cern.ch/record/1493602

Web End =CMS-PAS-HIG-12-042 (2012).

[66] CMS collaboration, Updated results on the new boson discovered in the search for the standard model Higgs boson in the ZZ 4 leptons channel in pp collisions at s = 7 and 8

TeV, http://cds.cern.ch/record/1494488

Web End =CMS-PAS-HIG-12-041 (2012).

[67] CMS collaboration, Search for the standard model Higgs boson produced in association with W or Z bosons, and decaying to bottom quarks, http://cds.cern.ch/record/1493615

Web End =CMS-PAS-HIG-12-043 (2012).

[68] CMS collaboration, Evidence for a new state decaying into two photons in the search for the standard model Higgs boson in pp collisions, http://cds.cern.ch/record/1460419

Web End =CMS-PAS-HIG-12-015 (2012).

[69] ATLAS collaboration, Observation of an excess of events in the search for the Standard Model Higgs boson in the gamma-gamma channel with the ATLAS detector, http://cds.cern.ch/record/1460410

Web End =ATLAS-CONF-2012-091 (2012).

[70] ATLAS collaboration, Search for charged Higgs bosons decaying via H+ in top quark pair events using pp collision data at s = 7 TeV with the ATLAS detector,

http://dx.doi.org/10.1007/JHEP06(2012)039

Web End =JHEP 06 (2012) 039 [arXiv:1204.2760] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1204.2760

Web End =INSPIRE ].

[71] G. Blanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs: a program for calculating the relic density in the MSSM, http://dx.doi.org/10.1016/S0010-4655(02)00596-9

Web End =Comput. Phys. Commun. 149 (2002) 103 [http://arxiv.org/abs/hep-ph/0112278

Web End =hep-ph/0112278 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0112278

Web End =INSPIRE ].

[72] G. Blanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs: version 1.3, http://dx.doi.org/10.1016/j.cpc.2005.12.005

Web End =Comput. Phys. Commun. 174 (2006) 577 [http://arxiv.org/abs/hep-ph/0405253

Web End =hep-ph/0405253 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0405253

Web End =INSPIRE ].

33

JHEP02(2013)084

[73] G. Blanger et al., Indirect search for dark matter with MicrOMEGAs2.4, http://dx.doi.org/10.1016/j.cpc.2010.11.033

Web End =Comput. Phys. Commun. 182 (2011) 842 [arXiv:1004.1092] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1004.1092

Web End =INSPIRE ].

[74] WMAP collaboration, E. Komatsu et al., Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation,http://dx.doi.org/10.1088/0067-0049/192/2/18

Web End =Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1001.4538

Web End =INSPIRE ].

[75] G. Ross and M. Serna, Unication and fermion mass structure, http://dx.doi.org/10.1016/j.physletb.2008.05.014

Web End =Phys. Lett. B 664 (2008) 97 [arXiv:0704.1248] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0704.1248

Web End =INSPIRE ].

[76] G. Elor, L.J. Hall, D. Pinner and J.T. Ruderman, Yukawa unication and the superpartner mass scale, http://dx.doi.org/10.1007/JHEP10(2012)111

Web End =JHEP 10 (2012) 111 [arXiv:1206.5301] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1206.5301

Web End =INSPIRE ].

[77] F. Staub, Sarah, arXiv:0806.0538 [http://inspirehep.net/search?p=find+EPRINT+arXiv:0806.0538

Web End =INSPIRE ].

[78] F. Staub, From superpotential to model les for FeynArts and CalcHep/CompHEP, http://dx.doi.org/10.1016/j.cpc.2010.01.011

Web End =Comput. Phys. Commun. 181 (2010) 1077 [arXiv:0909.2863] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0909.2863

Web End =INSPIRE ].

[79] F. Staub, Automatic calculation of supersymmetric renormalization group equations and self energies, http://dx.doi.org/10.1016/j.cpc.2010.11.030

Web End =Comput. Phys. Commun. 182 (2011) 808 [arXiv:1002.0840] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1002.0840

Web End =INSPIRE ].

[80] F. Staub, W. Porod and B. Herrmann, The electroweak sector of the NMSSM at the one-loop level, http://dx.doi.org/10.1007/JHEP10(2010)040

Web End =JHEP 10 (2010) 040 [arXiv:1007.4049] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1007.4049

Web End =INSPIRE ].

[81] LEP Working Group for Higgs boson searches, ALEPH, DELPHI, L3, OPAL collaboration, R. Barate et al., Search for the standard model Higgs boson at LEP,http://dx.doi.org/10.1016/S0370-2693(03)00614-2

Web End =Phys. Lett. B 565 (2003) 61 [http://arxiv.org/abs/hep-ex/0306033

Web End =hep-ex/0306033 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ex/0306033

Web End =INSPIRE ].

[82] D. Cerdeno, C. Hugonie, D. Lopez-Fogliani, C. Muoz and A. Teixeira, Theoretical predictions for the direct detection of neutralino dark matter in the NMSSM, http://dx.doi.org/10.1088/1126-6708/2004/12/048

Web End =JHEP 12 (2004) 048 [http://arxiv.org/abs/hep-ph/0408102

Web End =hep-ph/0408102 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0408102

Web End =INSPIRE ].

[83] A.J. Buras, P.H. Chankowski, J. Rosiek and L. Slawianowska, Md,s, B0d, s + and B Xs in supersymmetry at large tan , http://dx.doi.org/10.1016/S0550-3213(03)00190-1

Web End =Nucl. Phys. B 659 (2003) 3 [http://arxiv.org/abs/hep-ph/0210145

Web End =hep-ph/0210145 ]

[http://inspirehep.net/search?p=find+EPRINT+hep-ph/0210145

Web End =INSPIRE ].

[84] C. Bobeth, A.J. Buras, F. Krger and J. Urban, QCD corrections to B Xd,s

,

and KL + in the MSSM, http://dx.doi.org/10.1016/S0550-3213(02)00141-4

Web End =Nucl. Phys. B 630 (2002) 87

[http://arxiv.org/abs/hep-ph/0112305

Web End =hep-ph/0112305 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0112305

Web End =INSPIRE ].

[85] G. Hiller, B physics signals of the lightest CP odd Higgs in the NMSSM at large tan , http://dx.doi.org/10.1103/PhysRevD.70.034018

Web End =Phys. Rev. D 70 (2004) 034018 [http://arxiv.org/abs/hep-ph/0404220

Web End =hep-ph/0404220 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0404220

Web End =INSPIRE ].

[86] F. Domingo and U. Ellwanger, Updated constraints from B physics on the MSSM and the NMSSM, http://dx.doi.org/10.1088/1126-6708/2007/12/090

Web End =JHEP 12 (2007) 090 [arXiv:0710.3714] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0710.3714

Web End =INSPIRE ].

[87] R.N. Hodgkinson and A. Pilaftsis, Supersymmetric Higgs singlet e ects on B-meson FCNC observables at large tan , http://dx.doi.org/10.1103/PhysRevD.78.075004

Web End =Phys. Rev. D 78 (2008) 075004 [arXiv:0807.4167] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0807.4167

Web End =INSPIRE ].

[88] D. Cerdeno, E. Gabrielli, D. Lopez-Fogliani, C. Muoz and A. Teixeira, Phenomenological viability of neutralino dark matter in the NMSSM, http://dx.doi.org/10.1088/1475-7516/2007/06/008

Web End =JCAP 06 (2007) 008 [http://arxiv.org/abs/hep-ph/0701271

Web End =hep-ph/0701271 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0701271

Web End =INSPIRE ].

[89] Muon G-2 collaboration, G. Bennett et al., Final report of the muon E821 anomalous magnetic moment measurement at BNL, http://dx.doi.org/10.1103/PhysRevD.73.072003

Web End =Phys. Rev. D 73 (2006) 072003 [http://arxiv.org/abs/hep-ex/0602035

Web End =hep-ex/0602035 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ex/0602035

Web End =INSPIRE ].

[90] K. Hagiwara, R. Liao, A.D. Martin, D. Nomura and T. Teubner, (g 2) and (M2Z)

re-evaluated using new precise data, http://dx.doi.org/10.1088/0954-3899/38/8/085003

Web End =J. Phys. G 38 (2011) 085003 [arXiv:1105.3149] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1105.3149

Web End =INSPIRE ].

34

JHEP02(2013)084

Bd,s +, K

[91] F. Jegerlehner and A. Ny eler, The muon g 2, http://dx.doi.org/10.1016/j.physrep.2009.04.003

Web End =Phys. Rept. 477 (2009) 1

[arXiv:0902.3360] [http://inspirehep.net/search?p=find+EPRINT+arXiv:0902.3360

Web End =INSPIRE ].

[92] M. Davier, A. Hoecker, B. Malaescu and Z. Zhang, Reevaluation of the hadronic contributions to the muon g 2 and to MZ, http://dx.doi.org/10.1140/epjc/s10052-012-1874-8

Web End =Eur. Phys. J. C 71 (2011) 1515 [Erratum ibid.

C 72 (2012) 1874] [arXiv:1010.4180] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1010.4180

Web End =INSPIRE ].

[93] ATLAS collaboration, Search for the Standard Model Higgs boson in H decays in

proton-proton collisions with the ATLAS detector, http://cds.cern.ch/record/1493624

Web End =ATLAS-CONF-2012-160 (2012).

[94] U. Ellwanger, A. Florent and D. Zerwas, Discovering the constrained NMSSM with leptons at the LHC, http://dx.doi.org/10.1007/JHEP01(2011)103

Web End =JHEP 01 (2011) 103 [arXiv:1011.0931] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1011.0931

Web End =INSPIRE ].

[95] G. Blanger, S. Biswas, C. Boehm and B. Mukhopadhyaya, Light neutralino dark matter in the MSSM and its implication for LHC searches for staus, http://dx.doi.org/10.1007/JHEP12(2012)076

Web End =JHEP 12 (2012) 076 [arXiv:1206.5404] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1206.5404

Web End =INSPIRE ].

JHEP02(2013)084

35