Higgs and supersymmetry

Global frequentist fits to the CMSSM and NUHM1 using the MasterCode framework predicted Mh≃119 GeV in fits incorporating the (g−2)μ constraint and ≃126 GeV without it. Recent results by ATLAS and CMS could be compatible with a Standard Model-like Higgs boson around Mh≃125 GeV. We use the previous MasterCode analysis to calculate the likelihood for a measurement of any nominal Higgs mass within the range of 115 to 130 GeV. Assuming a Higgs mass measurement at Mh≃125 GeV, we display updated global likelihood contours in the (m0,m1/2) and other parameter planes of the CMSSM and NUHM1, and present updated likelihood functions for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$m_{\tilde{g}}, m_{\tilde{q}_{R}}$\end{document}, BR(Bs→μ+μ−) and the spin-independent dark matter cross section \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma^{\mathrm{SI}}_{p}$\end{document}. The implications of dropping (g−2)μ from the fits are also discussed. We furthermore comment on a hypothetical measurement of Mh≃119 GeV.

Notable predictions of these global fits included M h = 119.1 +3. 4 −2.9 GeV in the CMSSM and M h = 118.8 +2.7 −1.1 GeV in the NUHM1 (which should be combined with an estimated theory error M h = ±1.5 GeV). These two fits are based solely on the Higgs-independent searches including the (g − 2) μ constraint, i.e., they do not rely on the existing limits from LEP [47,48], the Tevatron [49], or the LHC [50, 51]. These predictions increase to M h = 124.8 +3. 4 −10.5 GeV in the CMSSM and 126.6 +0.7 −1. 9 GeV in the NUHM1 if the (g − 2) μ constraint is dropped.
Subsequently, the ATLAS and CMS Collaborations have released their official combination of the searches for a SM Higgs boson with the first ∼1/fb of LHC luminosity at E cm = 7 TeV [52 -54]. Impressively, the combination excludes a SM Higgs boson with a mass between 141 and 476 GeV. Most recently, the ATLAS and CMS Collaborations have presented preliminary updates of their results with ∼5/fb of data [55]. These results may be compatible with a SM-like Higgs boson around M h 125 GeV, though CMS also report an excess at M h 119 GeV in the ZZ * channel. We recall that, for low values of M h , the SM electroweak vacuum would be unstable [56], decaying into a state with Higgs vev >10 8 (10 10 ) GeV if M h = 119(125) GeV, and that a very plausible mechanism for stabilizing the vacuum is supersymmetry (SUSY) [57].
In this paper, we first report the likelihood function for an LHC measurement of M h with a nominal value ∈ (115, 130) GeV, incorporating the theoretical error ±1.5 GeV and an estimate ±1 GeV of the possible experimental error. In both the CMSSM and NUHM1, this likelihood function is minimized for M h 119 GeV if (g − 2) μ is included, and is contained within the theoretical uncertainty range shown previously as a 'red band' [3]. We then discuss the consequences of combining a measurement of M h 125 GeV (assuming that the current excess will be confirmed with more integrated luminosity) with our previous analysis [3] of constraints on the CMSSM and NUHM1 including (g − 2) μ .
We find that the best-fit values of m 0 and m 1/2 in the CMSSM and NUHM1 are moved to substantially higher values, especially in the case of m 1/2 . We also update our results on the best-fit regions in the (m 1/2 , tan β) and (M A , tan β) planes, where we find again the substantial increase in m 1/2 , as compared with our pre-LHC M h results. We present the corresponding one-dimensional likelihood functions for the gluino mass mg, an average right-handed squark mass mq R , the lighter scalar tau mass, mτ 1 , as well as in the (mχ0 is the mass of the lightest neutralino and σ SI p is the spin-independent dark matter scattering cross section. As could be expected, we find larger values of mg, mq R , mχ0 1 and mτ 1 than in our pre-LHC M h fit, and smaller values of σ SI Since M h 125 GeV is the value that was favored in the CMSSM/NUHM1 fits omitting the (g − 2) μ constraint [3], we also show some results for fits where (g −2) μ is dropped. In this case, we find that preferred regions of the (m 0 , m 1/2 ) planes are localized at relatively high values, corresponding to relatively large sparticle masses. Correspondingly, the spin-independent dark matter scattering cross section σ SI p would be relatively small in this case, though again there would be relatively little effect on BR(B s → μ + μ − ).
Finally, we show selected results for a hypothetical measurement of M h 119 GeV.

Prediction for M h
We recall that the independent parameters of the CMSSM  may be taken as the common values of the scalar and fermionic supersymmetry-breaking masses m 0 , m 1/2 at the GUT scale, the supposedly universal trilinear soft supersymmetry-breaking parameter, A 0 , and the ratio of Higgs v.e.v.'s, tan β. A study of the distribution of Higgs masses in the CMSSM was performed in [82]. Motivated by (g − 2) μ and, to a lesser extent, BR(b → sγ ), we assume that the Higgs mixing parameter μ > 0. In the case of the NUHM1 [83][84][85], we relax the universality assumption for the soft supersymmetry-breaking contributions to the two Higgs masses, In our previous papers [3,[19][20][21][22][23][24][25] we constructed a global likelihood function that receives contributions from electroweak precision observables, B-decay measurements, the XENON100 direct search for dark matter scattering [86] and the LHC searches for supersymmetric signals, calculated within the MasterCode framework [26]. This incorporates code based on [87,88] [100,101]. As before, we use a Markov Chain Monte Carlo (MCMC) approach to sample the parameter spaces of supersymmetric models, and the results of this paper are based on the sample of 70M CMSSM points and another 125M NUHM1 points, both extending up to m 0 , m 1/2 = 4000 GeV.
We used in [3] the public results of searches for supersymmetric signals using ∼1/fb of LHC data analyzed by the ATLAS and CMS Collaborations and ∼0.3/fb of data analyzed by the LHCb Collaboration. These include searches for jets + / E T events without leptons by ATLAS [102] and CMS [103], searches for the heavier MSSM Higgs bosons, H/A [50, 51], and new upper limits on BR(B s → μ + μ − ) from the CMS [104], LHCb [105,106] and CDF Collaborations [107,108]. Our global frequentist fit [3] yielded regions of the CMSSM and NUHM1 parameter spaces that are preferred at the 68 and 95 % CL.
This was the basis in [3] for the predictions M h = 119.1 +3.4 −2.9 GeV in the CMSSM and M h = 118.8 +2.7 −1.1 GeV in the NUHM1, if the (g − 2) μ constraint is included as calculated using the FeynHiggs code which is quoted as having a theoretical error ±1.5 GeV [13][14][15][16][17]. It is important to note that these best-fit values are well above the LEP lower limit and below the Tevatron/LHC upper limit on M h , which played no role in their determination. and 126.6 +0.7 −1.9 GeV in the NUHM1 if the (g − 2) μ constraint is dropped. The uncertainty on the M h prediction is somewhat asymmetric, which is due to the different constraints coming into play. At low M h values, the most important constraint is that due to the LHC, though other lowenergy constraints also play roles. On the other hand, at high values of M h , it rises logarithmically with the scalar top masses, so increasing M h increases exponentially the required supersymmetry-breaking mass scales, and worsens the agreement with other low-energy data and the CDM constraint.

Results without a Higgs-boson mass measurement
Within the supersymmetric frameworks discussed here, a confirmation of the excess reported by ATLAS and CMS [55] and consequently the discovery of a SM-like Higgs boson is expected to be possible in the coming year, with a mass in the range between 114 and 130 GeV [55]. We assume that this measurement will yield a nominal value of M h within this range, with an experimental error that we estimate as ±1 GeV. We now estimate the one-dimensional likelihood function for the nominal central value of M h , which may be written as h denotes the output of FeynHiggs (which was plotted in Fig. 12 of [3] for the fits including We see in Fig. 1 3 that the values of χ 2 for the nominal value of M h calculated in the CMSSM and NUHM1 with the (g − 2) μ constraint and including both the theoretical and experimental errors lie below the blue lines taken from Fig. 12 of [3]. This is to be expected, since the calculation of the dashed line incorporates additional uncertainties. As is also to be expected, in each case the calculated χ 2 lies within the previous red band. The most likely nominal value of the LHC measurement of M h remains M h 119 GeV in both the CMSSM and NUHM1. A value of M h 125 GeV is disfavored in our analysis by χ 2 = 2.2 in the CMSSM and by 1.6 in the NUHM1 if (g − 2) μ is included. For comparison, a nominal value of M h = 114 GeV, corresponding roughly to the lower limit set by LEP for an SM-like Higgs boson [47,48], has χ 2 = 0.8(1.5). On the other hand, if we drop (g − 2) μ there is essentially no χ 2 price to be paid by including a measurement of M h 125 GeV.

Implementation of the LHC constraint on M h
We now study the possibility that the LHC experiments confirm the excess reported around 125 GeV and indeed discover a SM-like Higgs boson. Assuming we incorporate this new constraint using the 'afterburner' approach discussed previously [3] for other observables. This value would be favored if (g − 2) μ were dropped from our global CMSSM or NUHM1 fit [3]. Alternatively, a measurement of such a high M h value could point to the realization of some different (possibly GUT-based) version of the MSSM (see, for instance, [109]). We also mention briefly some implications if M h 119 GeV.

Comments on the LHC data
As a preamble to these studies, we first comment on the results of the current ATLAS/CMS Higgs combination. We recall that the local p-value for the background-only hypothesis for the excess found in the ATLAS data at M h 125 GeV is p = 1.9 × 10 −4 , while that in the CMS data at M h 125 GeV has p = 5 × 10 −3 . In addition, CMS reports an excess in the ZZ * channel at M h = 119 GeV with similar significance, but this is not confirmed by ATLAS.
In order to assess the global p-value of a potential signal, one should take the 'look-elsewhere effect' (LEE) into account. This is conventionally estimated by adding to the local p-value the quantity N × exp(−Z 2 max /2), where N is the number of times the observed upper limit on the signal crosses over the μ = σ/σ SM = 0 level in the upward direction, and Z max is the maximal signal significance [55]. Accounting for the LEE, ATLAS assess the global p-value of their excess at 125 GeV In the range (110, 146) GeV to be 0.6 %, and CMS assess the significance of their excess at 125 GeV to be 1.9 % in the range (110,145) GeV.
On the other hand, as the CMSSM and NUHM1 naturally require M h < ∼ 130 GeV, the LEE factor is strongly reduced in these frameworks.
Since the excess around 125 GeV is common to both experiments and has the correct signal strength: μ ≈ 1 can be interpreted as a Higgs signal in either the SM or a supersymmetric framework. We focus here on this interpretation, commenting subsequently on some implications if M h 119 GeV.

What if M h = 125 GeV?
We first examine the effects on the global likelihood functions in various CMSSM and NUHM1 parameter planes, and then study implications for various observables of a potential LHC measurement M h 125 GeV, see Eq. (1). The (m 0 , m 1/2 ) planes shown in Fig. 2 are for the CMSSM (left) and NUHM1 (right). 4 The regions preferred at the 68 % CL are outlined in red, and those favored at the 95 % CL are outlined in blue. The solid (dotted) lines include (omit) the assumed LHC Higgs constraint. The open green star denotes the pre-Higgs best-fit point [3], whereas the solid green star indicates the new best-fit point incorporating a Higgs-boson mass measurement at 125 GeV.
Since in the CMSSM and NUHM1 the radiative corrections contributing to the value of M h are sensitive primarily to m 1/2 and tan β, and only to a lesser extent to m 0 (the stop masses, which are the most relevant for M h , depend mostly on m 1/2 due to the RGE running, and only mildly on m 0 ), we expect that the primary effect of imposing the M h constraint should be to affect the preferred ranges of m 1/2 and tan β, with a lesser effect on the preferred range of m 0 . This effect is indeed seen in both panels of Fig. 2. We see that the 68 % CL ranges of m 1/2 extend to somewhat larger values and with a wider spread than the pre-Higgs results, particularly in the NUHM1. However, the NUHM1 best-fit value of m 1/2 remains at a relatively low value of ∼800 GeV, whereas the best-fit value of m 1/2 in the CMSSM moves to ∼1900 GeV. This jump reflects the flatness of the likelihood function for m 1/2 between ∼700 GeV and ∼2 TeV, which is also reflected later in the one-dimensional χ 2 functions for some sparticle masses. 5 When we add the hypothetical M h constraint the total χ 2 at the best-fit points increases substantially, as seen in Table 1, and the p-value decreases correspondingly. The table compares fit probabilities for two different assumptions on the Higgs boson mass measurements 119, 125 GeV, see above, and with the option of dropping the (g − 2) μ constraint in the latter case. 6 The combination of the increase in χ 2 and in the increase in the number of d.o.f. leads to a substantially lower p-value after the inclusion of Eq. (1), if (g − 2) μ is taken into account. On the other hand, a hypothetical mass measurement at 119 GeV would yield an 4 We have omitted from the NUHM1 sample displayed here and in subsequent figures a grouping of points at large m 1/2 and small m 0 for which different codes yield discrepant values of the relic density. MicrOMEGAs [96][97][98] and DarkSusy [110,111] yield densities within the WMAP range for these points, whereas SuperIso Relic (see [95]) and SSARD [99] both yield substantially lower densities. The other figures shown in this paper are not affected significantly by the omission of these points (which have χ 2 > 5), pending resolution of this discrepancy. Tests in other regions of the NUHM1 sample have not revealed significant discrepancies between these codes. 5 Our fits are relatively insensitive to A 0 , so we do not display figures for this parameter. 6 The fit probabilities are indicative of the current experimental data preferences for one scenario over another but, as discussed in [3], but they do not provide a robust confidence-level estimation for the actual choice made by Nature.  Table 1 Comparison of the best-fit points found in the CMSSM and NUHM1 pre-Higgs [3] and for the two potential LHC Higgs mass measurements discussed in the text: M h 119 and 125 GeV. In the latter case, we also quote results if the (g − 2) μ constraint is dropped. At the best-fit NUHM1 points, the common values of the soft supersymmetry-breaking contributions to the Higgs squared masses are the following pre-Higgs: −1.2 × 10 6 GeV 2 , with M h 125 GeV and (g − 2) μ : −5.5 × 10 6 GeV 2 , with M h 125 GeV but without (g − 2) μ : −8.6 × 10 5 GeV 2 , with M h 119 GeV and (g − 2) μ : −1.2 × 10 6 GeV 2

Model
Minimum improvement in the fit. For comparison, we also show the parameters for the best-fit points. Since the uncertainties are large and highly non-Gaussian, we omit them from the table.
The restrictions that the hypothetical LHC M h constraint imposes on m 1/2 are also visible in Fig. 3, where we display the effects of an LHC M h constraint in the (m 1/2 , tan β) planes of the CMSSM and NUHM1. We see here that an LHC M h constraint enlarges visibly the 68 % CL range of tan β in the NUHM1, whereas the change is less pronounced in the CMSSM.
The results for the (M A , tan β) planes in the CMSSM and the NUHM1 are shown in Fig. 4. We observe a strong increase in the best-fit value of M A in both models, especially in the CMSSM, where now M A ∼ 1600 GeV is preferred. We re-emphasize, however, that the likelihood function varies relatively slowly in both models, as compared to the pre-LHC fits.
We now discuss the CMSSM and NUHM1 predictions for some of the most interesting supersymmetric observables for the LHC in light of a possible LHC measurement at M h 125 GeV.
The upper panels of Fig. 5 display the one-dimensional χ 2 functions for mg before and after applying the new LHC M h 125 GeV constraint (dashed and solid lines, re-   Fig. 2 spectively, in both cases including (g − 2) μ ). We also show as dotted lines the χ 2 functions for a fit including M h 125 GeV and dropping (g − 2) μ . As expected on the basis of Fig. 2, the preferred values mg ∼ 4 TeV in the CMSSM are much higher than in our pre-LHC fit and what would be preferred if M h 119 GeV, and presumably beyond the reach of the LHC. On the other hand, in the NUHM1 mg ∼ 2 TeV is marginally preferred. However, in both models the χ 2 function varies little over the range (2, 4) TeV. Similar features are found for mq R , as shown in the lower panels of Fig. 5. In both models, the regions of mg and mq R with χ 2 < ∼ 1 start at masses around 1.5 TeV, leaving a large range accessible to the SUSY searches at the LHC. In the case of the lighter stau mass mτ 1 for M h 125 GeV shown in Fig. 6, we again see preferred masses larger than in the pre-Higgs fit, with favored values extending up to mτ 1 ∼ 1 TeV.
We now turn to the predictions of our fits for BR(B s → μ + μ − ), shown in Fig. 7. This observable is not very sensitive directly to M h , and the indirect sensitivity via m 1/2 is not very strong, though smaller values of m 1/2 do lead to larger values of BR(B s → μ + μ − ), in general. As seen in Fig. 7, imposing the putative LHC M h constraint indeed has little effect on BR(B s → μ + μ − ). We recall that the best-fit values in the CMSSM and NUHM1 are both slightly larger than in the SM, and enhancements of up to O (30-40 %) with respect to the SM prediction could be detected at the LHC at the 3 σ level.
Finally, in Fig. 8 we show results for the preferred regions in the (mχ0 1 , σ SI p ) plane. As seen in Fig. 8, the fact that larger values of m 1/2 and hence mχ0 1 are favored by the larger values of M h implies that at the 68 % CL the preferred range of σ SI p is significantly lower when M h 125 GeV, when compared to our previous best fit with M h = 119 GeV, ren-     Fig. 2 dering direct detection of dark matter significantly more difficult. Again, this effect on mχ0 1 is more pronounced in the CMSSM, whereas in the NUHM1 the value of mχ0 1 for the best-fit point changes only slightly.

Results dropping the (g − 2) μ constraint
We have restricted our attention so far to M h 125 GeV assuming the (g − 2) μ constraint. However, this value of M h corresponds approximately to our best-fit points in [3] when the (g − 2) μ constraint is dropped. 7 Accordingly, we now consider the same measurement as given in Eq. (1), but with (g − 2) μ dropped from the fit. 8 In the following plots we show results for fits omitting (g − 2) μ , pre-Higgs (dotted) and post-Higgs (solid).
We see in Fig. 9 that the regions of the (m 0 , m 1/2 ) planes in the CMSSM and NUHM1 that are favored at the 68 % CL are concentrated at large values if the (g − 2) μ constraint is dropped. This reflects the relative harmony between the LHC / E T constraints and the hypothetical M h 125 GeV measurement if (g − 2) μ is omitted. The inclusion of Eq. (1) substantially sharpens the prediction at the 68 % CL, whereas it is less pronounced for the 95 % CL contours. Fig. 9 The (m 0 , m 1/2 ) planes in the CMSSM (left) and the NUHM1 (right), for M h 125 GeV, but dropping the (g − 2) μ constraint. Dotted lines show the contours found previously in [3] dropping the (g − 2) μ but without this M h constraint. Here the open green stars de-note the pre-Higgs best-fit points [3] (also dropping (g − 2) μ ), whereas the solid green stars indicate the new best-fit points. These best-fit points are essentially coincident in the NUHM1 case (Color figure online) Fig. 10 The (m 1/2 , tan β) planes in the CMSSM (left) and the NUHM1 (right), for M h 125 GeV, but dropping the (g − 2) μ constraint. The notations and significations of the contours are the same as in Fig. 9 As we see in Fig. 10, the concentration at relatively large m 1/2 is reflected in a correlated preference for large values of tan β. Furthermore, as seen in Fig. 11, the corresponding preferred range of M A is also concentrated at relatively large masses. Again the inclusion of Eq. (1) considerably sharpens the preferred parameter ranges.
Looking back now at the one-dimensional χ 2 functions for the fits without (g − 2) μ that are shown as dotted lines in Figs. 5 and 6, we see that the preference for large values of (m 0 , m 1/2 ) carries over into relatively large values of mg, mq R and mτ 1 . In particular, the (g − 2) μ -less scenarios offer somewhat gloomy prospects for sparticle detection at the LHC. On the other hand, as seen in Figs. 7, there is little change in the prediction for BR(B s → μ + μ − ) if (g − 2) μ is omitted.
Turning finally to the predictions for σ SI p if (g − 2) μ is omitted, shown in Fig. 12, we see that the relatively large values of m 1/2 seen in Fig. 9 are reflected in relatively large values of mχ0 1 , which correspond in turn to relatively low values of σ SI p . The inclusion of Eq. (1) again strongly reduces the preferred parameter ranges.
An alternative interpretation of a Higgs signal around M h 125 GeV would be that while the MSSM might still be realized, it is not the CMSSM nor the NUHM1 that describes Nature correctly, but another version of the MSSM. In this case, the prospects for sparticle detection at the LHC and dark matter detection might well be more cheerful than in the (g − 2) μ -less CMSSM and NUHM1 scenarios discussed here. However, the exploration of such possible alternative models lies beyond the scope of our analysis.  We have restricted our attention so far to M h 125 GeV, which corresponds to the excess seen in both CMS and AT-LAS. We now consider an alternative potential LHC measurement M h = 119 ± 1 GeV, which corresponds to the CMS ZZ * signal and our earlier predictions including the (g − 2) μ constraint, again allowing for a theoretical error ±1.5 GeV in the calculation of M h for any given set of CMSSM or NUHM1 parameters.
The (m 0 , m 1/2 ) planes shown in Fig. 13 for the CMSSM (left) and NUHM1 (right), the preferred regions are shown at the 68 % CL (red) and 95 % CL, with the solid (dotted) lines include (omit) the assumed LHC Higgs constraint. Since this assumed LHC value of M h coincides with the previous best-fit values in both the CMSSM and NUHM1, the best-fit points in these models (indicated by the green stars in Fig. 13) are nearly unaffected by the imposition of the putative LHC constraint. The effect of the hypothetical measurement restricting the range in m 1/2 is indeed seen in both panels of Fig. 13, though for the 68 % CL contour (shown in red) it is much more pronounced for the CMSSM than for the NUHM1, whereas for the 95 % CL contour (shown in blue) it is more significant for the NUHM1. This reflects the fact in the NUHM1 the global χ 2 function found in [3] rose quite steeply in the neighborhood of the best-fit point, resulting in a relatively tight 68 % CL contour, whereas the rise of χ 2 away from the best-fit point in the CMSSM was more gradual. This led previously to a larger 68 % CL contour and a broader range of M h at the 68 % CL, which is now more affected by an assumed LHC M h constraint. On the other hand, the 95 % CL contour in the NUHM1 extended previously to larger values of m 1/2 than in the CMSSM, and  these values are particularly susceptible to the LHC M h constraint.
Although we add another constraint (as discussed above), the total χ 2 at the best-fit points do not change. 9 For this reason, the p-values for the CMSSM and NUHM1 would increase for a hypothetical measurement M h 119 GeV, corresponding formally to better overall fits to the larger data set, as seen in Table 1.
As one might expect, such an LHC M h constraint would reduce considerably the 68 % CL range of tan β in the CMSSM. This is because, for m 1/2 close to the best-fit value, ∼700 to 800 GeV, fixing the Higgs mass at 119 GeV disfavors low values of tan β, which yield low values of M h . 9 They would change only slightly if the Higgs mass were assumed to differ by < ∼ 1 GeV from that obtained at the best-fit point.

Summary and conclusions
The ATLAS and CMS searches for the Higgs boson have already excluded a very large range of masses, with the only remaining windows for a SM-like Higgs boson being in the ranges M h ∈ (115.5, 127) GeV or >600 GeV [52 -55]. The latter range is disfavored by precision electroweak data, so attention naturally focuses on the low-mass range. It may or not be a coincidence that this range includes the range M h < ∼ 130 GeV accessible in simple supersymmetric models such as the CMSSM and NUHM1. Within this range, our previous global fits of these models including (g − 2) μ predicted M h ∼ 119 GeV if the (g − 2) μ constraint was included in the fit, and M h ∼ 126 GeV if (g − 2) μ was omitted [3]. The latest ATLAS and CMS results display an interesting fluctuation at M h ∼ 125 GeV (i.e. close to the latter result from [3]) and we have combined a hypothetical measurement of M h = 125 GeV with the global likelihood functions obtained in our previous fits [3].
As we have shown in this paper, this combination refines our previous predictions for the CMSSM and NUHM1 model parameters within global fits incorporating (g − 2) μ . In particular, the combination prefers a range of larger values of m 1/2 , resulting in larger values of mg and other sparticle masses being preferred, restricting the prospects for discovering supersymmetry at the LHC within these models. The predictions for σ SI p are pushed to higher masses and lower cross sections, particularly in the CMSSM. There are also smaller changes in the predictions for other observables such as BR(B s → μ + μ − ).
We have also shown the analogous CMSSM and NUHM1 fit results for a hypothetical measurement of M h 125 GeV if the (g − 2) μ constraint is omitted. In this case we find a stronger preference for larger values of (m 0 , m 1/2 ), and correspondingly larger values of tan β and M A , as well as larger values of mg, mq R , potentially lying beyond the reach of the LHC. We have also commented on the potential implications of a hypothetical Higgs discovery at M h 119 GeV.
Time will soon tell whether the LHC experiments are indeed discovering the Higgs boson. However, we have shown that M h = 125 GeV is a possibility within the CMSSM and NUHM1, although it lies at the upper range of what is possible within the CMSSM or NUHM1, and might suggest reduced prospects for discovering these particular models of supersymmetry at the LHC. Alternatively, it could well be that one should look beyond the frameworks of the models discussed here.
Note added in proof After acceptance of this paper for publication, we became aware of issues in the implementation of the FeynHiggs code and in the cold dark matter density calculation, which required extra sampling and reprocessing of the NUHM1 parameter space. We are grateful to Nazila Mahmoudi and Azar Mustafayev for discussions on dark matter density calculations.