Implications of improved Higgs mass calculations for supersymmetric models

Abstract

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

We discuss the allowed parameter spaces of supersymmetric scenarios in light of improved Higgs mass predictions provided by FeynHiggs 2.10.0. The Higgs mass predictions combine Feynman-diagrammatic results with a resummation of leading and subleading logarithmic corrections from the stop/top sector, which yield a significant improvement in the region of large stop masses. Scans in the pMSSM parameter space show that, for given values of the soft supersymmetry-breaking parameters, the new logarithmic contributions beyond the two-loop order implemented in FeynHiggs tend to give larger values of the light CP-even Higgs mass, ......, in the region of large stop masses than previous predictions that were based on a fixed-order Feynman-diagrammatic result, though the differences are generally consistent with the previous estimates of theoretical uncertainties. We re-analyse the parameter spaces of the CMSSM, NUHM1 and NUHM2, taking into account also the constraints from CMS and LHCb measurements of ......and ATLAS searches for ...... events using 20/fb of LHC data at 8 TeV. Within the CMSSM, the Higgs mass constraint disfavours ......, though not in the NUHM1 or NUHM2.

Eur. Phys. J. C (2014) 74:2809DOI 10.1140/epjc/s10052-014-2809-3

Regular Article - Theoretical Physics

Implications of improved Higgs mass calculations for supersymmetric models

O. Buchmueller1, M. J. Dolan2, J. Ellis3,4, T. Hahn5, S. Heinemeyer6,a, W. Hollik5, J. Marrouche1, K. A. Olive7,H. Rzehak8, K. J. de Vries1, G. Weiglein9

1 High Energy Physics Group, Blackett Lab., Imperial College, Prince Consort Road, London SW7 2AZ, UK

2 Theory Group, SLAC National Accelerator Lab., 2575 Sand Hill Road, Menlo Park, CA 94025-7090, USA

3 Theoretical Particle Physics and Cosmology Group, Department of Physics, Kings College London, London WC2R 2LS, UK

4 Theory Division, CERN, 1211 Geneva 23, Switzerland

5 Max-Planck-Institut fr Physik, Fhringer Ring 6, 80805 Munich, Germany

6 Instituto de Fsica de Cantabria (CSIC-UC), 39005 Santander, Spain

7 William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA

8 Physikalisches Institut, Albert-Ludwigs-Universitt Freiburg, 79104 Freiburg, Germany

9 DESY, Notkestrasse 85, 22607 Hamburg, Germany

Received: 9 January 2014 / Accepted: 4 March 2014 / Published online: 18 March 2014 The Author(s) 2014. This article is published with open access at Springerlink.com

Abstract We discuss the allowed parameter spaces of supersymmetric scenarios in light of improved Higgs mass predictions provided by FeynHiggs 2.10.0. The Higgs mass predictions combine Feynman-diagrammatic results with a resummation of leading and subleading logarithmic corrections from the stop/top sector, which yield a signi-cant improvement in the region of large stop masses. Scans in the pMSSM parameter space show that, for given values of the soft supersymmetry-breaking parameters, the new logarithmic contributions beyond the two-loop order implemented in FeynHiggs tend to give larger values of the light CP-even Higgs mass, Mh, in the region of large stop masses than previous predictions that were based on a xed-order Feynman-diagrammatic result, though the differences are generally consistent with the previous estimates of theoretical uncertainties. We re-analyse the parameter spaces of the CMSSM, NUHM1 and NUHM2, taking into account also the constraints from CMS and LHCb measurements of BR(Bs +)and ATLAS searches for /

ET events using 20/fb of LHC data at 8 TeV. Within the CMSSM, the Higgs mass constraint disfavours tan [lessorsimilar] 10, though not in the

NUHM1 or NUHM2.

1 Introduction

The ATLAS and CMS experiments did not discover super-symmetry (SUSY) during the rst, low-energy LHC run at 7

a e-mail: [email protected]

and 8 TeV. However, an optimist may consider that the headline discovery of a Higgs boson weighing 126 GeV [1,2]

has provided two additional pieces of indirect, circumstantial evidence for SUSY, beyond the many previous motivations. One piece of circumstantial evidence is provided by the Higgs mass, which falls within the range [lessorsimilar]135 GeV calculated in the minimal SUSY extension of the Standard Model (MSSM) for masses of the SUSY particles around 1 TeV [3 15]. The other piece of circumstantial evidence is provided by measurements of Higgs couplings, which do not display any signicant deviations from Standard Model (SM) predictions at the present level of experimental accuracy. This disfavours some composite models but is consistent with the predictions of simplied SUSY models such as the constrained MSSM (CMSSM) [1625] with universal input soft SUSY-breaking masses m0 for scalars, m1/2 for fermions as well as A0, the soft SUSY-breaking trilinear coupling and NUHM models that have non-universal soft SUSY-breaking contributions to Higgs supermultiplet masses: see [2630] and [31] for a review.

That said, the absence of SUSY in the rst LHC run and the fact that the Higgs mass is in the upper part of the MSSM range both suggest, within simple models such as the CMSSM and NUHM (see, e.g., [32,33]) as well as in the pMSSM, that the SUSY particle mass scale may be larger than had been suggested prior to the LHC, on the basis of ne-tuning arguments and in order to explain the discrepancy between calculations of (g 2) within the SM and the

experimental measurement [34]. A relatively large SUSY particle mass scale also makes it easier to reconcile SUSY

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with the experimental measurement of BR(Bs +)

[3537], particularly if tan (the ratio of SUSY Higgs vacuum expectation values, v.e.v.s) is large.

The mathematical connection between the Higgs mass and the SUSY particle spectrum is provided by calculations of the lightest SUSY Higgs mass Mh in terms of the SUSY particle spectrum [311,14,15]: see [3840] for reviews. As is well known, one-loop radiative corrections allow Mh to exceed MZ by an amount that is logarithmically sensitive to such input parameters as the top squark masses m

t in the

pMSSM, or the universal m1/2 and m0 masses in the CMSSM and NUHM. Inverting this calculation, the inferred values of m

t , or m1/2, m0 and A0 are exponentially sensitive to the measured value of Mh. For this reason, it is essential to make available and use the most accurate calculations of Mh within the MSSM, and to keep track of the unavoidable theoretical uncertainties in these calculations due to unknown higher-order corrections, which are now larger than the experimental measurement error.

Several codes to calculate Mh are available [4148]. In terms of low-energy parameters, the most advanced calculation is provided by FeynHiggs [14,4952]. The differences between the codes are in the few GeV range for relatively light SUSY spectra, but they may become larger for higher third family squark masses and values of m1/2, m0 and A0.

This is particularly evident in the phenomenological MSSM (pMSSM), where the soft supersymmetry-breaking inputs to the SUSY spectrum codes are specied at a low scale, close to the physical masses of the supersymmetric particles.

In this paper we revisit the constraints on the CMSSM and NUHM parameter spaces imposed by the Higgs mass measurement using the signicantly improved 2.10.0 version of the FeynHiggs code [4953] that has recently been released. We situate our discussion in the context of a comparison between this and the earlier version FeynHiggs2.8.6, which has often been used in phenomenological studies of SUSY parameter spaces (e.g., in [54]), as well as with SOFTSUSY 3.3.9 [41]. We also discuss the implications for constraints on SUSY model parameters. Updating previous related analyses [32,33], we also take into account the complementary constraint on the CMSSM and NUHM parameter spaces imposed by the recent experimental measurement of BR(Bs +), and we incorporate the 95 %

CL limit on m1/2 and m0 established within the CMSSM by ATLAS following searches for missing transverse energy, /

ET , events using 20/fb of LHC data at 8 TeV [55].

The layout of this paper is as follows. In Sect. 2 we rst summarise the main improvements between the results implemented in FeynHiggs 2.8.6 and 2.10.0, and then we present some illustrative results in the pMSSM, discussing the numerical differences between calculations made using FeynHiggs versions 2.8.6 and 2.10.0. We then display in Sect. 3 some representative parameter planes in

the CMSSM, NUHM1 and NUHM2, discussing the interplay between the different experimental constraints including BR(Bs +)as well as Mh. Section 4 contains a discus

sion of the variations between the predictions of Mh made in global ts to CMSSM and NUHM1 model parameters using different versions of FeynHiggs and SOFTSUSY. Finally, Sect. 5 summarises our conclusions.

2 Comparisons of Higgs mass calculations within the general MSSM

2.1 The improved Higgs mass calculation in FeynHiggs2.10.0

The evaluation of Higgs boson masses in the MSSM, in particular of the mass of the lightest Higgs boson, Mh, has recently been improved for larger values of the scalar top mass scale. This new evaluation has been implemented in the code FeynHiggs 2.10.0, whose details can be found in [53]. Here we just summarise some salient points.

The code FeynHiggs provides predictions for the masses, couplings and decay properties of the MSSM Higgs bosons at the highest currently available level of accuracy as well as approximations for LHC production cross sections (for MSSM Higgs decays see also [56] and references therein). The evaluation of Higgs boson masses within FeynHiggs is based on a Feynman-diagrammatic calculation of the Higgs boson self-energies. By nding the higher-order corrected poles of the propagator matrix, the loop-corrected Higgs boson masses are obtained.

The principal focus of the improvements in FeynHiggs2.10.0 has been to attain greater accuracy for large stop masses. The versions of FeynHiggs as used, e.g., previously in [54] included the full one-loop and the leading and subleading two-loop corrections to the Higgs boson self-energies (and thus to Mh). The new version, FeynHiggs2.10.0 [53], which is used for the evaluations here, contains in addition a resummation of the leading and next-to-leading logarithms of type log(m

t /mt) in all orders of perturbation theory, which yields reliable results for m

t , MA

MZ. To this end the two-loop Renormalisation-Group Equations (RGEs) [57,58] have been solved, taking into account the one-loop threshold corrections to the quartic coupling at the SUSY scale: see [59] and references therein. In this way at n-loop order the terms

logn(m t /mt), logn1(mt/mt) (1) are taken into account. The resummed logarithms, which are calculated in the MS scheme for the scalar top sector, are matched to the one- and two-loop corrections, where the on-shell scheme had been used for the scalar top sector. The

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rst main difference between FeynHiggs 2.10.0 and previous versions occurs at three-loop order. As we shall see, FeynHiggs 2.10.0 yields a larger estimate of Mh for stop masses in the multi-TeV range and a correspondingly improved estimate of the theoretical uncertainty, as discussed in [53]. The improved estimate of the uncertainties arising from corrections beyond two-loop order in the top/stop sector is adjusted such that the impact of replacing the running top-quark mass by the pole mass (see [14]) is evaluated only for the non-logarithmic corrections rather than for the full two-loop contributions implemented in FeynHiggs.

Other codes such as SoftSusy [41], SPheno [42,43] and SuSpect [44] implement a calculation of the Higgs masses based on a DR renormalisation of the scalar quark sector1. These codes contain the full one-loop corrections to the MSSM Higgs masses and implement the most important two-loop corrections. In particular, SoftSusy contains the O(2t), O(b ), O(2b), O(bs), O(ts), O(2) and

O(tb) corrections of [1113,15] evaluated at zero external momentum for the neutral Higgs masses. These codes do not contain the additional resummed higher-order terms included in FeynHiggs 2.10.0. We return in Sect. 4 to a comparison between SoftSusy3.3.9 and FeynHiggs2.10.0.

More recently a calculation of Mh taking into account leading three-loop corrections of O(t2s) has became avail

able, based on a DR or a hybrid renormalisation scheme for the scalar top sector, where the numerical evaluation depends on the various SUSY mass hierarchies, resulting in the code H3m [4648], which adds the three-loop corrections to the FeynHiggs result. A brief comparison between FeynHiggs and H3m can be found in [53,60].

A numerical analysis in the CMSSM including leading three-loop corrections to Mh (with the code H3m) was presented in [60]. It was shown that the leading three-loop terms can have a strong impact on the interpretation of the measured Higgs mass value in the CMSSM. Here, with the new version of FeynHiggs, we go beyond this analysis by including (formally) subleading three-loop corrections as well as a resummation to all orders of the leading and next-to-leading logarithmic contributions to Mh; see above.

2.2 Comparing the improved Higgs mass calculation in FeynHiggs 2.10.0 with FeynHiggs 2.8.6

In the following we examine the effect of including the resummation of leading and subleading logarithmic corrections from the (scalar) top sector in the pMSSM. We compare the new FeynHiggs version 2.10.0 with a previ-

1 Since the differences between the on-shell and DR renormalisation in the scalar quark sector are formally of higher order, comparisons can be used to assess the uncertainties in the predictions of the Higgs mass.

ous one, 2.8.6, where the only relevant difference in the Higgs mass calculation between the two codes consists of the aforementioned resummation effects. (A comparison including SOFTSUSY can be found in Sect. 4.) These corrections are most sensitive to the soft SUSY-breaking parameters in the stop sector, m [tildewide]

q3 in the diagonal entry (which we assume here to be equal for left- and right-handed stops) and the trilinear coupling At. To have direct control over these two parameters, we consider a 10-parameter incarnation of the MSSM, denoted as the pMSSM10. In the pMSSM10 we set the squark masses of the rst two generations to a common value m[tildewide]q12, the third-generation squark mass parameters to a different value m[tildewide]q3, the slepton masses to m[tildewide]land the trilinear couplings At = Ab = A = A. The remaining parameters of

the pMSSM10 are the soft SUSY-breaking parameters in the gaugino sectors, M1, M2, M3, the Higgs mixing parameter , the CP-odd Higgs mass scale MA as well as tan .

We generate 1000 random sets of the eight parameters m[tildewide]q12 m[tildewide]l, M1, M2, M3, tan , and MA, without regard to

the experimental constraints. For each of these sets we vary m[tildewide]q3 = 0.5, 1, 2, 3, 4 and 5 TeV and A/m[tildewide]q3 =

0, 1.0, 2.0, 2.4, and we calculate the corresponding

spectra using SOFTSUSY-3.3.9. Using these spectra, we calculate Mh with FeynHiggs 2.8.6 and FeynHiggs2.10.0. We stress that the pMSSM10 spectra are only meant to illustrate the size of the corrections as a function of m [tildewide]

q3 and the trilinear coupling A, and we do not necessarily correspond to phenomenologically interesting regions of parameter space.

The sizes of the corrections from the (scalar) top sector are given by the differences (Mh|FH2.10.0 Mh|FH2.8.6) shown

in Fig. 1 as functions of Mh|FH2.8.6. The different panels in

this gure correspond to the different third-generation squark masses m[tildewide]q3 = 0.5 TeV (upper left), 1 TeV (upper right),

2 TeV (middle left), 3 TeV (middle right), 4 TeV (lower left) and 5 TeV (lower right), whereas the colours dark blue, blue, light blue, light green, orange, red and dark red correspond to A/m[tildewide]q3 = 2.4, 2.0, 1.0, 0.0, 1.0, 2.0, 2.4, respectively.

At low stop masses of around 500 GeV we see that the resummation corrections are O(0.5) GeV, whereas with increasing

stop masses they may become as large as 5 GeV. The dependence on A/m[tildewide]q3 is less signicant. We also note that, for similar values of m[tildewide]q3, the resummation corrections tend to be smaller for models yielding Mh 125 GeV than for mod

els yielding smaller values of Mh.

The latter effect is related to the (random) choice of MA and tan , with lower Mh values corresponding to lower MA and smaller tan . If the Mh value without resummed corrections, i.e., from FeynHiggs 2.8.6, is smaller, the newly added correction, which is independent of MA and tan has a larger effect. We should furthermore mention that the size of the resummed correction stays (mostly) within the previously predicted estimate for the theoretical

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Fig. 1 The differences between Mh calculated using

FeynHiggs 2.10.0 and FeynHiggs 2.8.6, as a function of the FeynHiggs2.8.6 value, for third-generation squark masses m[tildewide]q3 = 0.5 TeV (upper left),

1 TeV (upper right), 2 TeV (middle left), 3 TeV (middle right), 4 TeV (lower left) and5 TeV (lower right)

uncertainties due to missing higher-order corrections. Consequently, a point in the MSSM parameter space that has a Higgs mass value of, for instance, 125 GeV as evaluated by FeynHiggs 2.10.0, should not have been excluded on the basis of a lower Mh as evaluated using FeynHiggs2.8.6. However, the parallel reduction in the theory uncertainty in FeynHiggs 2.10.0 leads to a more precise restriction on the allowed MSSM parameter space.

3 Examples of CMSSM and NUHM parameter planes

In our exploration of the FeynHiggs 2.10.0 results for Mh, we discuss their interplay with other experimental constraints, notably BR(Bs +) and the ATLAS

search for /

ET events with 20/fb of data at 8 TeV. In this section, results were produced using SSARD [61] coupled to FeynHiggs. These results update those in [32] for the

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CMSSM and [33] for the NUHM. In the case of the CMSSM, we consider several (m1/2, m0) planes for xed values of tan and A0/m0, all with > 0. In the NUHM1 model we also display two (m1/2, m0) planes for xed values of tan and A0/m0, one with xed = 500 GeV and one

with xed MA = 1000 GeV, and two (, m0) planes with

xed tan , m1/2 and A0/m0. In the NUHM2 we display two (, MA) planes with xed tan , m1/2, m0 and A0/m0.We also present one example of a (m1/2, m0) plane in the minimal supergravity (mSUGRA) model, in which the electroweak vacuum conditions x tan as a function of m1/2, m0 and A0.

We adopt the following conventions in all these gures.

Regions where the LSP is charged are shaded brown, those where there is no consistent electroweak vacuum are shaded mauve, regions excluded by BR(b s ) measurements

at the 2- level are shaded green,2 those favoured by the SUSY interpretation of (g 2) are shaded pink, with lines

indicating the 1 (dashed) and 2 ranges (solid),3 and

strips with an LSP density appropriate to make up all the cold dark matter are shaded dark blue. For reasons of visibility, we shade strips where 0.06 < h2 < 0.2, but when we quote ranges of consistency we require that the relic density satises the more restrictive relic density bound 0.115 < h2 < 0.125 [70]. The 95 % CL limit from the

ATLAS /

ET search is shown as a continuous purple contour,4 and the 68 and 95 % CL limits from the CMS and LHCb measurements of BR(Bs +) are shown as continuous

green contours. Finally, the labelled continuous black lines are contours of Mh calculated with FeynHiggs 2.10.0, and the dash-dotted red lines are contours of Mh calculated with FeynHiggs 2.8.6 (as used, e.g., in [32,33,54]), which we use for comparison.

3.1 The CMSSM

Figure 2 displays four examples of (m1/2, m0) planes for relatively low values of tan . We see in the upper left panel for

2 We use here BR(b s )exp = (3.55 0.24) 104 i [6267] in

addition to a combined systematic and theory error of 0.13104. The

green shaded region is excluded at 95 % CL. As established in previous studies of the CMSSM and NUHM, this constraint is typically more important for larger tan , negative and smaller MA and (m1/2, m0).

3 These lines are drawn for a (g 2) discrepancy of (30.2 8.8)

1010 [34,68], corresponding to a combined e+e estimate of the lowest-order hadronic polarisation contribution to the SM calculation of (g 2). The decay data used to indicate a reduction in the dis

crepancy by about one so that, for example, the outer solid lines in the gures would correspond approximately to the 1 contours. How

ever, a recent re-evaluation yields data results very similar to the e+e results [69].

4 The ATLAS /

ET limit was quoted for the CMSSM with the choices tan = 30 and A0/m0 = 2, but a previous study [54] showed that such

a contour is essentially independent of both tan and A0/m0, as well as the amount of non-universality in NUHM models.

tan = 10 and A0 = 0 that the contour for Mh = 114 GeV

(the lower limit set by the LEP experiments) changes very little between FeynHiggs 2.8.6 and 2.10.0, whereas that for 119 GeV is shifted by m1/2 150 GeV in the

region of the stau-coannihilation strip at low m0. The ATLAS 20/fb /

ET limit on m1/2 excludes robustly a SUSY solution to the (g 2) discrepancy in this particular CMSSM scenario,

but neither b s nor Bs + has any impact on

the allowed section of the dark matter strip, which extends to m1/2 900 GeV in this case. However, none of it is compati

ble with the measured value of Mh, even with the higher value and the correspondingly smaller theory uncertainty as evaluated by FeynHiggs 2.10.0 which is about 0.8 GeV

near the endpoint of the strip. There is a mauve region at small m1/2 and large m0 where the electroweak vacuum conditions cannot be satised, adjacent to which there is a portion of a focus-point strip, excluded by the ATLAS /

ET search, where Mh is smaller than the measured value.

In the upper right panel of Fig. 2, which displays the case tan = 10 and A0 = 2.5m0, we see that the FeynHiggs

2.10.0 Mh = 119 GeV contour intersects the stau

coannihilation strip when m1/2 600 GeV (a shift of less

than 100 GeV in m1/2 compared to FeynHiggs 2.8.6) and the tip of the strip corresponds to Mh 122 GeV. The

experimental value of Mh lies somewhat outside the range around this value that is allowed by the uncertainty estimated in FeynHiggs 2.10.0, which is about 1.0 GeV at this point. Consequently, although the use of FeynHiggs2.10.0 reduces signicantly the tension with the measurement of Mh for this value of tan in the CMSSM, it seems that this model requires a larger value of tan .

We note in this case the appearance of a brown region in the upper left part of the plane, where the lighter scalar top is the LSP (or tachyonic), with an adjacent stop-coannihilation strip. We nd Mh < 122 GeV in the displayed section of the strip where m0 < 2000 GeV, but larger values of Mh can be found at larger m0, which may be compatible with the LHC measurement, within the uncertainties. For example, at m1/2 = 1500 GeV, the stop-coannihilation strip is found

at m0 3450 GeV and the Higgs mass there computed

with FeynHiggs 2.10.0 is Mh 125 GeV, substan

tially higher than the value of 121 GeV found in FeynHiggs2.8.6, though with a larger uncertainty of 2 GeV.

The lower left panel of Fig. 2 displays the (m1/2, m0)

plane for tan = 30 and A0 = 0. Compared with the tan =

10, A0 = 0 case, the Higgs mass contours are similar, though

shifted somewhat to lower m1/2. The focus-point region is found at slightly larger m1/2 but is not very different from the tan = 10 case. We note also the appearance of the (green)

68 and 95 % CL constraints from BR(Bs +), though

the constraints from the ATLAS /

ET search and (particularly)

Mh are more important. Although the stau-coannihilation strip extends to slightly higher values of m1/2 1000 GeV

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tan = 10, A0 = 0, > 0

tan = 10, A0 = 2.5m0, > 0

2000

0

2000

mh = 122.5 GeV

119

114

126

127

124

mh = 125 GeV

122.5

119

114

m 0(GeV)

1000

m 0(GeV)

1000

0

100

1000

1500

100

0

1

0

0

1

5

0

0

m1/2 (GeV)

m1/2 (GeV)

tan = 30, A0 = 0, > 0

tan = 30, A0 = 2.5m0, > 0

2000

2000

mh = 122.5 GeV

119

114

127

125

124

122.5

mh = 126 GeV

119

m 0(GeV)

1000

m 0(GeV)

1000

0

0

100

0

0

1

0

1500

100

1000

1500

m1/2 (GeV)

m1/2 (GeV)

Fig. 2 The allowed regions in the (m1/2, m0) planes for tan = 10

and A0 = 0 (upper left), tan = 10 and A0 = 2.5m0 (upper right),

tan = 30 and A0 = 0 (lower left) and tan = 30 and A0 = 2.5m0

(lower right). The line styles and shadings are described in the text. The section of the dark blue coannihilation strip in the lower right panel in

the range m1/2 (840, 1050) GeV is compatible with the constraints

from BR(Bs +) (green line) and the ATLAS 20/fb /

ET search

(purple line), as well as with the LHC Mh measurement. Better consistency with all the constraints (except (g 2)) is found if the improved

FeynHiggs 2.10.0 code is used, for tan = 30 and A0 = 2.5m0

when A0 = 0, the Higgs mass at the endpoint is still only

122 0.8 GeV. It is well known that the calculated value of

Mh increases with the value of A0, and compatibility with the LHC measurement for this value of tan requires a larger value of A0.

Accordingly, in the lower right panel of Fig. 2 we show the case of tan = 30 and A0 = 2.5m0. As expected, the

situation along the stau-coannihilation strip is much more favourable for Mh. At the end point of the stau-coannihilation strip, which is now at about m1/2 1250 GeV, according to

the improved FeynHiggs 2.10.0 calculation the Higgs

mass is Mh 125.2 1.1 GeV, quite consistent with LHC

measurement, whereas the previous version of FeynHiggswould have yielded Mh 123.4 2.7 GeV. This point is

also compatible with the 68 % CL limit from BR(Bs

+). The 95 % CL upper limit on BR(Bs +)

requires m1/2 [greaterorsimilar] 700 GeV, already placing a SUSY interpretation of (g 2) beyond reach, and the ATLAS 20/fb /

ET

search requires m1/2 > 840 GeV.

In the upper left corner of the plane, we again see a stop LSP region with a stop-coannihilation strip of acceptable relic density due running along its side. As in the case

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tan = 40, A0 = 2.0m0, > 0

tan = 40, A0 = 2.5 m0, > 0

2000

2000

125

127

mh = 126 GeV

124

119

122.5

114

126 mh = 127 GeV

125

124

122.5

119

m 0(GeV)

1000

m 0(GeV)

1000

0

0

0

100

1000

1500

100

1000

1500

m1/2 (GeV)

m1/2 (GeV)

Fig. 3 The allowed regions in the (m1/2, m0) planes for tan = 40

and A0 = 2m0 (left), tan = 40 and A0 = 2.5m0 (right). The line

styles and shadings are described in the text. When tan = 40, con-

sistency is found only if the improved FeynHiggs 2.10.0 code is used, for the A0 = 2m0 case

of the tan = 10, the strip as shown here corresponds

to values of Mh that are too low. However, at larger m0, this too would be acceptable. At m1/2 = 1500 GeV and

m0 = 3750 GeV, for example, we nd Mh 124

2 GeV with FeynHiggs 2.10.0, whereas FeynHiggs2.8.6 would have yielded Mh [lessorsimilar] 120 GeV albeit with an uncertainty of 5 GeV. Thus, in the CMSSM with

tan = 30 and A0 = 2.5m0 there are two regions of

compatibility with the LHC measurement of Mh once the improved FeynHiggs 2.10.0 calculation of Mh is taken into account.

Figure 3 displays some analogous (m1/2, m0) planes for tan = 40. For A0 = 0 (not shown), the plane would be

qualitatively similar to that with tan = 30, though the con

straint from BR(Bs +) would be much stronger. In

this case, the 95 % CL constraint would intersect the coannihilation strip at roughly m1/2 = 950 GeV. Instead, we show

results for both A0 = 2m0 and 2.5m0. In the case A0 = 2m0

(left), we see that the BR(Bs +) 95 % CL constraint

allows only a small section of the stau-coannihilation strip with m1/2 1200 GeV. (The 68 % limit is at signicantly

higher values of m1/2, well past the endpoint of the coannihilation strip). In this case, the BR(Bs +) constraint is

signicantly stronger than the LHC /

ET constraint, and much of the region with m1/2 < 500 GeV is also excluded by b s . Whereas the previous version of FeynHiggs

would have yielded Mh < 123.3 2.6 GeV near the tip

of the stau-coannihilation strip, the improved FeynHiggs2.10.0 calculation yields Mh 125.0 1.1 GeV in this

region, so it may now also be considered compatible with all the constraints (except (g 2)).

In the right panel of Fig. 3, we show the case of tan = 40 and A0 = 2.5m0. In this case, the BR(Bs

+) constraint also is only compatible with the endpoint of the stau-coannihilation strip, which is now at m1/2 1250 GeV, where the Higgs mass computed with

FeynHiggs 2.10.0 is as large as 127 GeV.5 (Once again, the LHC /

ET constraint on m1/2 is weaker, as is the b s constraint.) In the upper left corner at m0 m1/2,

we again see a stop LSP region and a stop-coannihilation strip running along its side. The part of the strip shown is excluded by b s , but compatibility is found at larger

m0. For m1/2 = 1500 GeV and m0 = 4050 GeV, the stop-

coannihilation strip is compatible with both constraints on B

decays, but FeynHiggs 2.10.0 yields Mh = 120 GeV,

albeit with a larger uncertainty 2 GeV.

We have also considered the larger value tan = 55, but

we nd in this case that the BR(Bs +) constraint is

incompatible with the dark matter constraint.

3.2 The NUHM1

In the NUHM1, universality of the input soft SUSY-breaking gaugino, squark and slepton masses is retained, and the cor-

5 We take this opportunity to comment on the implications for ne-tuning of FeynHiggs 2.10.0. Since an LHC-compatible value of Mh can be obtained for smaller values of (m1/2, m0), other things being equal, the ne-tuning measure proposed in [71,72] is generally reduced. For example, a point in the right panel of Fig. 3 that lies on the coannihilation strip and has a nominal value of Mh = 125 GeV would require

ne-tuning of 700 if FeynHiggs 2.10.0 is used, compared to 1540 if FeynHiggs 2.8.6 is used.

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2809 Page 8 of 14 Eur. Phys. J. C (2014) 74:2809

tan = 10, = 500 GeV, A0 = 2.5 m0

tan = 30, mA = 1000 GeV, A0 = 2.5 m0, > 0

3000

0

3000

2000

2000

126

mh = 127 GeV

125

124

122.5

m 0(GeV)

m 0(GeV)

126

mh = 127 GeV

125

122.5 V 119

124

1000

1000

0

0

100

1000

2000

500

1000

1500

m1/2 (GeV)

m1/2 (GeV)

tan = 10, m1/2 = 1000 GeV, A0 = 2.5m0

tan = 10, m1/2 = 2000 GeV, A0 = 2.5m0

2000

2000

m 0(GeV)

m 0(GeV)

1000

126

124

mh = 125 GeV

122.5

1000

127

mh = 126 GeV

125

0

0

2000 1000 0 1000 2000

2000 1000 0 1000 2000

(GeV)

(GeV)

Fig. 4 Examples of parameter planes in the NUHM1. Two (m1/2, m0) planes shown in the upper panels have A0 = 2.5m0 for tan = 10

and = 500 GeV (left) and tan = 30 and MA = 1000 GeV (right).

Also shown are (, m0) planes with tan = 10 and m1/2 = 1000 GeV

(lower left) and m1/2 = 2000 GeV (lower right). In all the panels there

are regions of consistency with all the experimental constraints if the improved FeynHiggs 2.10.0 code is used

responding contributions to the Higgs multiplets are allowed to be different but assumed to be equal to each other. In this case, there is an additional free parameter compared with the CMSSM, which allows one to choose either the Higgs super-potential mixing parameter or the pseudoscalar mass MA as a free parameter while satisfying the electroweak vacuum conditions. Here and in the following we neglect the (g2)

constraint, which is compatible with the ATLAS /

ET searches only at around the 2.53 level in the cases studied.

The upper left panel of Fig. 4 displays the NUHM1 (m1/2, m0) plane for tan = 10, A0 = 2.5m0 and =

500 GeV. In this case, we see that the stau-coannihilation strip at low m0 is connected to the focus-point strip by a broader (dark blue) band with m1/2 1200 GeV that is

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compatible with the astrophysical dark matter constraint.

In this band, the composition of the LSP has a substantial Higgsino admixture that brings the relic density down into the astrophysical range, and its location depends on the assumed value of . The value chosen here, = 500 GeV,

places this band beyond the ATLAS 20/fb /

ET limit, and the BR(Bs +) constraint is not important for this value

of tan . Furthermore, we see from the Mh contours that all this band is compatible with the Higgs mass measurement if the improved code FeynHiggs 2.10.0 is used. Only the upper part of this strip would have appeared consistent if the previous version of FeynHiggs had been used. This example shows that the freedom to vary within the NUHM1 opens up many possibilities to satisfy the experimental constraints, e.g., a lower value of tan than was possible in the CMSSM.

The upper right panel of Fig. 4 displays the (m1/2, m0) plane for tan = 30, A0 = 2.5m0 and xed MA =

1000 GeV.6 In this case there is a spike at m1/2 1100 GeV

in which the dark matter density is brought down into the range allowed by astrophysics and cosmology by rapid LSP annihilations into the heavy Higgs bosons H/A, a mechanism that operates whenever m

01 MA/2, namely

500 GeV in this case. All of the spike is comfortably consistent with the ATLAS 20/fb /

ET constraint and the upper limit on BR(Bs +). We see that in the upper part of

this spike FeynHiggs 2.10.0 yields a nominal value of Mh (125, 126) GeV, an increase of about 1.5 GeV over

FeynHiggs 2.8.6, but lower parts of the spike may also be consistent with the LHC Higgs mass measurement, given the theoretical uncertainties. On the other hand, only limited consistency in the lower part of the strip would have been found with the previous version of FeynHiggs. This example shows that the freedom to vary MA within the NUHM1 opens up many possibilities to satisfy the experimental constraints.

In the lower left panel of Fig. 4 we display a different type of slice through the NUHM1 parameter space, namely a (, m0) plane for xed tan = 10, m1/2 = 1000 GeV and

A0 = 2.5m0. With this choice of m1/2, the ATLAS 20/fb /

ET

constraint is automatically satised throughout the plane, and with this choice of tan the BR(Bs +) constraint is

also satised everywhere. We see two near-vertical dark blue bands where the relic LSP density falls within the cosmological range, again because of a large admixture of Higgsino in the LSP composition associated with the near-degeneracy of two neutralino mass eigenstates. These bands stretch between a stop LSP region at large m0 and a stau LSP region at low m0, which is anked by charged slepton LSP regions at large

||. We see that over much of this plane the value of Mh cal-

6 Here and in the lower left panel, in the black shaded region the LSP is a charged slepton other than the lighter stau.

culated with FeynHiggs 2.10.0 is 1 GeV higher than

the 2.8.6 value. The upper parts of the dark blue bands again yield a nominal value of Mh (125, 126) GeV, and

much of the rest of the bands may be compatible within the theoretical uncertainties.

The same is true in the lower right panel of Fig. 4, where we display an analogous (, m0) plane for tan = 10, m1/2 =

2000 GeV and A0 = 2.5m0. Here we see that the stau LSP

regions have expanded to larger m0, and there are again near-vertical dark matter bands rising from them, whilst the stop LSP region has receded to larger m0. In general, values of

Mh are larger than previously, with FeynHiggs 2.10.0yielding nominal values [greaterorsimilar]127 GeV for m0 > 1000 GeV.

This is roughly 3 GeV higher than found in FeynHiggs2.8.6. In this case, values of Mh as low as 125 GeV are attained only at the lower tips of the dark matter bands, very close to the stau LSP region with m0 300 GeV. However,

the entire bands are probably compatible with the LHC measurement of Mh when the theoretical uncertainties are taken into account.

We conclude from the analysis in this section that values of Mh 125 to 126 GeV are unexceptional in the NUHM1

and possible, e.g., for smaller values of tan than in the CMSSM, though disfavouring a supersymmetric interpretation of (g 2).

3.3 The NUHM2

In the NUHM2, the soft SUSY-breaking contributions to the masses of the two Higgs multiplets are allowed to vary independently, so there are two additional parameters compared to the CMSSM, which may be taken as and MA.

Figure 5 displays illustrative (, MA) planes for xed values of the other parameters tan = 10, A0 = 2.5m0 and

m1/2 = m0 = 1000 GeV (left), m1/2 = m0 = 1200 GeV

(right). We see immediately that the b s constraint is

stronger for < 0 (which is one of the reasons that more studies have been made of models with > 0) and that Mh is generally larger for > 0 than for < 0, if equal values of the other model parameters are chosen. The vertical dark matter strips correspond to large Higgsino admixtures, as in the NUHM1 examples discussed earlier, and the horizontal funnels are due to enhancement of LSP annihilation by direct-channel H/A poles: these move to higher (lower) MA for larger (smaller) m1/2, as seen by comparing the left and right panels of Fig. 5.

All the dark matter-compatible points in the left panel would correspond to values of Mh consistent with the experimental measurements within the theoretical uncertainties. In this case, the shift in Mh from FeynHiggs 2.8.6 to

FeynHiggs 2.10.0 is about 1 GeV at m1/2 = m0 =

1000 GeV and somewhat larger at higher m1/2, m0 as seen in the right panel. In the right panel we see that typical nomi-

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2809 Page 10 of 14 Eur. Phys. J. C (2014) 74:2809

tan = 10, m1/2 = 1000 GeV, m0 = 1000 GeV

tan = 10, m1/2 = 1200 GeV, m0 = 1200 GeV

2000

2000

mh = 124 GeV

125

A0 = 2.5m0

A0 = 2.5m0

mh = 126 GeV

125

m A(GeV)

m A(GeV)

1000

1000

100

100

2000 1000 0 1000 2000

2000 1000 0 1000 2000

(GeV)

(GeV)

Fig. 5 Examples of (, MA) planes in the NUHM2 for tan = 10

and A0 = 2.5m0, with m1/2 = m0 = 1000 GeV (left) and with

m1/2 = m0 = 2000 GeV (right). Using the improved FeynHiggs

2.10.0 code, consistency with the measured value of Mh is found over all the dark matter bands in both panels

A0/m0 = 2 , > 0

nal FeynHiggs 2.10.0 values of Mh are larger than the measured value, though they are consistent with experiment, given the theoretical uncertainties.

3.4 mSUGRA

Finally, we consider a scenario that is more restrictive than the CMSSM, namely minimal supergravity (mSUGRA). In this case, there is a universal input scalar mass m0 equal to the gravitino mass m3/2 and the soft bilinear and trilinear soft SUSY-breaking masses are related by A0 = (B0+1)m0;

see [31] for a review. The rst constraint means that we do not have the luxury of assuming m3/2 to be arbitrarily large, and there are regions of the (m1/2, m0) plane where the LSP is necessarily the gravitino. The relation between A0 and B0 implies that tan is determined at any point in the (m1/2, m0)

plane once A0 is xed.

Both these features are visible in Fig. 6, where the (m1/2, m0 = m3/2) plane for A0 = 2m0 and > 0

exhibits (grey) contours of tan and a wedge where the LSP is the lighter stau, anked by a neutralino LSP region at larger m0 = m3/2 and a gravitino LSP region at smaller

m0 = m3/2. The ATLAS 20/fb /

ET search is directly applicable only in the neutralino LSP region, and it requires reconsideration in the gravitino LSP region. In addition, in this region there are important astrophysical and cosmological limits on long-lived charged particles (in this case staus) that we do not consider here, so we concentrate on the neutralino LSP region above the stau LSP wedge. The ATLAS 20/fb /

ET constraint intersects the dark matter coannihilation strip just above this wedge where m1/2 850 GeV, and the

2000

mh = 127 GeV

126

125

tan = 40

124

122.5

119

114

tan = 35

tan = 30

m 0(GeV)

1000

0

100

1000

2000

m1/2 (GeV)

Fig. 6 The allowed regions in the (m1/2, m0) plane in a mSUGRA model with A0/m0 = 2. In addition to the line and shade descriptions

found in the text, shown here are labelled solid grey contours showing the derived value of tan . Using the improved FeynHiggs 2.10.0code, consistency with the measured value of Mh is found near the tip of the stau-coannihilation strip

BR(Bs +) constraint intersects the coannihilation

strip at m1/2 1050 GeV, whereas the tip of the strip is

at m1/2 1250 GeV. In this section of the coannihilation

strip the nominal value of Mh provided by the improved FeynHiggs 2.10.0 calculation is (124, 125) GeV,

compatible with the experimental measurement within the

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Fig. 7 Scatter plots of 10000 points each selected randomly from scans [54] in the CMSSM (left) and the NUHM1 (right), displayed in (Mh|FH2.10.0 Mh|SS3.3.9, Mh|FH2.10.0) planes and colour-coded according to their 2 values

theoretical uncertainties due to the 12 GeV shift in Mh found in this new version of FeynHiggs.

4 Higgs mass Predictions from global ts within the CMSSM and NUHM1

We saw in previous sections that different calculations of Mh may differ signicantly, particularly at large values of m1/2 and/or m0. With the improved Mh calculation in FeynHiggs 2.10.0, the theory uncertainty has now been reduced to allow more precise Mh evaluations also for larger values of the relevant SUSY parameters. Taking this into account, we found regions in the CMSSM that were compatible with the LHC measurement of Mh and other constraints when the improved FeynHiggs 2.10.0 code is used, as well as broader possibilities for compatibility in the NUHM1 and NUHM2. In this Section we consider the possible implications for global ts to SUSY model parameters that include Mh in the construction of the global likelihood function, concentrating for deniteness on the CMSSM and NUHM1 ts presented in [54].

In the following we will compare FeynHiggs 2.10.0with SoftSusy 3.3.9. While the higher-order corrections included in FeynHiggs 2.10.0 are more complete than those in SoftSusy, a very large discrepancy between the two codes would indicate a parameter region that is potentially unstable under higher-order corrections in at least one of the codes. Figure 7 displays planes of Mh|FH2.10.0

Mh|SS3.3.9 vs. the theoretical uncertainty Mh|FH2.10.0 esti

mated within FeynHiggs 2.10.0 (see [53] for details), displaying 10000 points chosen randomly from the samples in [54] (but with an upper limit on 2 < 20 to concentrate on the parts of parameter space of most phenomenological relevance) for the CMSSM (left panel) and the NUHM1 (right panel). The points are colour-coded according to the

differences found in [54] between their 2 values and those of the best-t points in the CMSSM and NUHM1, respectively, with low- 2 points in blue and high- 2 points in red.

The differences between the two codes are found in the region of |Mh|FH2.10.0 Mh|SS3.3.9| = 1.02.0 GeV with a

theoretical uncertainty prediction (for only the FeynHiggscalculation) between 0.6 and 1.5. The consistent dif

ference between the two codes can be attributed to the more complete inclusion of higher-order corrections in FeynHiggs, which is reected in the fact that the difference often exceeds the FeynHiggs theory uncertainty. On the other hand, no phenomenologically relevant parameter points are found with an unexpectedly large difference between the two codes. This indicates that the relevant parameter regions are not located in parts of the CMSSM/NUHM1 parameter space that lead to an unstable Mh evaluation. This supports the viability of the constraints imposed by Mh on these models.

A similar inference can be drawn from Fig. 8. For this plot we have selected 100 CMSSM points from the sample in [54] that have the lowest 2 for each bin in Mh|SS3.3.9. We show

their values of Mh|FH2.10.0 Mh|SS3.3.9 (in dark blue) and

of Mh|FH2.8.6 Mh|SS3.3.9 (in red) on the vertical axis, using

Mh|SS3.3.9 as the horizontal axis. In both cases the respective

Mh uncertainty calculations of FeynHiggs are indicated via vertical lines. We see that both FeynHiggs 2.10.0and 2.8.6 yield values of Mh that are systematically larger than SoftSusy 3.3.9. In most cases, 1 GeV [lessorsimilar]

Mh|FH2.10.0 Mh|SS3.3.9 [lessorsimilar] 2 GeV, 0 [lessorsimilar] Mh|FH2.8.6

Mh|SS3.3.9 [lessorsimilar] 1 GeV and Mh|FH2.10.0 Mh|FH2.8.6 1 GeV.

The change from version 2.8.6 to version 2.10.0 reects the size of the newly included resummed corrections to Mh for a relevant part of the parameter space.

The theoretical Mh uncertainty evaluated in FeynHiggs2.8.6 embraced the SoftSusy predictions as well as the

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Fig. 8 Values of Mh|FH2.10.0 Mh|SS3.3.9 (in dark blue) and of

Mh|FH2.8.6 Mh|SS3.3.9 (in red) plotted against Mh|SS3.3.9, for 100

CMSSM points from the sample in [54] that have the lowest 2 for each bin in Mh. The vertical lines indicate the respective Mh uncertainty calculations as evaluated by FeynHiggs

updated FeynHiggs2.10.0 prediction for Mh. The latter, in particular, gives condence that the uncertainty calculation indeed captures the missing higher-order corrections. The new theoretical uncertainty as evaluated using FeynHiggs2.10.0 does not include, in general, the older FeynHiggs prediction, nor does it include (in all cases) the SoftSusy prediction. This again demonstrates the effects and the relevance of the newly included resummed logarithmic corrections in FeynHiggs.

5 Summary and conclusions

As we have shown in this paper, the improved Higgs mass calculations provided in the improved FeynHiggs 2.10.0code have signicant implications for the allowed parameter spaces of supersymmetric models. We have illustrated this point with examples in the pMSSM, CMSSM, NUHM1 and NUHM2 frameworks.

In a random scan of the pMSSM10 parameter space we exhibited the change in the Higgs mass Mh in FeynHiggs2.10.0 compared to the previous version FeynHiggs2.8.6. This averages below 2 GeV for third family squark masses below 2 TeV, but it can increase up to Mh 5 GeV

for m[tildewide]q3 = 5 TeV. The update to FeynHiggs 2.10.0 is

therefore particularly relevant in light of the measured value of Mh and the strengthened LHC lower limits on sparticle masses.

The CMSSM is under strong pressure from the LHC searches for jets + /

ET events, which exclude small values of m1/2, the measurement of BR(Bs +), which

disfavours large values of tan , the measurement of Mh, which favours large values of m1/2 and/or tan , and pos-

itive values of A0, and the cosmological dark matter density constraint. We have shown that these constraints can be reconciled for suitable intermediate values of tan if FeynHiggs 2.10.0 is used to calculate Mh in terms of the input CMSSM parameters (with the exception of (g 2)). The pressure on the CMSSM would have been

much greater if an earlier version of FeynHiggs had been used, which yielded lower values of Mh because it did not include the leading and next-to-leading logarithms of type log(m

t /mt) in all orders of perturbation theory as incorporated in FeynHiggs 2.10.0.

The LHC constraints are satised more easily in the NUHM1 (and NUHM2), with their one (or two) extra parameters that offer more options for satisfying the cosmological dark matter density constraint at larger values of m1/2 than in the CMSSM. The extra degree(s) of freedom in the NUHM1 (NUHM2) allow the Higgs mixing parameter or (and) MA to be adjusted so that a sizable Higgsino component is present increasing the annihilation cross section, and/or allowing and/or rapid direct-channel

01

01 H/A annihilation

to bring the cosmological dark matter density into the allowed range. Reconciling all the constraints would have been possible already with the earlier version of FeynHiggs, but it is easier to achieve when the improved FeynHiggs 2.10.0version is used.

In addition to the higher values of Mh yielded by FeynHiggs 2.10.0, this code also provides a correspondingly reduced estimate of the theoretical uncertainty in the mass calculation. This must also be taken into account when analysing the consistency with other constraints within the CMSSM, NUHM1, NUHM2 or any other models. Taken together, the improved mass calculations and uncertainty estimates in FeynHiggs 2.10.0 make it a preferred tool for the analysis of supersymmetric models.

Acknowledgments The work of J.E. was supported in part by the London Centre for Terauniverse Studies (LCTS), using funding from the European Research Council via the Advanced Investigator Grant 267352. The work of K.A.O. was supported in part by DOE grant DEFG02-94ER-40823 at the University of Minnesota. The work of S.H. is supported in part by CICYT (Grant FPA 2010-22163-C02-01) and by the Spanish MICINNs Consolider-Ingenio 2010 Program under grant MultiDark CSD2009-00064. The work of G.W. was supported by the Collaborative Research Center SFB676 of the DFG, Particles, Strings, and the early Universe.

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Funded by SCOAP3 / License Version CC BY 4.0.

References

1. G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 716, 1 (2012). http://arxiv.org/abs/arXiv:1207.7214

Web End =arXiv:1207.7214 [hep-ex]

123

Eur. Phys. J. C (2014) 74:2809 Page 13 of 14 2809

2. S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B 716, 30 (2012). http://arxiv.org/abs/arXiv:1207.7235

Web End =arXiv:1207.7235 [hep-ex]

3. J.R. Ellis, G. Ridol, F. Zwirner, Phys. Lett. B 257, 83 (1991)4. J.R. Ellis, G. Ridol, F. Zwirner, Phys. Lett. B 262, 477 (1991)5. Y. Okada, M. Yamaguchi, T. Yanagida, Prog. Theor. Phys. 85, 1 (1991)

6. A. Yamada, Phys. Lett. B 263, 233 (1991)7. H.E. Haber, R. Hemping, Phys. Rev. Lett. 66, 1815 (1991)8. M. Drees, M.M. Nojiri, Phys. Rev. D 45, 2482 (1992)9. P.H. Chankowski, S. Pokorski, J. Rosiek, Phys. Lett. B 274, 191 (1992)

10. P.H. Chankowski, S. Pokorski, J. Rosiek, Phys. Lett. B 286, 307 (1992)

11. G. Degrassi, P. Slavich, F. Zwirner, Nucl. Phys. B 611, 403 (2001). http://arxiv.org/abs/hep-ph/0105096

Web End =hep-ph/0105096

12. A. Brignole, G. Degrassi, P. Slavich, F. Zwirner, Nucl. Phys. B 631, 195 (2002). http://arxiv.org/abs/hep-ph/0112177

Web End =hep-ph/0112177

13. A. Brignole, G. Degrassi, P. Slavich, F. Zwirner, Nucl. Phys. B 643, 79 (2002). http://arxiv.org/abs/hep-ph/0206101

Web End =hep-ph/0206101

14. G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich, G. Weiglein, Eur. Phys. J. C 28, 133 (2003). http://arxiv.org/abs/arXiv:hep-ph/0212020

Web End =arXiv:hep-ph/0212020

15. B.C. Allanach, A. Djouadi, J.L. Kneur, W. Porod, P. Slavich, JHEP 0409, 044 (2004). http://arxiv.org/abs/arXiv:hep-ph/0406166

Web End =arXiv:hep-ph/0406166

16. M. Drees, M.M. Nojiri, Phys. Rev. D 47, 376 (1993). http://arxiv.org/abs/arXiv:hep-ph/9207234

Web End =arXiv:hep-ph/ http://arxiv.org/abs/arXiv:hep-ph/9207234

Web End =9207234

17. G.L. Kane, C.F. Kolda, L. Roszkowski, J.D. Wells, Phys. Rev. D 49, 6173 (1994). http://arxiv.org/abs/arXiv:hep-ph/9312272

Web End =arXiv:hep-ph/9312272

18. H. Baer, M. Brhlik, Phys. Rev. D 53, 597 (1996). http://arxiv.org/abs/arXiv:hep-ph/9508321

Web End =arXiv:hep-ph/ http://arxiv.org/abs/arXiv:hep-ph/9508321

Web End =9508321

19. H. Baer, M. Brhlik, Phys. Rev. D 57, 567 (1998). http://arxiv.org/abs/arXiv:hep-ph/9706509

Web End =arXiv:hep-ph/ http://arxiv.org/abs/arXiv:hep-ph/9706509

Web End =9706509

20. J.R. Ellis, T. Falk, K.A. Olive, M. Schmitt, Phys. Lett. B 388, 97 (1996). http://arxiv.org/abs/arXiv:hep-ph/9607292

Web End =arXiv:hep-ph/9607292

21. V.D. Barger, C. Kao, Phys. Rev. D 57, 3131 (1998). http://arxiv.org/abs/arXiv:hep-ph/9704403

Web End =arXiv:hep-ph/ http://arxiv.org/abs/arXiv:hep-ph/9704403

Web End =9704403

22. L. Roszkowski, R. Ruiz de Austri, T. Nihei, JHEP 0108, 024 (2001). http://arxiv.org/abs/arXiv:hep-ph/0106334

Web End =arXiv:hep-ph/0106334

23. A. Djouadi, M. Drees, J.L. Kneur, JHEP 0108, 055 (2001). http://arxiv.org/abs/arXiv:hep-ph/0107316

Web End =arXiv: http://arxiv.org/abs/arXiv:hep-ph/0107316

Web End =hep-ph/0107316

24. U. Chattopadhyay, A. Corsetti, P. Nath, Phys. Rev. D 66, 035003 (2002). http://arxiv.org/abs/arXiv:hep-ph/0201001

Web End =arXiv:hep-ph/0201001

25. J.R. Ellis, K.A. Olive, Y. Santoso, New J. Phys. 4, 32 (2002). http://arxiv.org/abs/arXiv:hep-ph/0202110

Web End =arXiv: http://arxiv.org/abs/arXiv:hep-ph/0202110

Web End =hep-ph/0202110

26. J. Ellis, K. Olive, Y. Santoso, Phys. Lett. B 539, 107 (2002). http://arxiv.org/abs/arXiv:hep-ph/0204192

Web End =arXiv: http://arxiv.org/abs/arXiv:hep-ph/0204192

Web End =hep-ph/0204192

27. J.R. Ellis, T. Falk, K.A. Olive, Y. Santoso, Nucl. Phys. B 652, 259 (2003). http://arxiv.org/abs/arXiv:hep-ph/0210205

Web End =arXiv:hep-ph/0210205

28. H. Baer, A. Mustafayev, S. Profumo, A. Belyaev, X. Tata, Phys.

Rev. D 71, 095008 (2005). http://arxiv.org/abs/arXiv:hep-ph/0412059

Web End =arXiv:hep-ph/0412059

29. H. Baer, A. Mustafayev, S. Profumo, A. Belyaev, X. Tata, JHEP 0507, 065 (2005). http://arxiv.org/abs/hep-ph/0504001

Web End =hep-ph/0504001

30. J.R. Ellis, K.A. Olive, P. Sandick, Phys. Rev. D 78, 075012 (2008). http://arxiv.org/abs/arXiv:0805.2343

Web End =arXiv:0805.2343 [hep-ph]

31. S.S. AbdusSalam et al., Eur. Phys. J. C 71, 1835 (2011). http://arxiv.org/abs/arXiv:1109.3859

Web End =arXiv: http://arxiv.org/abs/arXiv:1109.3859

Web End =1109.3859 [hep-ph]

32. J. Ellis, K.A. Olive, Eur. Phys. J. C 72, 2005 (2012). http://arxiv.org/abs/arXiv:1202.3262

Web End =arXiv:1202. http://arxiv.org/abs/arXiv:1202.3262

Web End =3262 [hep-ph]

33. J. Ellis, F. Luo, K.A. Olive, P. Sandick, Eur. Phys. J. C 73, 2403 (2013). http://arxiv.org/abs/arXiv:1212.4476

Web End =arXiv:1212.4476 [hep-ph]

34. T. Blum, A. Denig, I. Logashenko, E. de Rafael, B. L. Roberts, T.

Teubner, G. Venanzoni, http://arxiv.org/abs/arXiv:1311.2198

Web End =arXiv:1311.2198 [hep-ph]

35. S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. Lett. 111, 101804 (2013). http://arxiv.org/abs/arXiv:1307.5025

Web End =arXiv:1307.5025 [hep-ex]

36. R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. 111, 101805 (2013). http://arxiv.org/abs/arXiv:1307.5024

Web End =arXiv:1307.5024 [hep-ex]

37. R. Aaij et al. [LHCb and CMS Collaborations], LHCb-CONF-2013-012, CMS PAS BPH-13-007 (2013)

38. A. Djouadi, Phys. Rept. 459, 1 (2008). http://arxiv.org/abs/arXiv:hep-ph/0503173

Web End =arXiv:hep-ph/0503173 39. S. Heinemeyer, Int. J. Mod. Phys. A 21, 2659 (2006). http://arxiv.org/abs/hep-ph/0407244

Web End =hep-ph/ http://arxiv.org/abs/hep-ph/0407244

Web End =0407244

40. S. Heinemeyer, W. Hollik, G. Weiglein, Phys. Rept. 425, 265 (2006). http://arxiv.org/abs/hep-ph/0412214

Web End =hep-ph/0412214

41. B.C. Allanach, Comput. Phys. Commun. 143, 305 (2002). http://arxiv.org/abs/hep-ph/0104145

Web End =hep-ph/ http://arxiv.org/abs/hep-ph/0104145

Web End =0104145

42. W. Porod, Comput. Phys. Commun. 153, 275 (2003). http://arxiv.org/abs/hep-ph/0301101

Web End =hep-ph/ http://arxiv.org/abs/hep-ph/0301101

Web End =0301101

43. W. Porod, F. Staub, Comput. Phys. Commun. 183, 2458 (2012). http://arxiv.org/abs/arXiv:1104.1573

Web End =arXiv:1104.1573 [hep-ph]

44. A. Djouadi, J.-L. Kneur, G. Moultaka, Comput. Phys. Commun. 176, 426 (2007). http://arxiv.org/abs/hep-ph/0211331

Web End =hep-ph/0211331

45. J.S. Lee, A. Pilaftsis, M.S. Carena, S.Y. Choi, M. Drees, J.R. Ellis, C.E.M. Wagner, Comput. Phys. Commun. 156, 283 (2004). http://arxiv.org/abs/hep-ph/0307377

Web End =hep-ph/ http://arxiv.org/abs/hep-ph/0307377

Web End =0307377

46. R. Harlander, P. Kant, L. Mihaila, M. Steinhauser, Phys. Rev. Lett. 100, 191602 (2008a)

47. R. Harlander, P. Kant, L. Mihaila, M. Steinhauser, Phys. Rev. Lett. 101, 039901 (2008b). http://arxiv.org/abs/arXiv:0803.0672

Web End =arXiv:0803.0672 [hep-ph]

48. R. Harlander, P. Kant, L. Mihaila, M. Steinhauser, JHEP 1008, 104 (2010). http://arxiv.org/abs/arXiv:1005.5709

Web End =arXiv:1005.5709 [hep-ph]

49. S. Heinemeyer, W. Hollik, G. Weiglein, Eur. Phys. J. C 9, 343 (1999). http://arxiv.org/abs/arXiv:hep-ph/9812472

Web End =arXiv:hep-ph/9812472

50. S. Heinemeyer, W. Hollik, G. Weiglein, Comput. Phys. Commun. 124, 76 (2000). http://arxiv.org/abs/arXiv:hep-ph/9812320

Web End =arXiv:hep-ph/9812320

51. M. Frank et al., JHEP 0702, 047 (2007). http://arxiv.org/abs/arXiv:hep-ph/0611326

Web End =arXiv:hep-ph/0611326 52. T. Hahn, S. Heinemeyer, W. Hollik, H. Rzehak, G. Weiglein, Comput. Phys. Commun. 180, 1426 (2009). See http://www.feynhiggs.de

Web End =http://www.feynhiggs. http://www.feynhiggs.de

Web End =de

53. T. Hahn, S. Heinemeyer, W. Hollik, H. Rzehak, G. Weiglein, http://arxiv.org/abs/arXiv:1312.4937

Web End =arXiv: http://arxiv.org/abs/arXiv:1312.4937

Web End =1312.4937 [hep-ph]

54. O. Buchmueller, R. Cavanaugh, M. Citron, A. De Roeck, M.J. Dolan, J.R. Ellis, H. Flacher, S. Heinemeyer et al., Eur. Phys. J. C 72, 2243 (2012). http://arxiv.org/abs/arXiv:1207.7315

Web End =arXiv:1207.7315

55. ATLAS Collaboration, https://twiki.cern.ch/twiki/bin/view/AtlasPublic/CombinedSummaryPlots#SusyMSUGRASummary

Web End =https://twiki.cern.ch/twiki/bin/view/ https://twiki.cern.ch/twiki/bin/view/AtlasPublic/CombinedSummaryPlots#SusyMSUGRASummary

Web End =AtlasPublic/CombinedSummaryPlots#SusyMSUGRASummary

56. S. Heinemeyer et al. [LHC Higgs Cross Section Working Group Collaboration], http://arxiv.org/abs/arXiv:1307.1347

Web End =arXiv:1307.1347 [hep-ph]

57. J.R. Espinosa, M. Quiros, Phys. Lett. B 266, 389 (1991)58. H. Arason et al., Phys. Rev. D 46, 3945 (1992)59. M.S. Carena, H.E. Haber, S. Heinemeyer, W. Hollik, C.E.M. Wagner, G. Weiglein, Nucl. Phys. B 580, 29 (2000). http://arxiv.org/abs/hep-ph/0001002

Web End =hep-ph/ http://arxiv.org/abs/hep-ph/0001002

Web End =0001002

60. J.L. Feng, P. Kant, S. Profumo, D. Sanford, Phys. Rev. Lett. 111, 131802 (2013). http://arxiv.org/abs/arXiv:1306.2318

Web End =arXiv:1306.2318 [hep-ph]

61. Information about this code is available from K.A. Olive: it contains important contributions from T. Falk, A. Ferstl, G. Ganis, F. Luo,A. Mustafayev, J. McDonald, K.A. Olive, P. Sandick, Y. Santoso,M. Srednicki62. M. Misiak et al., Phys. Rev. Lett. 98, 022002 (2007). http://arxiv.org/abs/arXiv:hep-ph/0609232

Web End =arXiv:hep-ph/ http://arxiv.org/abs/arXiv:hep-ph/0609232

Web End =0609232

63. M. Ciuchini, G. Degrassi, P. Gambino, G.F. Giudice, Nucl. Phys. B 534, 3 (1998). http://arxiv.org/abs/arXiv:hep-ph/9806308

Web End =arXiv:hep-ph/9806308

64. G. Degrassi, P. Gambino, G.F. Giudice, JHEP 0012, 009 (2000). http://arxiv.org/abs/arXiv:hep-ph/0009337

Web End =arXiv:hep-ph/0009337

65. M.S. Carena, D. Garcia, U. Nierste, C.E.M. Wagner, Phys. Lett. B 499, 141 (2001). http://arxiv.org/abs/arXiv:hep-ph/0010003

Web End =arXiv:hep-ph/0010003

66. G. DAmbrosio, G.F. Giudice, G. Isidori, A. Strumia, Nucl. Phys. B 645, 155 (2002). http://arxiv.org/abs/arXiv:hep-ph/0207036

Web End =arXiv:hep-ph/0207036

67. The Heavy Flavor Averaging Group, D. Asner et al., http://arxiv.org/abs/arXiv:1010.1589

Web End =arXiv:1010. http://arxiv.org/abs/arXiv:1010.1589

Web End =1589 [hep-ex], with updates available at http://www.slac.stanford.edu/xorg/hfag/osc/end_2009

Web End =http://www.slac.stanford. http://www.slac.stanford.edu/xorg/hfag/osc/end_2009

Web End =edu/xorg/hfag/osc/end_2009

123

2809 Page 14 of 14 Eur. Phys. J. C (2014) 74:2809

68. O. Buchmueller et al., Eur. Phys. J. C 72, 1878 (2012). http://arxiv.org/abs/arXiv:1110.3568

Web End =arXiv:1110. http://arxiv.org/abs/arXiv:1110.3568

Web End =3568 [hep-ph]

69. M. Benayoun, P. David, L. DelBuono, F. Jegerlehner, Eur. Phys. J.

C 73, 2453 (2013). http://arxiv.org/abs/arXiv:1210.7184

Web End =arXiv:1210.7184 [hep-ph]

70. P.A.R. Ade et al. [Planck Collaboration], http://arxiv.org/abs/arXiv:1303.5076

Web End =arXiv:1303.5076 [astroph.CO]

71. J.R. Ellis, K. Enqvist, D.V. Nanopoulos, F. Zwirner, Nucl. Phys. B 276, 14 (1986)

72. R. Barbieri, G.F. Giudice, Nucl. Phys. B 306, 63 (1988)

123