The CMSSM and NUHM1 in Light of 7 TeV LHC, B_s to mu+mu- and XENON100 Data

We make a frequentist analysis of the parameter space of the CMSSM and NUHM1, using a Markov Chain Monte Carlo (MCMC) with 95 (221) million points to sample the CMSSM (NUHM1) parameter spaces. Our analysis includes the ATLAS search for supersymmetric jets + MET signals using ~ 5/fb of LHC data at 7 TeV, which we apply using PYTHIA and a Delphes implementation that we validate in the relevant parameter regions of the CMSSM and NUHM1. Our analysis also includes the constraint imposed by searches for B_s to mu+mu- by LHCb, CMS, ATLAS and CDF, and the limit on spin-independent dark matter scattering from 225 live days of XENON100 data. We assume M_h ~ 125 GeV, and use a full set of electroweak precision and other flavour-physics observables, as well as the cold dark matter density constraint. The ATLAS 5/fb constraint has relatively limited effects on the 68 and 95% CL regions in the (m_0, m_1/2) planes of the CMSSM and NUHM1. The new B_s to mu+mu- constraint has greater impacts on these CL regions, and also impacts significantly the 68 and 95% CL regions in the (M_A, tan beta) planes of both models, reducing the best-fit values of tan beta. The recent XENON100 data eliminate the focus-point region in the CMSSM and affect the 68 and 95% CL regions in the NUHM1. In combination, these new constraints reduce the best-fit values of m_0, m_1/2 in the CMSSM, and increase the global chi^2 from 31.0 to 32.8, reducing the p-value from 12% to 8.5%. In the case of the NUHM1, they have little effect on the best-fit values of m_0, m_1/2, but increase the global chi^2 from 28.9 to 31.3, thereby reducing the p-value from 15% to 9.1%.


Introduction
The LHC searches for jets + / E T events, as well as searches for heavy Higgs bosons H/A and the rare decay B s → µ + µ − , are placing ever-stronger constraints on supersymmetric models, in particular those in which R-parity is conserved and the lightest neutralinoχ 0 1 is the stable lightest supersymmetric particle and provides the cosmological dark matter. There have been a number of analyses of the constraints imposed by AT-LAS and CMS using ∼ 1/fb at 7 TeV [1][2][3] and other data on the parameter spaces of simplified versions of the minimal supersymmetric extension of the Standard Model (MSSM) [4], particularly the constrained MSSM (CMSSM) [5] in which the soft supersymmetry-breaking parameters m 0 , m 1/2 and A 0 are universal at the GUT scale, and some also of the LHC constraints on models in which the soft supersymmetry-breaking contributions to the masses of the Higgs multiplets are non-universal but equal to each other, the NUHM1 models [6]. There have also been analyses of the CMSSM and NUHM1 of the prospective implications of a Higgs boson weighing ∼ 125 GeV [2,[7][8][9][10], and analyses within the CMSSM and NUHM1 [8][9][10][11] that incorporate LHC searches for jets + / E T events with ∼ 5/fb of LHC data at 7 TeV [12,13]. Here we extend our previous frequentist analyses of the CMSSM and NUHM1 [1,2,[14][15][16][17][18][19][20] to include the ATLAS jets + / E T results with ∼ 5/fb [12] of data as well as M h ∼ 125 GeV and recent data on BR(B s → µ + µ − ) from the ATLAS [21], CDF [22], CMS [23] and LHCb [24] Collaborations [25], and the recent CMS exclusion of H/A → µ + µ − [26]. We also implement the constraint on the spin-independent dark matter scattering cross section imposed by 225 live days of XENON100 data [27]. We give a critical discussion of the extent to which the CMSSM and NUHM1 can be said to be disfavoured by the available data from the LHC and elsewhere.
The results of experimental searches for jets + / E T events are typically presented within the framework of the CMSSM for some fixed A 0 and tan β. The applicability of these analyses to other A 0 and tan β values, as well as to constraining the NUHM1, requires some study and justification. Within the CMSSM, one must verify that the constraints used are indeed independent of A 0 and tan β, as often stated in the experimental papers on searches for jets + / E T events. Similarly, within the NUHM1 one must verify whether, for any specific set of values of m 0 , m 1/2 , A 0 and tan β, the sensitivities of ATLAS and CMS searches for jets + / E T events might depend on the degree of non-universality in the NUHM1. A second issue arising in the NUHM1 is that the range of m 0 that is consistent with theχ 0 1 LSP requirement depends on the degree of non-universality. In the CMSSM, for any given value of m 1/2 there is a lower limit on m 0 that is, in general, violated in the NUHM1. Since the LHC experiments generally quote results only for the region of the (m 0 , m 1/2 ) plane allowed within the CMSSM, a dedicated study is needed to estimate the correct extrapolation of LHC results outside this region.
In order to explore the sensitivity to more general CMSSM and NUHM parameters of the published LHC searches for supersymmetry within specific CMSSM models, we use a version of the Delphes [28] generic simulation package with a 'card' that emulates the performance of the AT-LAS detector. As described below, in the specific case of the 7 TeV ATLAS 5/fb jets + / E T analysis, Delphes reproduces reasonably accurately the quoted 95% CL limits on CMSSM models with A 0 = 0 and tan β = 10, as well as other confidence levels in the CMSSM (m 0 , m 1/2 ) plane. These are well described by scaling of event numbers ∝ 1/M 4 , where M ≡ m 2 0 + m 2 1/2 , as assumed in [1]. We also use the Delphes simulation to confirm that the ATLAS 5/fb jets + / E T constraint in the (m 0 , m 1/2 ) plane of the CMSSM is relatively insensitive to tan β and A 0 .
Having validated the application of the Delphes simulation to the CMSSM, we then study whether the results of [12] are sensitive to the degree of Higgs non-universality in the NUHM1. Although the supersymmetric decay cascades to which this analysis is most sensitive are independent of the details of the supersymmetric Higgs sector, they do in principle have some sensitivity to the Higgs mixing parameter µ, which is in general different in the NUHM1 from its value in the CMSSM. We find that in practice the jets + / E T constraint is essentially independent of the degree of non-universality in the NUHM1. We then use Delphes to estimate the sensitivity of the ATLAS analysis to the region with m 0 smaller than is allowed in the CMSSM, finding that the ATLAS jets + / E T constraint is essentially independent of m 0 in this range.
Following these validations of our implementation of Delphes in the NUHM1, we use the Markov Chain Monte Carlo (MCMC) technique to sample the CMSSM and NUHM1 parameter spaces with ∼ 95 × 10 6 and ∼ 221 × 10 6 points, respectively. Given the constraints from M h and the LHC 1/fb data, we find that the ATLAS 5/fb jets + / E T constraint by itself has a relatively limited impact on the 68 and 95% CL regions in the (m 0 , m 1/2 ) planes of the CMSSM and NUHM1, whereas the new BR(B s → µ + µ − ) constraint has larger effects in both these and the (M A , tan β) planes, and the new XENON100 constraint also impacts significantly both the (m 0 , m 1/2 ) and (M A , tan β) planes of the CMSSM and NUHM1. After the inclusion of these constraints, we find that in the favoured regions in the CMSSM and NUHM1 in m 0 , m 1/2 and tan β the global χ 2 function varies little, giving less relevance to the best-fit values of these parameters. Nevertheless, we note that the best-fit values of m 0 and m 1/2 are decreased in the CMSSM, and the best-fit values of tan β are decreased in both the CMSSM and the NUHM1. Within the CMSSM, the global χ 2 increases from 31.0 to 32.8 and the p-value is correspondingly reduced from 12% to 8.5%. Within the NUHM1, the value of tan β rises to a value similar to that in the CMSSM, while the total χ 2 rises from 28.9 to 31.3, reducing the p-value from 15% to 9.1%. The perilously low p-values of the CMSSM and NUHM1 reflect the growth in tension between LHC constraints and low-energy measurements such as (g − 2) µ [29,30].

Analysis Procedure
We follow closely the procedure described in [1]. As in [1], the sampling is based on the Metropolis-Hastings algorithm, with a multi-dimensional Gaussian distribution as proposal density. The width of this distribution is adjusted during the sampling, so as to keep the MCMC acceptance rate between 20% and 40% in order to ensure efficient sampling. We emphasize that we do not make use of the sampling density to infer the underlying probability distribution. Rather, we use the MCMC method to construct a global likelihood function that receives contributions from the usual full set of electroweak precision observables including (g − 2) µ [29], measurements of B-meson mixing and other flavour-physics observables [25,31], the cosmologicalχ 0 1 density and the XENON100 direct search for dark matter scattering [32], as well the LHC searches for the Higgs boson and supersymmetric signals.
Our treatment of the non-LHC constraints is similar to that in [1], with the exceptions that we use updated values of M W = 80.385 ± 0.015 GeV [33] and m t = 173.2 ± 0.9 GeV [34]. Our treatment of BR(B s → µ + µ − ) is based on a compilation of the recent measurements by AT-LAS [21], CDF [22], CMS [23] and LHCb [24,25]. As already mentioned, we incorporate the public results of the search for jets + / E T events without leptons using ∼ 5/fb of LHC data at 7 TeV analyzed by ATLAS [12], which has greater sensitivities to the models discussed here than do searches with leptons and b-quarks in the final state as well as searches with less integrated luminosity. We also include the CMS constraint on the heavier MSSM Higgs bosons, H/A [26], which has greater sensitivity than the corresponding ATLAS search [35].
Concerning the Higgs boson, the situation has evolved rapidly since our previous analysis [2] and the data reported earlier this year [39,40], with the recently-announced discovery by the CMS [36] and ATLAS Collaborations [37], consistent with evidence from the CDF and D0 Collaborations [38], of a new particle that is a very strong candidate to be a Higgs boson resembling that in the Standard Model. In the absence of an official combination of these results, we model them by assuming, as in [2], that and we incorporate this new constraint using the same 'afterburner' approach as in [2]. The contributions of these observables to the global likelihood function are calculated within the MasterCode framework [41]. This incorporates a code for the electroweak observables based on [42] as well as the SoftSUSY [43], FeynHiggs [44], SuFla [45], and MicrOMEGAs [46] codes, interfaced via the SUSY Les Houches Accord [47]. We use the SuperIso [48] and SSARD [49] codes as comparisons for B-physics observables 1 and for the cold dark matter density, using also DarkSUSY [50] as a comparison for the latter. We use SSARD for the spin-independent dark matter scattering cross section, comparing with MicrOMEGAs and DarkSUSY.

Validation and Extension of Jets + / E T Constraints
ATLAS and CMS results on SUSY searches for jets + / E T are typically shown as 95% CL exclusion bounds in the CMSSM (m 0 , m 1/2 ) plane for fixed tan β and A 0 , e.g., tan β = 10 and A 0 = 0 [12,53]. We first validate for these values of tan β and A 0 our implementation of the ATLAS constraint using PYTHIA [54] and the generic Delphes [28] simulation code with an ATLAS detector 'card'. Next we extend it to other values of the CMSSM parameters, and then to the NUHM1 2 .
Validation in the (m 0 , m 1/2 ) plane As a first step in the validation procedure, we used SoftSUSY [43] to generate the spectra for various points in the (m 0 , m 1/2 ) plane of the CMSSM for tan β = 10 and A 0 = 0. We then used PYTHIA [54] to generate 50,000 events for each of these points, which were subsequently 1 We do not include the isospin asymmetry in B → K ( * ) µ + µ− decays [51] or the measurement of BR(B → D ( * ) τ ν) [52] in our analysis, in view of the present experimental and theoretical (long-distance) uncertainties. 2 We have made a similar validation analysis for the CMS α T search for jets + / E T events using ∼ 1/fb of data at 7 TeV [53]. We do not discuss this validation in detail, as it does not contribute to the the likelihood function analyzed here, but it does validate a posteriori our previous treatments [1,2] of the CMS α T analysis. It also indicates that the CMS sensitivity with 5/fb of data at 7 TeV [13] is similar to the ATLAS 5/fb jets + / E T data discussed here.
passed through the Delphes [28] simulation code using the ATLAS detector 'card'. We then used information from [12] to calculate the efficiencies for observing events that would survive the cuts used in the ATLAS jets + / E T analysis using 5/fb of data at 7 TeV. Taking into account the observed number of events, together with the information in Table 3 of [12], we then calculated the confidence levels of these points, using the same prescription as ATLAS. We recall that the ATLAS analysis combined searches using several different channels A, A , B, C, D and E, which, depending on the channel, may have 'tight', 'medium' and 'loose' event selections. Following the procedure used in the ATLAS analysis, for each set of CMSSM parameters we used the limit set by the most sensitive of these various channel selections.
The left panel of Fig. 1 displays how closely this work flow reproduced the ATLAS CL for 34 test points along its 95% CL exclusion line, sampling the range m 0 ∈ (200, 3500) GeV in 100 GeV steps. Our results indicate a mean difference CL Delphes -CL ATLAS = (−2.8 ± 3.6)%, so we conclude that our simulation using PYTHIA and Delphes reproduces quite accurately the 95% CL exclusion contour in the (m 0 , m 1/2 ) plane for tan β = 10 and A 0 = 0 reported by ATLAS.
Since it is not computationally feasible to use PYTHIA and Delphes in this way for every point generated in our MCMC analysis, we make use of a simple analytic approximation to their results in order to extrapolate their results to other regions of the (m 0 , m 1/2 ) plane. The right panel of Fig. 1 compares the CL values estimated using this Delphes implementation, for a number of CMSSM points with tan β = 10, A 0 = 0 and varying m 0 and m 1/2 , with the CL calculated assuming, as in [1], that the numbers of events for different points in the CMSSM (m 0 , m 1/2 ) plane scale as 1/M 4 (solid line). We see that the agreement is quite good along rays in the (m 0 , m 1/2 ) plane with m 1/2 /m 0 = 1/3 (blue circles), 1 (red squares) and 3 (green triangles), indicating that this scaling law is an adequate approximation to the true sensitivity of the ATLAS 5/fb jets + / E T analysis. and M 0 is the value of M at the point on the LHC jets + / E T 95% exclusion line with the same ratio m 0 /m 1/2 . The red squares (blue circles, green triangles) were chosen along rays in the (m 0 , m 1/2 ) plane with m 0 /m 1/2 = 1/3, 1, 3, respectively. These points compare well with the solid line, which is the CL calculated assuming that the number of signal events surviving the LHC cuts scales as 1/M 4 .

Extension to other tan β and A 0 values
The next step is to use our Delphes implementation to evaluate the sensitivity of the AT-LAS analysis to other values of tan β and A 0 . To this end, for each of the 34 points along the 95% CL contour in the (m 0 , m 1/2 ) plane for tan β = 10 and A 0 = 0 mentioned previously, we used PYTHIA and Delphes to estimate the confidence levels of these points as the other parameters are varied, as shown in Fig. 2. The left panel exhibits the variation of the confidence level with tan β for fixed A 0 = 0. We see that the CL is quite stable, with its central value ranging between 95 and 90% and its 68% CL range lying between 99% and 84% and always including the 95% CL found by ATLAS for tan β = 10 and A 0 = 0 3 . The right panel of Fig. 2 displays a similar analysis for varying A 0 /m 0 ∈ [−3, 3] with tan β fixed at 10. We see again that the CL is quite stable, with central values between 95 and 92% and the 68% CL ranges lying between 100% and 88% and again always including the 95% CL found by AT-LAS for tan β = 10 and A 0 = 0. These results are consistent with the statement by ATLAS [12] that their (m 0 , m 1/2 ) exclusion contours are largely independent of tan β and A 0 , as we have assumed previously [1], and also provide consistency checks on our Delphes implementation.

Extensions to Non-Universal Higgs Masses
Following these validations, as a third step we now use our Delphes implementation to extend the interpretation of the ATLAS 5/fb jets + / E T analysis to models with non-universal Higgs masses. We recall that in the CMSSM, the electroweak vacuum conditions can be used to fix the Higgs mixing parameter µ and M A for any given choice of the parameters m 0 , m 1/2 , A 0 and tan β. Introducing the single extra degree of freedom m 2 Hu /m 2 0 = m 2 H d /m 2 0 in the NUHM1, one can treat either µ or M A as a free parameter, whereas these quantities may be treated as two free parameters in the NUHM2, in which m 2 Hu /m 2 0 and m 2 H d /m 2 0 are treated as two independent parameters [55]. The effects of varying µ and M A on the gluino mass and the spectra of squarks (the main sparticles expected to be produced at the LHC) are of secondary importance 4 . However, they may also affect the branching fractions of the cascade decays to which the LHC experiments are sensitive, and so could in principle have some effect on the sensitivity of the ATLAS 5/fb jets + / E T search in the (m 0 , m 1/2 ) plane.
For this reason, we have taken the same 34 points along the 95% CL contour in the (m 0 , m 1/2 ) for tan β = 10 and A 0 = 0 studied above, and used PYTHIA and Delphes to estimate how the confidence levels of these points vary as the Higgs non-universality parameters m 2 Hu /m 2 0 and m 2 H d /m 2 0 are varied. The red squares in the left panel of Fig. 3 show how the CL depends on the common non-universality parameter m 2 Hu /m 2 0 = m 2 H d /m 2 0 in the NUHM1. As before, we see that the CL does not depart sig-nificantly from the CMSSM value of 95%. Also shown in the left panel of Fig. 3 (as blue circles) are PYTHIA and Delphes estimates of the confidence levels of points with the same values of m 0 , m 1/2 , tan β = 10 and A 0 = 0 but with Higgs non-universality parameters of opposite signs for the two Higgs doublets: Fig. 3 shows how the CL in the NUHM2 varies as a function of m 2 H d for fixed m 2 Hu = 0 (red squares) and as a function of m 2 Hu for fixed m 2 H d = 0 (blue circles). We again see that the CL is similar to the 95% found in the CMSSM for the same values of m 0 , m 1/2 , tan β = 10 and A 0 = 0.
Extension to m 2 0 < 0 To complete the validation for the NUHM1, and in preparation for future analyses in the NUHM2, we have also investigated the applicability of the ATLAS 5/fb jets + / E T results to models with smaller values of m 2 0 than in the CMSSM, including negative values. We have evaluated the CL along a line of points with tan β = 10, A 0 = 0, m 1/2 = 630 GeV and −(150 GeV) 2 < m 2 0 < +(150 GeV) 2 , i.e., M 0 ≡ sign(m 2 0 ) × |m 2 0 | ∈ (−150, +150) GeV, as shown in Fig. 4. We see that the CL remains constant, within errors, over this range of M 0 , and is quite consistent with the 95% CL reported for the ATLAS 5/fb jets + / E T analysis at m 0 = 100 GeV.

Combination of BR(B
Since our previous analysis [2], new constraints on BR(B s → µ + µ − ) have been published by AT-LAS [21], CDF [22], CMS [23] and LHCb [24] Collaborations [25]. Their measurements are to be compared with the theoretical (TH) value in the SM, which we take to be BR(B s → µ + µ − ) SM,TH = (3.2 ± 0.2) × 10 −9 [57]. This comparison is not direct, because experiments measure the time-averaged (TA) branching ratio, which differs from the TH value because of the difference between the lifetimes of the heavier and lighter B s mesons [58,59]. In general, in the SM and y s = 0.088 ± 0.014. Thus we compare the measurements to the SM prediction for the time-averaged branching ratio: We use for this comparison an unofficial combination of the ATLAS, CDF, CMS and LHCb data [21][22][23][24][25], from which we compute a χ 2 penalty for each possible (calculated) value of BR(B s → µ + µ − ). In Fig. 5 we show the probability distribution (left) and the log-likelihood function for the ratio BR(B s → µ + µ − )/BR(B s → µ + µ − ) SM,TA , folding together the theoretical and experimental errors. The log-likelihood function is used as the ∆χ 2 penalty for the values of this observable as they are calculated in the CMSSM and NUHM1 5 .

The Constraint on Spin-Independent
Dark Matter Scattering from 225 Live Days of XENON100 Data The XENON100 Collaboration has recently published the result of a search for spinindependent dark matter scattering based on 225 live days of data [27]. They report two events in a fiducial region where 1.0 ± 0.2 background events were expected, i.e., no evidence for any excess, quote a 90% CL upper limit of σ SI p < 2.0 × 10 −45 cm 2 for a dark matter particle mass of 55 GeV, and provide a 90% CL exclusion line for other masses.
Following the procedure used in [20] for the previous XENON100 constraint, we use a CL s calculator, now implemented in our Delphes framework, to model the contribution to the global χ 2 function of this new XENON100 constraint from the number of signal events as a Gaussian with mean µ = 1.0 and standard deviation σ = 2.7 events. This corresponds to the mean (2 -1 = 1 event) given in [27] and the upper limit of 5.1 signal events at the 90% CL given by the CL s calculator, which we identify with the published XENON100 90% exclusion line. For models predicting values of σ SI p above or below the 90% CL line in [27], we rescale linearly the number of events and estimate the ∆χ 2 contribution of XENON100 using the Gaussian model described above.
We use SSARD [49] to calculate σ SI p , assuming a nominal value of the π-N σ term Σ πN = 50 MeV, and assigning an asymmetric error +14 −7 MeV. This accounts for the fact that Σ πN = σ 0 ∼ 36 MeV if N |ss|N = 0, while allowing for significantly larger values of Σ πN as suggested by some analyses [60].
The XENON100 analysis assumes that the local dark matter density is 0.3 GeV/cm 3 , and makes supplementary assumptions on the dark matter velocity distribution. We have explored the potential implications of the uncertainties in these quantities by convoluting with our abovementioned model of the XENON100 constraint on σ SI p a fractional uncertainty of a factor √ 2

±1
at the 68% CL. We find that it has negligible im-pact on the results shown below, which are for the nominal dark matter distribution parameters assumed by XENON100.
6. The CMSSM and NUHM1 after ATLAS 5/fb , BR(B s → µ + µ − ) and XENON100 As already mentioned, in addition to the Delphes implementation of the ATLAS 5/fb jets + / E T constraint, the implementation of the combined BR(B s → µ + µ − ) constraints described above, and the new CMS constraint on H/A → τ + τ − [26], we include in our global fit the constraint M h = 125 ± 1.0 ± 1.5 GeV and the other constraints included in [2], with updated values of the W boson mass [33] and the top quark mass [34], see above. We note the existence in the CMSSM of a grouping of points in the focus-point region at large m 0 and small m 1/2 that were previously allowed at the 95% CL but are now disallowed 6 . This exclusion is due to the new XENON100 constraint [27]. The main effect of the ATLAS 5/fb jets + / E T constraint is to shave off a slice of points at low m 1/2 and moderate m 0 . We also note the appearance in the NUHM1 sample of a grouping of points at large m 1/2 that have smaller m 0 than is possible in the CMSSM, and are allowed at the 95% CL. The relic density in this region is brought into the WMAP range by multiple neutralino and chargino coannihilation processes. Points are found in this region using each of the codes MicrOMEGAs [46], DarkSUSY [50], SuperIso [48] and SSARD [49], though they yield somewhat different values of the relic density. As mentioned previously, here we use MicrOMEGAs as our default.
The values of χ 2 in the most-favoured regions of the CMSSM and NUHM1 are relatively shallow functions of m 0 , m 1/2 and tan β, so that little importance can be attributed to the positions of the best-fit points or to their movements relative to those in [2]. Nevertheless, we note that, as summarized in Table 1, the nominal best-fit point in the CMSSM moves to smaller m 0 and m 1/2 , whereas that in the NUHM1 moves little in this plane. The best-fit points have χ 2 = 32.8 in the CMSSM and 31.3 in the NUHM1, and the p-values of these models are reduced to 8.5 and 9.1%, respectively.
We see in Fig. 6 that the 95% CL region in the CMSSM extends to m 0 ∼ 4000 GeV and m 1/2 ∼ 2400 GeV. The corresponding region in the NUHM1 extends to smaller m 0 but larger m 1/2 . We also note that the CMSSM fit features two disconnected 68% CL 'islands', the one at lower m 0 and m 1/2 corresponding to the stau coannihilation region, and that at larger m 0 and m 1/2 corresponding to the rapid-annihilation funnel region. We note, however, that our sampling also includes a few intermediate points that also have ∆χ 2 < 2.30, reflecting the relative flatness of the global χ 2 function along the band between (m 0 , m 1/2 ) ∼ (300, 900) GeV and ∼ (1100, 1900) GeV. Typically, these points sit in rapid-annihilation funnels, and it is possible that a more complete sampling might reveal a lower 'isthmus' connecting these islands, as happens in the NUHM1.
We report in Table 1 the values of m 0 , m 1/2 , A 0 and tan β for the best fits in both the CMSSM 'islands', as well as for the best fit in the NUHM1, which is at relatively low masses, and a local minimum of the NUHM1 χ 2 function at high masses. We note that the best fit in the low-mass CMSSM 'island' is similar to the best fit in the NUHM1, and that both have smaller tan β than in the previous best fits to the LHC 1/fb data set in these models. As we discuss later, this effect is due to the new BR(B s → µ + µ − ) constraint. On the other hand, the best fit in the high-mass CMSSM 'island' is more similar to the previous best fit to the LHC 1/fb data set. In general terms, we see that the area of the NUHM1 (m 0 , m 1/2 ) plane that is allowed at the 68 and 95% CL is larger than in the (m 0 , m 1/2 ) plane of the CMSSM. This reflects the fact that the dependence of the global χ 2 function on these variables is weaker in the NUHM1 than in the CMSSM, reflecting the additional freedom offered by the degree of Higgsmass non-universality.
In particular, the 68% CL region in the NUHM1 is connected, and extends to larger m 0 than in the CMSSM. This extension reflects the fact that in the NUHM1 a rapid-annihilation funnel region may appear at smaller m 1/2 and tan β than in the CMSSM for the same value of m 0 , thanks to the variation in M A that is possible in the NUHM1, allowing M A ∼ 2mχ0 1 in different regions of the (m 0 , m 1/2 ) plane. It is this freedom in the location of the rapid-annihilation funnel, a , a combination of the ATLAS [21], CDF [22], CMS [23] and LHCb [24] constraints on BR(B s → µ + µ − ) [25] and the recent XENON100 result [27], assuming M h = 125 ± 1 (exp.) ± 1.5 (theo.) GeV. The results of the current fits are indicated by solid lines and filled stars, and previous fits based on ∼ 1/fb of LHC data are indicated by dashed lines and open stars. The blue lines denote 68% CL contours, and the red lines denote 95% CL contours.
characteristic of the NUHM1, that is largely responsible for the expansion in the region of the (m 0 , m 1/2 ) plane that is favoured at the 68% CL in the NUHM1, compared with the CMSSM 7 . Table 2 summarizes some interesting contributions to the global χ 2 function, namely those contributing ∆χ 2 > 1, ATLAS 5/fb jets + / E T and the new global combination of BR(B s → µ + µ − ) measurements. We present their contributions at the best-fit point in the CMSSM (which has relatively high mass parameters), at the local best-fit point in the low-mass 'island' in Fig. 6, at the best-fit point in the NUHM1, and at a high-mass point in the NUHM1. We see that BR(b → sγ) favours lower masses in the NUHM1, whereas BR(B u → τ ν τ ) applies an essentially constant ∆χ 2 penalty 8 . None of the preferred models 7 The relic density may also be brought into the WMAP range because theχ 0 1 acquires a relatively large higgsino component, another possibility made possible by the variation in µ that is possible in the NUHM1. 8 We note that the Belle Collaboration has recently reported a new measurement of BR(Bu → τ ντ ) that is in better agreement with the Standard Model and the classes of supersymmetric models discussed here [56].
gives a good fit to (g − 2) µ , since they reproduce approximately the SM value, though lower masses are somewhat preferred, particularly in the NUHM1. The lower-mass fits worsen the fit to M W and that in the CMSSM (NUHM1) worsens (improves) the fit to A (SLD), but there are only small changes in σ 0 had . We note that the ATLAS 5/fb jets + / E T constraint favours higher masses, whereas the new BR(B s → µ + µ − ) constraint favours the low-mass region in the CMSSM and (marginally) in the NUHM1, and all the models fit XENON100 equally well.
The (tan β, m 1/2 ) planes As can be seen in the left panel of Fig. 7, where the (tan β, m 1/2 ) plane in the CMSSM is shown, the two 'islands' visible in the (m 0 , m 1/2 ) plane of the CMSSM (left panel of Fig. 6) correspond to different ranges of tan β. Large values of tan β ∼ 45 are favoured only at large m 1/2 > 1500 GeV, and values of tan β as low as ∼ 10 come within the ∆χ 2 = 2.30 (68% CL) region for m 1/2 ∼ 800 GeV, consistent with their association with funnel and stau coannihilation regions  Table 1 The best-fit points found in global CMSSM and NUHM1 fits using the ATLAS 5/fb jets + / E T constraint [12], the combination of the ATLAS [21], CDF [22], CMS [23] and LHCb [24] BR(B s → µ + µ − ) [25] constraints and the updated values of M W and m t , compared with those found previously in global fits based on the LHC 1/fb data set. In both cases, we include a measurement of M h = 125 ± 1.0 ± 1.5 GeV and the new XENON100 constraint [27]. In the case of the CMSSM, we list the parameters of the best-fit points in both the low-and high-mass 'islands' in Fig. 6, and we quote results for a high-mass NUHM1 point as well as the low-mass best-fit point in this model. We note that the overall likelihood function is quite flat in bot the CMSSM and the NUHM1, so that the precise locations of the best-fit points are not very significant, and we do not quote uncertainties. For completeness, we note that in the best NUHM1 fit m 2 H ≡ m 2 Hu = m 2 H d = −6.5 × 10 6 GeV 2 , compared with −5.5 × 10 6 GeV 2 previously.
respectively. We see again in the right panel of Fig. 7 that the region of the (tan β, m 1/2 ) plane that is allowed in the NUHM1 at the 68% CL is connected, and there is no strong separation between the low-and high-mass regions. As in Fig. 6, the region of the (tan β, m 1/2 ) plane allowed at the 95% CL is also enlarged in the NUHM1, compared to the CMSSM. The region at large m 1/2 and relatively small tan β corresponds to the grouping of points at low m 0 and large m 1/2 already noted in the right panel of Fig. 6.

The (M A , tan β) planes
We see in the left panel of Fig. 8, where the (M A , tan β) plane in the CMSSM is shown, that relatively large values of M A are favoured in this model, M A > 1200 GeV at the 68% CL and > 1000 GeV at the 95% CL. As is seen by comparing the solid contours corresponding to ∆χ 2 contours in this fit with the dotted lines corresponding to the analysis in [2], we see substan-tial retreats at small M A and large tan β that are due to the updated BR(B s → µ + µ − ) constraint. In the NUHM1, smaller values of M A are allowed at low tan β, as low as ∼ 500 GeV at the 68% CL and ∼ 350 GeV at the 95% CL. On the other hand, a substantial region of the NUHM1 (M A , tan β) plane at small M A and large tan β is also excluded by the new BR(B s → µ + µ − ) constraint 9 .

Relative
Impacts of ATLAS 5/fb , BR(B s → µ + µ − ) and XENON100 In this Section we analyze in more detail the different impacts of the new ATLAS 5/fb jets + / E T , BR(B s → µ + µ − ) and XENON100 constraints on the CMSSM and NUHM1.  Table 2 Summary of the contributions of the most important observables to the global χ 2 function at the best-fit high-and low-mass points in the CMSSM and NUHM1 (those with ∆χ 2 > 1) , and of the main updated observables ATLAS 5/fb jets + / E T , BR(B s → µ + µ − ) and XENON100.  , a combination of the ATLAS [21], CDF [22], CMS [23] and LHCb [24] constraints on BR(B s → µ + µ − ) [25]. In both cases, we include a measurement of M h = 125 ± 1.0 ± 1.5 GeV and the new XENON100 constraint [27]. The results of the current fits are indicated by solid lines and filled stars, and previous fits based on ∼ 1/fb of LHC data are indicated by dashed lines and open stars. The blue lines denote 68% CL contours, and the red lines denote 95% CL contours. In both cases, we include a measurement of M h = 125 ± 1.0 ± 1.5 GeV and the new XENON100 constraint [27]. The results of the current fits are indicated by solid lines and filled stars, and previous fits based on ∼ 1/fb of LHC data are indicated by dashed lines and open stars. The blue lines denote 68% CL contours, and the red lines denote 95% CL contours. Fig. 9 displays the impacts in the (m 0 , m 1/2 ) planes of the CMSSM (left panels) and the NUHM1 (right panels) of dropping the ATLAS 5/fb jets + / E T constraint (top panels), the new BR(B s → µ + µ − ) constraint (middle panels), or the new XENON100 constraint (bottom panels). In each panel, we compare the 68 and 95% CL contours in the full global fit (dashed lines) with a fit dropping one of the constraints (solid lines). The corresponding best fit points are shown as open and closed stars.
In the CMSSM case, very little effect is seen when the ATLAS 5/fb jets + / E T constraint is dropped. On the other hand, when BR(B s → µ + µ − ) is dropped there are significant extensions of the 68 and 95% CL regions: the two 68% CL 'islands' at low m 0 merge and extend to larger m 0 , and the 95% band extending to large m 0 broadens to a much larger range of m 1/2 . When the new XENON100 constraint is dropped, the main effect is the appearance of the focus-point region at large m 0 and small m 1/2 .
In the NUHM1 case, dropping the ATLAS 5/fb jets + / E T constraint again has little effect on the contours, except at small m 0 and m 1/2 . Dropping the BR(B s → µ + µ − ) constraint has more effect on the 68 and 95% CL contours in the NUHM1. The effect of dropping the new XENON100 constraint is qualitatively similar to that of dropping the new BR(B s → µ + µ − ) constraint, except that it allows a larger region at small m 1/2 and large m 0 . Similarly, Fig. 10 displays the impacts in the (M A , tan β) planes of the CMSSM (left) panels and the NUHM1 (right panels) of dropping the ATLAS 5/fb jets + / E T constraint (top panels), the new BR(B s → µ + µ − ) constraint (middle panels) or the new XENON100 constraint (bottom panels). As in the (m 0 , m 1/2 ) planes, we see relatively little impact in either the CMSSM or the NUHM1 from dropping the ATLAS 5/fb jets + / E T constraint, and a much bigger effect from dropping the new BR(B s → µ + µ − ) constraint, particularly at small M A and large tan β. In both cases, the BR(B s → µ + µ − ) constraint reduces drastically the value of tan β at the best-fit point from ∼ 46 (27) Figure 9. The (m 0 , m 1/2 ) planes in the CMSSM (left panels) and the NUHM1 (right panels) displaying the effects of dropping the ATLAS 5/fb jets + / E T constraint (top panels), the new BR(B s → µ + µ − ) constraint (middle panels) and the new XENON100 constraint (bottom panels). In each case, the full global fit is represented by an open green star and dashed blue and red lines for the 68 and 95% CL contours, whilst the fits to the incomplete data sets are represented by closed stars and solid contours.
ping the new XENON100 constraint is to expand the preferred region at large M A and tb < 40.
We analyse the various χ 2 contributions and best-fit points in more detail in Table 3. Here we display the principal changes in the best-fit parameters from the new global fit (second column) when dropping the ATLAS 5/fb constraint (third column), dropping the new BR(B s → µ + µ − ) constraint (fourth column), dropping the new XENON100 constraint (fifth column), and dropping all three new constraints, i.e., the analysis of [2] (last column). We see that it is BR(B s → µ + µ − ) that, among the new constraints, has the most significant impact on the best-fit parameters of the NUHM1, principally tan β. In the lower rows we show the χ 2 contributions of the direct SUSY searches, denoted as ∆χ 2 for / E T , BR(B s → µ + µ − ) and (g − 2) µ . One can clearly observe that the contribution of (g−2) µ to the total χ 2 function increases when BR(B s → µ + µ − ) and the other new constraints are incorporated, demonstrating once again that the new data are pushing simple supersymmetry-breaking models such as the NUHM1 (and CMSSM) out of the 'sweet spot' where the experimental measurement of (g − 2) µ could easily be explained.

Predictions for Physical Observables
In this section we present one-dimensional χ 2 likelihood functions for slected physical observables, based on the above surveys of the CMSSM and NUHM1 parameter spaces, comparing results based on the LHC 1/fb and LHC 5/fb data sets.
The Gluino Mass Fig. 11 displays the χ 2 functions for mg in the CMSSM (left panel) and the NUHM1 (right panel), for fits to the LHC 5/fb data including the new BR(B s → µ + µ − ) and XENON100 limits (solid lines) and to the LHC 1/fb data including the BR(B s → µ + µ − ) limits then available (dashed lines). In the case of the CMSSM, we see a bimodal distribution, with local minima at mg ∼ 2000 GeV and ∼ 4000 GeV, corresponding to the best fits in the low-and high-mass islands discussed above, whose values of χ 2 are almost indistinguishable. Intermediate values of mg are disfavoured by ∆χ 2 < ∼ 2, though the envelope of the χ 2 function could only be reduced by further sampling. In the case of the NUHM1, a much more weakly bimodal distribution is visible. In the CMSSM, values of mg between ∼ 1500 GeV and ∼ 4800 GeV are allowed at the ∆χ 2 < 2 level, and in the NUHM1 values over 6000 GeV are allowed at this level. Once again, the ability to move to large masses (in this case the gluino mass or m 1/2 ) can be traced to the freedom in the NUHM1 of adjusting M A ∼ 2m χ so that the relic density is at the WMAP value. At such large masses, there is essentially no further price paid by g µ − 2 or other low energy observables as we approach the decoupling limit.
The Squark Mass Fig. 12 displays the χ 2 functions for the average mass of the supersymmetric partners of the five lightest right-handed quarks, mq, in the CMSSM (left panel) and the NUHM1 (right panel), for fits to the LHC 5/fb , BR(B s → µ + µ − ) and new XENON100 data (solid lines) and the LHC 1/fb data (dashed lines), as in Fig. 11. In the case of the CMSSM, we see local minima of χ 2 at mq ∼ 1800 and 3500 GeV, separated again by a range with ∆χ 2 < ∼ 2. At this level of ∆χ 2 , any value of mq between ∼ 1200 GeV and ∼ 4200 GeV is allowed. In the case of the NUHM1, there is a similar structure, but it is less pronounced and the intermediate range has ∆χ 2 ∼ 1. Only squark mass values above ∼ 5.4 TeV receive a substantial χ 2 penalty, which is due to large m 0 being disfavoured in this model. Fig. 13 displays the χ 2 functions for the lighter stop squark mass mt 1 in the CMSSM (left panel) and the NUHM1 (right panel), for fits to the LHC 5/fb , BR(B s → µ + µ − ) and new XENON100 data set (solid lines) and the LHC 1/fb data (dashed lines), as in Fig. 11. We see that the CMSSM χ 2 is minimized for mt 1 ∼ 1100 GeV, with a secondary minimum for mt 1 ∼ 2900 GeV, whereas in the NUHM1 χ 2 is minimized for mt 1 ∼ 1700 GeV with values above around 4.5 TeV being disfavoured. In both models, values of mt 1 < mq are expected.   Table 3 Principal changes in the best-fit parameters in the NUHM1 from the new global fit (second column) when dropping the ATLAS 5/fb constraint (third column), dropping the new BR(B s → µ + µ − ) constraint (fourth column), dropping the new XENON100 constraint (fifth column) and dropping all three new constraints, i.e., the analysis of [2] (last column). The bottom four lines display the contributions to χ 2 of the / E T , BR(B s → µ + µ − ), XENON100 and (g − 2) µ constraints. The numbers marked by * are for the implementations of these constraints in [2]. and the LHC 1/fb data (dashed lines), as in Fig. 11. In this case, in the CMSSM χ 2 is minimized for mτ 1 ∼ 400 and ∼ 800 GeV, whereas in the NUHM1 χ 2 is minimized for mτ 1 ∼ 700 GeV with an upper limit around 2.5 TeV.

The Higgs Mass
In Fig. 15 we show as solid lines the χ 2 functions for M h in the CMSSM (left panel) and the NUHM1 (right panel), for fits to the LHC 5/fb , BR(B s → µ + µ − ) and new XENON100 data set, but omitting all the direct constraints on the Higgs mass from the LHC, LEP and Tevatron. Thus, Fig. 15 displays the predictions for M h in the CMSSM and NUHM1 on the basis of the other constraints. As in previous publications (see [1,2,14] and references therein), the plots in Fig. 15 include a red band with a width of 1.5 GeV to represent the theoretical uncertainty. These plots show directly the extent to which the indirect prediction of M h agrees with the (provisional) direct measurement. Also shown in Fig. 15 is the LEP exclusion for a SM Higgs boson (shaded yellow), and the range indicated by the LHC discovery (shaded green). We see that the LHC measurement of M h is somewhat larger than would be indicated by our best fit based on other data, but not disastrously so, with ∆χ 2 ∼ 1.5 in the CMSSM and ∼ 0.5 in the NUHM1. Fig. 16 displays the χ 2 functions for BR(B s → µ + µ − ) in the CMSSM (left panel) and the NUHM1 (right panel), for fits to the LHC 5/fb , BR(B s → µ + µ − ) and new XENON100 data set (solid lines) and the LHC 1/fb data (dashed lines), as in Fig. 11. Comparing the solid and dotted lines, we see the strong impact of the recent BR(B s → µ + µ − ) update. In both the CMSSM and the NUHM1, values of BR(B s → µ + µ − ) above the SM value are preferred over values below the SM value. We see that, in either case, a measurement of BR(B s → µ + µ − ) at the level of 30%, which may soon be possible, would greatly restrict the preferred ranges of both the CMSSM and NUHM1 parameter spaces. σ SI p Fig. 17 displays the best-fit points and the 68% and 95% CL contours (red and blue, respectively) in the (mχ0 1 , σ SI p ) planes in the CMSSM (left panel) and and the NUHM1 (right panel). The solid lines are for the global fit to the LHC 5/fb BR(B s → µ + µ − ) and new XENON100 data set, and the dashed lines for the previous LHC 1/fb fit, and the solid (open) green stars mark the corresponding best-fit points 10 . We see that the region The solid lines are for fits including all the available data including (g − 2) µ but excluding the direct LEP [61,62], Tevatron [?] and LHC [36,37] constraints on M h , with a red band indicating the estimated theoretical uncertainty in the calculation of M h of ∼ 1.5 GeV. The shaded ranges are those excluded by LEP searches for a SM Higgs boson (yellow) and indicated by the LHC discovery (green). of the (mχ0 1 , σ SI p ) favoured in the CMSSM is now more restricted, in particular at small mχ0 1 . The main effect of the new XENON100 constraint has been to remove focus points with large σ SI p that were previously allowed at the 95% CL.

Comparison with other Analyses
We are not aware of any global analyses incorporating the new XENON100 constraint [27]. The two global analyses including LHC 5/fb data that are most similar to ours are [9] and [10], and we take this opportunity to comment on the relations and differences between those and the present work.
As in this work, Ref. [9] incorporates the constraints imposed by the LHC 5/fb data using an implementation of Delphes that is reported to reproduce the 95% CL limits published previously by ATLAS using 165/pb and 1/fb of data and shown to reproduce approximately the 95% CL limits for tan β = 10 and A 0 found in the ATLAS analysis used here and the CMS razor analyss with 5/fb of data [13]. However, the ATLAS 5/fb jets + / E T analysis has apparently not been modelled in detail, and full information is not available on its validation for other values of the CMSSM parameters, nor on its extension to the NUHM1. In contrast to previous papers by the same collaboration that used the MasterCode, Ref. [9] uses only a reduced set of precision electroweak and flavour observables, a topic we comment on below. In contrast, Ref. [9] uses AstroFit, which provides input from both direct and indirect dark matter searches, whereas we use only the direct XENON100 search. However, Ref. [9] finds that the indirect dark matter searches have negligible impact at the present time. When the constraint M h = 126±2±3 GeV is imposed in [9], the results for the CMSSM are relatively similar to ours, whereas the results for the NUHM1 are only qualitatively similar.
Ref. [10] implements the CMS razor analysis using 5/fb of data, and provides more details of its efficiency and likelihood maps, and also compares with the 95% CL limit obtained in the ATLAS 5/fb jets + / E T analysis. This paper favours values of the CMSSM mass parameters (m 0 , m 1/2 ) that are considerably larger than in our analysis and in [9]. However, Ref. [10] does favour the stau coannihilation strip and the rapid-annihilation funnel regions of the CMSSM, disfavouring the focus-point region that had been advocated in previous fits by the same group. Ref. [10] does not discuss the NUHM1, but does consider the possibilities that µ < 0 and of dropping the (g − 2) µ constraint.

Conclusions
We have presented in this paper new global fits to the CMSSM and NUHM1 based on the 7 TeV ATLAS 5/fb jets + / E T constraint and the latest global combination of limits on BR(B s → µ + µ − ), the new XENON100 constraint, a Higgs mass measurement M h ∼ 125 GeV, and minor updates for other observables. Before the advent of the LHC, low-energy data, in particular (g−2) µ , gave hope that the scales of supersymmetry breaking in these models might be within reach of the LHC within its first year of operation at 7 TeV in the centre of mass. This has not been the case, and the p-values of the CMSSM and NUHM1 have declined to 8.5 and 9.1%, respectively, prompting a re-evaluation of their status.
Two possibilities remain open at this point: either supersymmetry is relatively light but manifests itself differently from the CMSSM or NUHM1, or the supersymmetry-breaking mass scale is heavier, possibly even beyond the reach of the LHC. In the first case, several possibilities suggest themselves (see, e.g., Ref. [63]): other models of supersymmetry breaking, light thirdgeneration squarks, F-SU(5) [11], the pMSSM, R-violating models, etc., and a discussion of these possibilities lies beyond the scope of this work. As for the second case, the global fits presented here in the CMSSM and NUHM1 give limited guidance on the possible supersymmetric mass scale.
Perhaps surprisingly, the ATLAS 5/fb jets + / E T data are not much more problematic for the CMSSM and the NUHM1 than were the LHC 1/fb data in combination with the Higgs mass constraint. The latter two had already constrained the CMSSM and NUHM1 parameters to lie beyond the range where they could fully 'solve' the (g − 2) µ problem, and the contribution of the AT-LAS 5/fb jets + / E T constraint to the global χ 2 function is not large, even at the local best-fit point within the low-mass CMSSM 'island'. A new feature of this analysis is the impact of the latest BR(B s → µ + µ − ) constraint, and we stress the importance of the constraint from the search for spin-independent dark matter scattering by the XENON100 Collaboration [27].
The most important upper limit on the supersymmetry-breaking mass scales in the CMSSM and the NUHM1 is now provided by the cold dark matter density constraint, and indications on the possible sparticle masses within the range allowed by this constraint are now quite weak. The (g − 2) µ constraint still offers some preference for low sparticle masses, but this is largely counterbalanced by other constraints such as BR(B s → µ + µ − ). As we have seen, any value of mg ∈ (1500, 5000) GeV is allowed at the ∆χ 2 < 2 level. The lower part of this range may be explored with LHC operating at 8 TeV, and the middle part with the LHC at 13 or 14 TeV, but the upper part of the allowed range of mg would lie beyond the reach of the LHC. On the other hand, one must keep in mind that the increasing tension within the CMSSM and NUHM1 between the low-energy data, mainly (g − 2) µ and the LHC 5/fb and BR(B s → µ + µ − ) data on the other side, has resulted over time in a monotonously-increasing χ 2 and a correspondingly lower fit probability. Consequently, looking beyond the CMSSM and NUHM1, to models with a different connection between the coloured and uncoloured sector, not only seems timely now, but mandatory. We expect that some model with such a different connection will give a substantially better fit to all existing experimental data and present more favorable expectations for subsequent LHC runs or a future LC.