What next for the CMSSM and the NUHM: Improved prospects for superpartner and dark matter detection

We present an updated analysis of the CMSSM and the NUHM using the latest experimental data and numerical tools. We map out favored regions of Bayesian posterior probability in light of data from the LHC, flavor observables, the relic density and dark matter searches. We present some updated features with respect to our previous analyses: we include the effects of corrections to the light Higgs mass beyond the 2-loop order using FeynHiggs v2.10.0; we include in the likelihood the latest limits from direct searches for squarks and gluinos at ATLAS with ~20/fb; the latest constraints on the spin-independent scattering cross section of the neutralino from LUX are applied taking into account uncertainties in the nuclear form factors. We find that in the CMSSM the posterior distribution now tends to favor smaller values of Msusy than in the previous analyses. As a consequence, the statistical weight of the A-resonance region increases to about 30% of the total probability, with interesting new prospects for the 14 TeV run at the LHC. The most favored region, on the other hand, still features multi-TeV squarks and gluinos, and ~1TeV higgsino dark matter whose detection prospects by current and one-tonne detectors look very promising. The same region is predominant in the NUHM, although the A-resonance region is also present there as well as a new solution, of neutralino-stau coannihilation through the channel stau stau ->hh at very large \mu. We derive the expected sensitivity of the future CTA experiment to ~1 TeV higgsino dark matter for both models and show that the prospects for probing both models are realistically good. We comment on the complementarity of this search to planned direct detection one-tonne experiments.


Introduction
The recent discovery of a Higgs boson at the LHC [1,2] raised widespread excitement in the particle physics community and spurred a lot of activity to interpret the new discovery in the context of the Standard Model (SM) and models of new physics. In particular, the mass of the newly discovered particle, m h 126 GeV, is well within (albeit on the upper side) the predictions of low-scale supersymmetry (SUSY). In fact, since in SUSY the quartic coupling of the scalar potential is related to the gauge couplings of the electroweak (EW) sector, the lightest Higgs mass can deviate from the masses of the W and Z bosons only through radiative corrections so that its value is effectively bounded to be less than about 135 GeV.
The implications of the Higgs discovery for the parameter space of the popular Constrained Minimal Supersymmetric Standard Model (CMSSM) [3] and Non-Universal Higgs Model (NUHM), have been intensely investigated (see, e.g., [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] for some of the papers that followed the Higgs discovery). Many of those studies, including our own ones, explored statistical combinations of the constraints from the Higgs measurements at the LHC with other pieces of experimental information: the measurement of the dark matter relic density [19]; a number of EW precision observables; measurements of rare-decay branching ratios like BR B → X s γ [20], BR (B u → τ ν) [21], or the recent measurement of a SM-like BR (B s → µ + µ − ) at the LHC [22,23]; the anomalous magnetic moment of the muon [24,25], etc. Additional constraints came from direct SUSY searches at the LHC. For instance, in our previous CMSSM and NUHM analyses [11,16] the likelihood function included limits from the CMS razor 4.4 fb −1 analysis at 7 TeV [26] and the CMS α T 11.7 fb −1 analysis at 8 TeV [27], which were obtained by simulating the SUSY signal and detector response and comparing them to the observed and background yields in different channels given by the experimental collaboration.
It is important to point out that, besides the Higgs boson mass measurement and LHC direct bounds, the constraint showing by far the strongest impact on the parameter space of the Minimal Supersymmetric SM (MSSM) is the relic density. It is measured very precisely and its value tends to be too large in broad regions of the parameter space. The mechanisms for reducing the relic abundance are quite general and insensitive to the particular pattern of scalar mass unification with the exception, obviously, of solutions requiring the presence of light sleptons, which in the CMSSM/NUHM are excluded by direct LHC limits on the squarks. In other words, while featuring a limited number of free parameters that make them more predictive than general phenomenological parametrizations defined at the scale of the lightest SUSY partners, the CMSSM and the NUHM produce solutions to the relic density that are present and play an important role in more general models. From this point of view, the CMSSM ansatz and its most immediate extension, the NUHM, are very useful frameworks to investigate the predictions for dark matter in constrained frameworks within the MSSM with gaugino unification at the GUT scale.
The picture that emerged particularly in the analyses [15,16] for the CMSSM and [14,16] for the NUHM, is that the relatively large value of the Higgs mass, the SM-like nature of its couplings to the other SM particles, the measured values of the flavor physics observables in great agreement with the SM, and the non-observation of SUSY particles below ∼ 1 − 1.5 TeV at the LHC, can all be easily accommodated in an extended region of the parameter space characterized by squarks and gluinos in the multi-TeV regime and the heavy Higgs sector effectively decoupled. In this region, the relic density can naturally assume the value measured by PLANCK, as the lightest SUSY particle (LSP) is an almost pure higgsino neutralino with a mass m χ 1 TeV. 1 The existence of the ∼ 1 TeV higgsino solution for DM in the MSSM has been long known [28,29] but in the framework of unified SUSY was first pointed out in a pre-LHC study of the NUHM [30].
Interestingly, parameter space regions with sparticles in the multi-TeV regime and ∼ 1 TeV higgsino dark matter in agreement with the value of the relic density were shown to be very favored also in scans of the phenomenological MSSM [31], in the Next-to-Minimal Supersymmetric SM [32], and in a variety of models with non-universal boundary conditions at the GUT scale [33]. Incidentally, it was shown in [33] that for some of these models focus point-like mechanisms significantly increase the naturalness of the ∼ 1 TeV higgsino region with respect to the CMSSM, without affecting dark matter properties and prospects for detection. As a matter of fact, the best prospects for detection of the ∼ 1 TeV higgsino region indeed come from dark matter direct detection experiments, particularly at 1-tonne detectors, as the spin-independent neutralino-proton cross section, σ SI p , is well 1 While other regions of the parameter space, characterized by bino dark matter and such that the relic abundance is saturated through mechanisms of A-resonance or stau co-annihilation, are consistent with the constraints at the 1 or 2σ level, the ∼ 1 TeV higgsino region shows by far the best agreement with all of them with the exception of δ (g − 2) µ , which favors low MSUSY below ATLAS/CMS bounds in unified models.
within the projected sensitivities of the currently running and future 1-tonne experiments. Also very interestingly, recent studies of the sensitivity of the Cherenkov Telescope Array (CTA) [34] show the largest projected reach in the region characterized by dark matter mass and annihilation cross section typical of the ∼ 1 TeV higgsino region [35,36], thus opening up the enticing possibility of complementary detection for these scenarios.
In this paper, we update the global Bayesian analyses of the CMSSM and the NUHM previously produced by our group, by including the following new elements: • We calculate the Higgs mass with FeynHiggs 2.10.0 [47], which incorporates results beyond two loops with a resummation of leading and sub-leading logarithms in the top/stop sector.
• We update the likelihood map for direct SUSY searches with the most constraining limits from ATLAS with 20 fb −1 at 8 TeV.
• We include the recent constraints from the LUX experiment [52] in the likelihood function.
• We add an analysis of the prospect for CTA to independently explore the favored regions.
We will focus in particular on the properties of the regions that present the highest posterior probability, favored by the value of the dark matter relic density. We will show that the bulk of the posterior still lies on the ∼ 1 TeV higgsino region, but in the CMSSM its statistical significance is not as overwhelmingly predominant as previously shown. We will touch on the prospects for detection at the LHC and in future colliders, but will focus particularly on dark matter searches like the above-mentioned 1-tonne detectors and the CTA.
The paper is organized as follows. In Sec. 2 we describe the statistical setup, the constraints included in the likelihood function, the parameter prior ranges and distributions, and the numerical tools used in our scans. In Sec. 3 we present the results of the Bayesian analysis of the CMSSM, including prospects at collider and dark matter experiments. In Sec. 4 we present equivalent results for the NUHM. We give our summary and conclusions in Sec. 5.

Scanning methodology and experimental constraints
Our goal is to determine the regions in the parameter space of the CMSSM and the NUHM that are favored by all of the experimental data available. We follow a Bayesian approach outlined in [11,16,53,54] and map out the 68% and 95% credible regions in two-dimensional (2D) projections of the marginalized posterior probability density function (pdf) and/or the one-dimensional (1D) marginalized pdf of some interesting parameters. The posterior pdf (or, simply, the posterior), p(m|d), is given by Bayes' Theorem, where m is the set of model parameters, π(m) is prior probability distribution of the parameters m, p(d|m) ≡ L(m) is the probability of obtaining the experimental data d given the model parameters, known as the likelihood function, and p(d) is a normalization factor called the evidence, which is required for the comparison of different models. In this framework the likelihood function encodes all of our information from experimental constraints and their associated uncertainties. We can consider marginalized posterior distributions of subsets of the parameters m by integrating over the remaining parameters. The posterior distribution of a subset of parameters ψ 1...r from the full set of parameters m 1...N is then given by This leads to a natural prescription for dealing with nuisance parameters, since these can be included as parameters of the model with suitable prior probability distributions and then marginalized over to obtain posterior distributions of the parameters of interest.
We construct the likelihood function from the experimental data. We account for positive measurements with a gaussian likelihood function and combine experimental and theoretical errors in quadrature. A summary of the experimental constraints used in this analysis is given in Table 1. In addition, we adopt a specific procedure for incorporating the constraints from Higgs boson searches at the LHC, direct searches for SUSY, and the constraints from dark matter direct detection at LUX.
The discovery of a SM-like Higgs boson with m h 126 GeV presents a challenging constraint. The experimental collaborations have published the Higgs signal rates in several channels and we make use of this information by interfacing with the public code HiggsSignals v1.0.0 [55]. We supply HiggsSignals with the Higgs boson production cross section and branching ratios calculated by FeynHiggs [40][41][42][43] and use the calculated χ 2 result in the likelihood function. An accurate prediction for the lightest Higgs boson is important due to the small width of the observed experimental signal. Recently [47] FeynHiggs v2.10.0 has incorporated results beyond two loops with a resummation of leading and sub-leading logarithms in the top/stop sector. We include these in our scan. We fix the uncertainty in the mass of the lightest Higgs to 2 GeV, as a conservative estimate of the remaining sources of theory error. As well as the observed signal at ∼ 126 GeV, Higgs searches in other mass ranges may constrain the heavy Higgs bosons. We use HiggsBounds v4.1.0 [56][57][58] to reject points excluded at 95% C.L. by those searches.
The contribution to the likelihood arising from the results of the LUX experiment [52] is derived as was explained in [33], i.e., by applying the procedure developed in Ref. [  for the likelihood of XENON100 [70] to the data from LUX. We assume that the number of observed events follows a Poisson distribution centered on the predicted signal plus background. A likelihood map in the (m χ , σ SI p ) plane is generated by simulating signal events in micrOMEGAs [71] and marginalizing over the uncertainty in the expected number of background events. In Fig. 1(a) we plot the 68.3%, 90%, and 99.7% C.L. exclusion bounds obtained with our procedure. The dashed black line gives the official 90% C.L. exclusion bound. In our scans, we also account for uncertainties in the predicted elastic scattering cross section [72,73] by including the nuclear form factors σ s and Σ πN as nuisance parameters.
We finally account for the direct SUSY searches at the LHC by updating the method developed in [11,16]. We generate a grid in the (m 0 , m 1/2 ) plane at 50-GeV intervals. At each point we generate squark-and gluino-production events using Madgraph [74] and produce the parton shower in pythia [75]. The cross sections are calculated using nll − fast [76][77][78][79][80] to include the next-to-leading order and next-to-leading log contributions. We evaluate the expected number of events in a given signal region for the searches considered using CheckMATE [59][60][61][62][63][64][65][66][67]. CheckMATE includes a number of validated SUSY searches and includes an advanced tuning of the fast detector simulation. We calculate a likelihood for each search from the product of Poisson distributions for each signal region. We account for the uncertainties in the background rate by marginalizing over the background rate with a gaussian distribution. When calculating the likelihood, we consider the two searches that give the strongest limits in the CMSSM: a 0 lepton 2-6 jets ATLAS search [81] and a 0-1 lepton 3 b-jets ATLAS search [82]. We scale the total squark and gluino production rate by a small constant factor to match the limit achieved by the experimental analyses in order to account for the remaining differences in efficiencies due to the fast detector simulation. To combine the results of the two ATLAS searches we evaluate at each point which of the two searches has the largest expected exclusion and then use that search to  calculate the likelihood for that point. The combination of the two searches compared to the official 95% C.L. line from ATLAS (where we have combined the lines from the two different searches) is shown in Fig. 1(b). The agreement is very good across the entire range of m 0 and m 1/2 .
In this study, we also estimate the sensitivity of the Cherenkov Telescope Array (CTA) [34] for the favored parameter space of the CMSSM and the NUHM. The results will be shown in Sec. 3.2 and Sec. 4.2, respectively.
The CTA project will build the next generation air Cherenkov telescope observatory. For dark matter masses greater than ∼ 100 GeV CTA is expected to significantly exceed current experimental limits for dark matter annihilations such as those from HESS [83] and Fermi-LAT [84]. CTA may even probe cross sections below the canonical thermal relic value for some final states [36].
Reference [36] estimated the future sensitivity of CTA to dark-matter annihilation in the Galactic Center (GC) for the final states bb, µ + µ − and τ + τ − assuming 500 hours of observation time. In order to directly apply their limits to more generic neutralino annihilations, whose final states also include gauge bosons, ZZ and W + W − , we infer from [36] the 95% C.L. limit on the expected flux of signal photons per J-factor, N γ,95 , by convolving the photon flux with the effective area given in [85] in a single energy bin between 30 GeV and the dark matter mass: where t obs is the observation time, σv 95 is the projected 95% C.L. limit for each final state, and N γ,obs is given by where A eff is the effective area, dN γ (E)/dE is the energy spectrum per annihilation and for simplicity we have neglected the effect of finite energy resolution. For validation, one must make sure that the N γ,95 obtained from the different final-state bounds of [36] are all in very good agreement. Once N γ,95 is derived, the photon flux is calculated point by point in our scans using micrOMEGAs. In Fig. 2 we show the approximate 95% C.L. limit in the plane of the annihilation cross section times velocity at zero momentum, σv ≡ lim p→0 σv , versus the neutralino mass, m χ . The limit is extracted by testing each point against the expected N γ,95 , and showing them in red if they are excluded. The large statistical sample shown in Fig. 2 includes the scans performed for this study and those used in [31].
Note that the limit is derived for the photon flux, so that there is no corresponding clear-cut limit in σv. Nevertheless, we show with a gray solid line the maximum extent that can be probed with this method, and we will apply the obtained limit to the figures in Sec. 3.2 and Sec. 4.2.
The scans in this study are performed with the BayesFITS package [11,16,31,86], which interfaces several publicly available tools to direct the scanning procedure and calculate physical observables. The sampling is performed by MultiNest [87] with 4000 and 10000 live points for the CMSSM and NUHM respectively. The evidence tolerance is set to 0.5 and the sampling efficiency to 0.8 for all the scans. We use SoftSusy v. 3 Table 2: Prior distributions of the CMSSM and nuisance parameters used in the scans. All dimensionful parameters are given in TeV unless indicated otherwise.
The prior distributions of the model and nuisance parameters for the CMSSM are given in Table 2. Additionally the parameters scanned in the NUHM are indicated with an asterisk. The sign of µ is fixed for each scan. Note that for tan β < 3 it becomes very difficult to obtain at the same time EWSB, the correct value of the relic density, or the correct Higgs mass, as the parameters m Hu , m H d , tan β, and the one-loop tadpole corrections must be fine-tuned very precisely. Note also that for the scans with µ < 0 we do not include δ (g − 2) µ in the likelihood as it is known to be poorly fitted. We use logarithmic priors for the universal mass parameters m 0 and m 1/2 to reduce volume effects.

Posterior distributions and prospects for collider searches
In Fig. 3(a) we show the 68% and 95% credible regions of the marginalized 2D pdf in the (m 0 , m 1/2 ) plane of the CMSSM, for µ > 0. The gray dashed contours mark the previous 68% and 95% regions obtained in [16], which we present for comparison to highlight the impact of the new more precise calculation of m h and the new improved constraints. As has been long standing practice, in the CMSSM the modes of the posterior pdf are identified according to the respective mechanisms to satisfy the relic density constraint. The little, round, 95% credibility region just above the ATLAS line at low m 0 is the staucoannihilation region [91]; the large region immediately above it, for m 0 5 TeV and m 1/2 ∼ > 1.2 TeV is the A-resonance region [92]; the remaining mode for m 0 > 5 TeV and m 1/2 ∼ > 1.5 TeV is the above-mentioned ∼ 1 TeV higgsino region. The different shape of the present pdf relative to the one given in [16] is due to the new higher-order determination of the Higgs mass. Over the whole parameter space, given equivalent M SUSY = (mt 1 mt 2 ) 1/2 , the value of the Higgs mass has increased by about 2 GeV. In practice, this means that in the ∼ 1 TeV higgsino region, where the Higgs mass constraint is always more easily satisfied thanks to the large scalar masses, the favored m 0 values are now limited to less than 12 TeV, above which the Higgs mass becomes too heavy. In the A-resonance and stau-coannihilation regions, the Higgs mass value has increased from an average 122-123 GeV to values closer to 126 GeV, thus improving the χ 2 . As a consequence, the statistical weight of the A-resonance region has now much increased, with new, improved prospects for collider phenomenology, as we shall see later.
In spite of higher mass values for the Higgs boson, the stau-coannihilation region is now becoming disfavored by increasing tension with direct SUSY limits at the LHC, and it will be most likely probed in its entirety in the 14 TeV run. Note also that, with respect to [16], the focus point region [93][94][95], which is shown in Fig. 3(a) as a 95% dashed contour just above the ATLAS line at m 0 4 TeV, is now disfavored. Interestingly enough, the new estimate for the Higgs mass in the focus point region is now much closer to the experimental value than before, but the region is disfavored by the LUX results: as is well known, the neutralino there is a mixed composition of bino and higgsino with a mass of m χ 600 GeV. Its large σ SI p is now excluded by LUX at 90% C.L. We will come back to this point in Sec. 3.2.
In Fig. 3(b) we show the credible regions of the 2D pdf in the (A 0 , tan β) plane of the CMSSM, for µ > 0. The three favored modes of the posterior are not as clearly separated as in Fig. 3(a), or as they were in the (A 0 , tan β) plane shown in [16]. One can now recognize an elongated 68% credible region for 0 A 0 2 TeV and 8 tan β 45, which belongs to the ∼ 1 TeV higgsino region and extends to slightly larger, positive A 0 values for tan β ∼ > 45. An elongated 95% credible area is adjacent to it to the left: it encompasses part of the ∼ 1 TeV higgsino region, and the stau-coannihilation region. Finally, a roundish 68% and 95% credibility region at −3 TeV A 0 2 TeV and large tan β is the A-resonance region.
The most striking difference with the results of [16] is that now the favored A 0 range is much reduced, from a maximum span of approximately 28-30 TeV, covering almost the full parameter space, to the present span of about 10 TeV, centered around zero. By comparing the solid contours in color with the previous ones in dashed lines, one can see that the two modes that were previously predominant at large |A 0 | in the ∼ 1 TeV higgsino region are not as favored in the present scan and do not appear at 95% credibility. This is because in [16] one needed solutions with larger M SUSY to fit the Higgs mass measurement. When m 0 becomes very large, electroweak-symmetry breaking (EWSB) can only be obtained with large trilinear couplings, which enhance the RGE running of m 2 Hu . However, as we said above, the correct value of the Higgs mass can now be obtained with an M SUSY on average smaller, even in the ∼ 1 TeV higgsino region. Thus, the scanning program can more naturally find solutions with a reduced |A 0 |.
In Fig. 3(c) we show the 68% and 95% credible regions of the 2D pdf in the (m 0 , m 1/2 ) plane of the CMSSM for µ < 0. Two of the modes of the posterior are the same as in the µ > 0 case, with the exception of the A-resonance region, which does not appear for negative µ because the conditions for EWSB are not met there. 3 In Fig. 3(d) we show the corresponding 2D pdf in the (A 0 , tan β) plane.
In Fig. 4(a) we show in solid red the marginalized 1D posterior distribution for the lightest Higgs mass. We also show with a dashed blue line the distribution obtained in [16], to facilitate comparison. The posterior is in good agreement with the previous study, in which the Higgs-mass likelihood was a simple gaussian function centered about the measured CMS value, with experimental and theoretical uncertainties added in quadrature. The present likelihood function is instead determined by the sum of the χ 2 contributions of the individual Higgs searches, encoded in the HiggsSignals program. Note that the two 3 To be precise, the A-resonance region is absent not because it is disfavored by any particular constraint, but because at large tan β SoftSusy easily incurs negative values of the DR pseudoscalar mass squared, m 2 A (DR), during the iterative procedure of RGE running. The matter was solved in earlier versions of the program by switching to the pole mass at each iteration while looking for convergence. It is debatable whether such a solution is enough to produce the correct EWSB. Thus, following the default setting in recent versions of SoftSusy, we have decided not to include the points of the A-resonance region for µ < 0. We also abstain from showing a direct comparison with the results of [16] in this case, as they were obtained with an earlier modified version of SoftSusy. main peaks in the distribution, characteristic of the A-resonance region about 124-125 GeV, and of the ∼ 1 TeV higgsino region for larger m h , are now much more in agreement with each other than in the previous study. This is the effect of including the higher order Higgs corrections: there are virtually no regions left in the parameter space for which constraints other than the Higgs searches push the posterior distribution toward m h < 123 GeV.
The equivalent distribution for the case with µ < 0 is shown in Fig. 4(b). In Fig. 5 we show the marginalized 1D posteriors for the heavy Higgs bosons and a selection of superpartner masses for µ > 0. Again, the dashed blue line in the figures shows the distribution for the scan of Ref. [16].
In Fig. 5(a) we show the pdf for the mass of the lightest neutralino. The posterior presents three main modes, corresponding to the regions defined in Fig. 3(a). From the left to the right one can can see: the stau-coannihilation region, with 0.3 TeV m χ 0.6 TeV, subtending approximately 1% of the total probability; the A-resonance region, 0.6 TeV m χ 0.9 TeV, with a probability of ∼ 30%; and the ∼ 1 TeV higgsino region for m χ ∼ > 0.9 TeV, with ∼ 69% probability. The inclusion of higher order corrections to the Higgs mass has caused the shift of a substantial fraction of posterior probability to the Aresonance region. As the dashed blue line shows, the ∼ 1 TeV higgsino region was strongly favored in [16], featuring ∼ 94% of the total probability, while the remainder was split in approximately equal parts between the other two regions. Note also that the average m χ in the ∼ 1 TeV higgsino region is slightly larger than in [16], as the PLANCK-measured value of the relic density is a little larger than the one measured by WMAP [96].
The 1D pdf for the heavy Higgs masses is shown in Fig. 5(b). As could be expected, the distribution features a sharp peak in the A-resonance region, for m A ≈ 2m χ 2.5 TeV. The ∼ 1 TeV higgsino region is instead characterized by a much broader range of values, extending up to ∼ 15 TeV. We will show below that a large fraction of the A-resonance regions is within the reach of Higgs searches at the LHC 14 TeV run.
The 1D posterior distributions for the mass of the lightest stop, mt 1 , and that of the left-handed first and second generation squarks, generically indicated with mũ L , are shown in Figs. 5(c) and 5(d), respectively. While the lightest squark masses in the figures, typical of the stau-coannihilation region, are now disfavored by the present limits from direct SUSY searches at the LHC, the increased relevance of the A-resonance region, which features in general lighter squarks than the ∼ 1 TeV higgsino region, leads to a moderate optimism for squark detection in future-generation colliders. In particular, by comparing the solid red and dashed blue lines in, e.g., Figs. 5(c) and 5(a), one can see that in [16] there was a ∼ 30% of probability favoring mt 1 ∼ > 8 TeV (with m χ ∼ > 1 TeV) that has now been virtually erased. On the other hand, the parameter space featuring mt 1 4 TeV (with m χ 0.8 TeV) is now favored by roughly the same odds.
Equivalently, one can see in Fig. 5(e), where we show the 1D pdf for the gluino mass mg, that the increased relevance of the A-resonance region leads to the emergence of a new peak in probability at mg 3 − 4 TeV.
Finally, we show in Fig. 5(f) the 1D posterior for the lightest chargino mass, m χ ± 1 . The bulk of the probability is subtended by the ∼ 1 TeV higgsino region, in which the lightest chargino is also higgsino-like and almost degenerate with the neutralino, in the To the left and to the right of this larger mode, one can see the modes for the stau-coannihilation and A-resonance region, respectively. In both of them, the neutralino is bino-like, the chargino wino-like, and one finds m χ ± 1 ≈ 2m χ . An ATLAS study [97] of the sensitivity reach for direct SUSY searches at the LHC 14 TeV run showed that the chances of probing in this way squark masses typical of the A-resonance region are scant, to say the least. For example, with 3000 fb −1 of integrated luminosity, 0-and 1-lepton searches for third generation squarks have the potential, when combined, to exclude at the 95% C.L. simplified models with stop next-to-LSP (NLSP) up to mt 1 1.4 − 1.5 TeV for m χ 0.6 TeV . However, it was shown in [98] that if the same luminosity were obtained at a future 33 TeV proton collider, one could exclude at the 95% C.L. simplified models with gluino NLSP up to mg 5 TeV for m χ 2 TeV, or first-two generation squark NLSP up to mũ L 3.5 TeV for m χ 1 TeV.
The reach for the CMSSM is going to be reduced with respect to the simplified models, due to complex decay chains that include intermediate charginos and neutralinos. Nevertheless, the same paper [98] also showed that 3000 fb −1 in a 100 TeV machine can extend the sensitivity for gluino NLSP to mg 12 TeV for m χ 4 TeV, or first-two generation squark NLSP up to mũ L 8 TeV for m χ 2 TeV.
Obviously, it seems that the ∼ 1 TeV higgsino region of the CMSSM remains for the most part beyond the direct reach of conceivable future colliders. Note, however, that it was shown in [33] that this is not necessarily the case when the assumptions of GUT-scale universality are relaxed.
For µ < 0 the 1D distributions of particle masses share identical features with the positive µ case with the exception that the peaks associated with the A-resonance region described above are absent. Since this generally leaves only posterior probability in the region of large superpartner masses far beyond the reach of the LHC we do not show these distributions.
In Fig. 6(a) we show the marginalized 2D pdf projected to the (m A , tan β) plane. In the A-resonance region, characterized by m A < 2.5 TeV and tan β > 45, the posterior appears to be well localized. In the CMSSM, this limited range of m A and tan β values is a proper feature of the A-resonance region, as was extensively explained in [16], namely large tan β value and neutralino not excessively heavy must conspire to produce a region of resonance, m A ≈ 2 m χ , and a cross section large enough to yield the relic density measured at PLANCK. One can see that m A and tan β are not as tightly constrained for the two remaining modes, so that the posterior spreads over a broad range of values. In particular, the stau-coannihilation region is localized in m A , m A 1.5 − 2 TeV, but not in tan β; the ∼ 1 TeV higgsino region covers instead the majority of the parameter space with m A ∼ > 2.5 TeV, tan β ∼ > 5. To make this feature more visible we superimposed in the figure a sample of points drawn from the posterior distribution.
It was shown in [16] that, since the points of the A-resonance region are well localized in the (m A , tan β) plane, the whole region can be easily tested through precise measurement of BR (B s → µ + µ − ), which is proportional to tan 6 β/m 4 A . Here, we show that the same features also make a large fraction of the points testable at the LHC through Higgs searches in the τ + τ − channel.
In Fig. 6(b) we show a zoomed-in fraction of the (m A , tan β) plane. The limits from direct A → τ + τ − searches at CMS with ∼ 17 fb −1 [100] are included in HiggsBounds. In

Prospects for dark matter detection
In Fig. 7(a) we show the 2D posterior distribution in the (m χ , σ SI p ) plane for µ > 0. The different regions are well separated and can be identified from left to right as the staucoannihilation, A-resonance and ∼ 1 TeV higgsino regions. We show the current best upper limit from LUX 90% C.L. as a red solid line, the previous one from XENON100 as a gray dot-dashed line, and the projected sensitivity of XENON-1T [103] as a magenta dashed line. The bino-like neutralino typical of the stau-coannihilation and A-resonance regions has a suppressed coupling to the nucleus, so that both regions lie well below the current LUX bound and it is very unlikely they will be tested, even with the improved sensitivity of XENON-1T. In contrast, the ∼ 1 TeV higgsino region lies almost entirely within the projected XENON-1T sensitivity. The entire 68% and nearly all of the 95% credibility region have the potential to be probed in the next few years, encompassing about 70% of the points in the scan. This makes dark matter direct detection searches the predominant tool for exploration of the CMSSM.
In the CMSSM the largest cross section values, σ SI p ∼ > 10 −8 pb, are obtained in the focus point region. One can see the beginning of the horizontal branch joining the higgsino and focus point regions, at m χ 0.7 − 0.8 TeV. The effect of the LUX limit in the likelihood is visible, as the credibility region is cut off rapidly after crossing the 90% C.L. bound, shown in red. In contrast to [16], this causes the focus point region to be disfavored by the scan. In the µ < 0 scenario we obtain the same results albeit with the absence of the A-resonance region. The sign of the µ parameter has little impact on σ SI p for the neutralino and the ∼ 1 TeV higgsino region with µ < 0 can also be entirely probed by XENON-1T.
In Fig. 7(b) we show the 2D posterior distribution in the (m χ , σv) plane. The node at σv 10 −28 cm 3 /s is the stau-coannihilation region, which has a much reduced σv in the present day due to the absence of co-annihilations with the stau NLSP, which are instead only present in the early Universe. The A-resonance and ∼ 1 TeV higgsino regions are visible at larger σv, from left to right, respectively. The A-resonance region is characterized by a broad range of cross section values, with a deep funnel at 95% credibility that extends down to σv 10 −28 cm 3 /s. This corresponds to a large resonant effect in the early Universe when the neutralinos are distributed thermally, but the present value of σv is small since the colliding neutralinos have insufficient energy to produce the pseudoscalar on shell (see, e.g., Appendix B in [31]). σv is reduced by orders of magnitude in this funnel and is effectively impossible to probe via indirect detection.
As was the case for direct detection, the ∼ 1 TeV higgsino region presents a particularly promising target for indirect detection since the annihilation cross section is restricted to a small range close to the thermal value compared to other dark matter candidates in the MSSM which can have much lower annihilation cross sections. The magenta dashed and dot-dashed lines in Fig. 7(b) show the expected sensitivity of CTA derived in Sec. 2 under the assumptions of the NFW [105] and Einasto [106] halo profile, respectively. The dotted line shows the projected sensitivity of CTA to the W + W − final state, as obtained in Ref. [104] under a more optimistic setup including more telescopes in the array. As previously discussed, limits on single final states may not automatically exclude all points in the posterior since the neutralino will usually annihilate into several different final states depending on its mass and composition. The W + W − final state does however provide a good approximation in the ∼ 1 TeV higgsino region and points in this region lying above the W + W − line have the potential to be constrained. We note that current limits from the Cherenkov telescope array HESS [83] are approximately an order of magnitude larger than the projected CTA sensitivity and so do not constrain the posterior regions found.
One can see that the derived CTA limits lie just above above the 68% credibility posterior region for either choice of dark matter profile, but significant improvements to the limits are possible by improving the experimental setup. It should be noted that a factor of five improvement in the model independent limit on the number of observed gamma rays would be sensitive to the entire ∼ 1 TeV higgsino region and to the bulk of the A-resonance region, thus the vast majority of the favored points in the CMSSM.
The higgsino and stau-coannihilation regions in the negative µ case share the same properties as the positive µ case and have the same prospects for detection, we therefore do not show their distribution here.

Posterior distributions and prospects for collider searches
We proceed now to the analysis of the NUHM. The parameters m 0 , m 1/2 , A 0 , and tan β were scanned in the same ranges as in the CMSSM. The parameters m 2 H d and m 2 Hu were allowed to assume negative values at the GUT scale; see Table 2. We limit ourself to the case with µ > 0, which, as was seen for the CMSSM, presents a greater number of solutions. One must keep in mind that the solutions with µ < 0 can generally be mapped to a subset of the ones we present in here, without novel phenomenological features.
In Fig. 8(a) we show the marginalized 2D posterior in the (m 0 , m 1/2 ) plane. The 68% and 95% credible regions are indicated by inner and outer solid contours, respectively. In this and the following figures we superimpose on the clearly marked credible regions a set of points drawn from the posterior distribution. We include those points since, unlike in the CMSSM, the points that satisfy the relic density constraint are not always found in regions of parameter space well separated along different mechanisms of neutralino annihilation. Thus, the distribution and position of the points in the plots highlight details not always easy to infer from the contours and help indicate where additional solutions beyond the 95% credibility regions can be found. The mechanisms to reduce the relic density are for the most part in common with the CMSSM: stau co-annihilation and A-resonance of bino-like neutralinos, and annihilation and co-annihilation of ∼ 1 TeV higgsino-like neutralinos and charginos. We shall see, though, that the NUHM also presents some additional ways of obtaining the correct relic density. Moreover, all of those mechanisms can be obtained for m 0 not too large, in contrast with the ∼ 1 TeV higgsino region of the CMSSM, thanks to the additional freedom in the Higgs sector. Thus the posterior shows a more compact shape in (m 0 , m 1/2 ) plane, due also to the effect of log prior distributions. Had we used flat priors, volume effects would inflate the region of large m 0 and m 1/2 and therefore increase the importance of the ∼ 1 TeV higgsino region in the NUHM.
The marginalized posterior in the (A 0 , tan β) plane is shown in Fig. 8(b). As was the case for the CMSSM, the solutions tend to be distributed over the entire tan β range, but now favor relatively smaller values of |A 0 | than in previous scans.
In Fig. 8(c) we show the marginalized 2D pdf in the (m Hu ,m H d ) plane. 4 One can see here a previously unexplored 95% credibility region featuring negative values form Hu at the GUT scale and, for the majority of the points involved, alsom H d < 0 .
Large negative values of m 2 Hu at the GUT scale lead to large negative value for the same parameter at M SUSY . Through the EWSB condition, these points thus feature very large values of µ, up to ranges previously unexplored in NUHM analyses. We show the marginalized 2D pdf in the (µ, m A ) plane in Fig. 8(d). The described solutions can be seen on the lower right end of the plot, for values of µ that can be as large as 9 TeV. 5 The correct relic density for these points is obtained through mechanisms of staucoannihilation. In fact, values of µ so large strongly enhance the coupling of the lightest stau to the H u component of the lightest Higgs, thus increasing the efficiency of the annihilation channelττ → hh. Theττ h vertex, proportional to µ, leads to a µ 4 enhancement of the annihilation cross section, which becomes the dominant mechanism when the lightest stau and neutralino are almost degenerate in mass. We show in Fig. 9(a) the 2D pdf in the (m χ , mτ 1 ) plane. One can see that because of the above considerations, stau-coannihilation in the NUHM is efficient up to m χ 2 TeV, thus significantly extending the range observed in the CMSSM, or in previous studies performed with more limited ranges of µ [11,14]. Hu and m 2 H d , and at the weak scale, µ 1 TeV. Thus, as was the case for the CMSSM, in the NUHM the largest number of solutions belong to the ∼ 1 TeV higgsino region. The predominance of this region was also shown in Ref. [14], where it was the only region found, due to their choice of input parameters and prior ranges. The extended stau-coannihilation region shown in Figs. 8 and 9 is instead a novel finding of this study.
Moreover, as was mentioned at the beginning of this section, in the NUHM there are also a significant number of solutions for which the neutralino annihilates via the resonance with heavy Higgs bosons, as already pointed out in [16,30]. We show in Fig. 9(b) the 2D pdf in the (m χ , m A ) plane, which shows the presence of many points at m A ≈ 2m χ . Those points cannot be identified as easily in other plots: for example, in Fig. 8(c) they are shown 4 HeremH u andmH d refer to the signed square root of the absolute value of m 2 Hu and m 2 H d , respectively. E.g.,mH u = m 2 Hu / |m 2 Hu |. 5 It is clear that these solutions present uncomfortably large values of EW fine tuning due the large µ parameter, so that they might be unappealing from a theoretical point of view. However, in this paper we are only concerned with the existence of viable phenomenological solutions, independently of theoretical considerations. We will therefore treat these solutions without further mentioning the fine-tuning issue. as diffuse points lying between the two high posterior probability modes described above, and as a subset of points in the right hand mode restricted tom H d < 4 TeV (above this value m 2 H d drives m A to be too large to find solutions with m A ≈ 2m χ ). We point out here that, while in the CMSSM the points of the A-resonance region feature neutralinos with very large bino composition, and very large tan β values, this is not always the case in the NUHM. Thus, while in the CMSSM the main annihilation channel for those points is χχ → bb, many of the A-resonance points with m χ > 1.2 TeV in Fig. 9(b) feature much larger higgsino fraction and moderate tan β values, so that the correct relic density is obtained in a combined fashion: with tt final states in addition to bb, and through resonance with the heavy scalar H, degenerate with A, in addition to the pseudoscalar. As we shall see in Sec. 4.2 this fact has important consequences for dark matter direct detection. Figure 9(b) neatly shows the different annihilation mechanisms described above: the large concentration of points at m χ 1 TeV gives the ∼ 1 TeV higgsino region; at m A ≈ 2m χ there is the strip of points belonging to the just-described A/H-resonance region, which induces a lobe in the 95% credible region of the posterior for m χ ∼ > 1.2 TeV; and, finally, the stau-coannihilation region, which produces a lobe in the posterior with m χ 1 TeV, but can in fact extend up to m χ 2 TeV.
We show in Fig. 10 the 1D pdf distribution of the lightest Higgs mass, m h . The black dot-dashed line shows the distribution obtained for the CMSSM with µ > 0 for comparison. One can see that the posterior is prevalently uni-modal due to the statistical dominance of the ∼ 1 TeV higgsino region in the NUHM.
In Fig. 11 we present the marginalized 1D posterior distributions for the heavy Higgs bosons and a selection of superpartner masses. As a comparison we show the correspond-  Figure 11(a) shows the distribution for m χ . One can see one single peak at m χ 1 TeV, indicating that in the NUHM the ∼ 1 TeV higgsino region dominates the posterior probability, with the other two regions significantly less favored and spread over a broad range of m χ values.
In Fig. 11(b) we show the distribution of the heavy Higgs masses. As mentioned above, the A/H-resonance region extends over a large range of m A values, and the posterior probability associated with it is much reduced relative to the CMSSM. As a consequence, values of m A > 2 − 3 TeV, typical of the ∼ 1 TeV higgsino region, are instead favored in the NUHM, thus making the prospects for sensitivity at the LHC (A → τ + τ − direct searches) much bleaker than in the CMSSM.
Analogous conclusions pertain to the prospects for LHC observation of the other SUSY particles. In Figs. 11(c) and 11(d) we show the distributions for the lightest stop mass and squark masses for the first two generations, respectively. In Fig. 11(e) we show the distribution for the gluino mass. The bulk of the squark mass distributions are peaked around mass values significantly smaller than in the corresponding ∼ 1 TeV higgsino region of the CMSSM, as the posterior does not extend as much in m 0 , but they are still well outside the most optimistic reach for direct detection at the LHC.
One observes some solutions in common with the CMSSM, in the stau-coannihilation region, characterized by mt 1 1.5 TeV, mũ L 3 TeV, or mg 3 TeV, and a neutralino that can be as light as 0.4 TeV. Those might begin to be probed at the 14 TeV run of the LHC. However, as was explained above, the stau-coannihilation region in the NUHM extends significantly with respect to the CMSSM, reaching quite large m 1/2 values. Thus, it favors heavier gluinos, neutralinos, and scalars, and the statistical weight of the parameter space in reach of the LHC is much reduced.
Finally, we show for completeness in Fig. 11(f) the 1D pdf for the lightest chargino. like χ ± 1 , accompanied by a lower tail that extends to larger mass values, typical of the wino-dominated charginos.

Prospects for dark matter detection
In Fig. 12(a) we show the marginalized 2D posterior distribution in the (m χ , σ SI p ) plane. As was the case in the CMSSM, shown in Fig. 7(a), one can easily identify the ∼ 1 TeV higgsino region as the large 68% and 95% credible region at m χ 1 − 1.2 TeV right below the LUX limit.
The characteristics of this region are largely independent of the model, so that the prospects for detection are similar to the CMSSM. However, the relative probability of this region is larger in the NUHM, being greater than 90%, versus approximately 70% of the total probability in the same region of the CMSSM.
On top of this, as was mentioned when discussing Fig. 9(b), many of the solutions in the A/H-resonance region of the NUHM feature mixed composition, bino-higgsino neutralinos with m χ ∼ > 1.2 TeV, with consequently enhanced couplings to the nucleus. Those points can be seen in Fig. 12(a) scattered below the LUX limit, well in reach of the XENON-1T sensitivity, shown with a magenta dashed line, On the negative side, one can see that the remaining 95% credible region, the staucoannihilation region, now extends to much smaller values of σ SI p and for neutralinos heavier than m χ 0.8 TeV it lies below the onset of irreducible neutrino background [107,108] calculated in [109], shown with a black dotted line. For σ SI p below the black dotted line the background of atmospheric and diffuse supernova neutrinos becomes important, so that the sensitivity scales with square root of exposure, making the neutralino more difficult to detect via direct detection experiments.
Finally, we show in Fig. 12(b) 2D posterior distribution in the (m χ , σv) plane. As was explained in Sec. 2 the estimated CTA sensitivity is indicatively shown for the NFW and Einasto halo profile as a magenta dashed and dot-dashed line, respectively. One must remember that the sensitivity of the individual points in the scan strongly depends on the annihilation final states, so that the lines in Fig. 12(b) must be taken with care. However, the indicated sensitivity is robust for final states characterized by gauge bosons, which are very typical of the ∼ 1 TeV higgsino region, shown in the figure as the predominant 68% and 95% posterior region.
Thus, one can extend to the NUHM the conclusion already stated for the CMSSM in Sec. 3.2. The projected sensitivity in the minimal configuration studied here 6 seems to fall just short of biting significantly into the parameter space of the model. But extended configurations considered in the literature or, alternatively, an improvement in the estimated sensitivity, have the potential to deeply probe the bulk of the model's parameter space, thus yielding a complementary test with respect to direct detection searches.

Summary and conclusions
In this paper we performed a Bayesian analysis of the CMSSM and the NUHM. We presented the 68% and 95% credible regions of the marginalized 2D posterior pdf and the 1D distributions of relevant parameters and observables in light of the latest experimental constraints and updated numerical tools.
In particular, we updated the results of our previous study [16] by a) including the corrections to the lightest Higgs mass beyond the 2-loop order using FeynHiggs v2.10.0, which calculates the leading and next-to-leading log corrections in the top/stop sector resummed at all orders in perturbation theory; b) including in the likelihood function the latest constraints from direct SUSY searches at the LHC with ∼ 20 fb −1 at 8 TeV; and c) including in the likelihood function the most recent constraints from direct detection of dark matter at LUX.
We find that the higher-order corrections to the Higgs mass induce modifications to the posterior probability distribution with respect to [16]. The correct value of the Higgs boson mass now requires an M SUSY in general lower, so that the 95% credible regions do not extend beyond m 0 12 TeV in the CMSSM. Moreover, regions of the parameter space that in the past struggled to produce a ∼ 126 GeV Higgs mass, can now do it more easily. As a consequence, we observe increased statistical relevance of the A-resonance region of the CMSSM relative to [16], with approximately 30% of the total probability. This improves the chances for direct observations of the pseudoscalar Higgs at the LHC 14 TeV run, in the A → τ + τ − channel. It also potentially favors direct testing in sparticle searches at future, higher-energy proton colliders.
On the other hand, the bulk of the probability still lies in the ∼ 1 TeV higgsino region, comprising ∼ 70% of the total in the CMSSM and ∼ 90% in the NUHM. Given the almost pure higgsino nature of the dark matter candidate in this region the prospect for probing the vast majority of the parameter space of both models through dark matter detection searches is enticing.
The constraining power of future 1-tonne direct detection experiments like XENON-1T on the parameter space of the CMSSM and the NUHM has been long known, and is confirmed once more in here. In this study we also showed that indirect detection of dark matter through γ-rays from the GC at CTA is a realistic possibility in the CMSSM and the NUHM. We applied the results of Ref. [36] for the sensitivity of CTA to several annihilation final states to the case of annihilation to multiple final states, as is the MSSM. We find that the configuration studied in [36] falls just short of biting significantly into the parameter space, but a factor of 5 improvement on the sensitivity can probe ∼ 90% of the favored parameter space in both models.
In summary, in both models all the regions favored by the latest constraints show good prospects for future observation. In the CMSSM, the stau-coannihilation region (1% of the total pdf) will be most likely probed in its entirety through direct SUSY searches at the LHC 14 TeV run; ∼ 50% of the A-resonance region (corresponding to 15% of the total pdf) might be probed in Higgs searches at the LHC, while it was shown in [16] that the whole region is also very sensitive to improvements in the measurement of BR (B s → µ + µ − ); the ∼ 1 TeV higgsino region (70% of the pdf) will be probed via dark matter direct detection in 1-tonne experiments. Simultaneously, optimistic but not unrealistic improvements in the projected sensitivity of CTA might potentially test the whole ∼ 1 TeV higgsino region and almost all of the A-resonance region.
This becomes even more important in the NUHM, where dark matter searches become the privileged instrument to probe the parameter space. In particular the largest part of the ∼ 1 TeV higgsino region and a large number of A/H resonance solutions, that together cover approximately ∼ 90% of the favored parameter space can be simultaneously probed at 1-tonne detectors and at CTA, if the estimated sensitivity of the latter increases as shown in this study. A Impact of a recent calculation of the sensitivity of CTA In a recent paper [110] we calculated the projected sensitivity of CTA to the WIMP annihilation cross section, under the assumption of the Einasto or the NFW DM halo profile. We used a binned likelihood function, and the details of the calculation are presented in Appendix A of [110]. Our likelihood function leads to a higher sensitivity than the one obtained in [36], which was used in this paper to draw the projected limits shown in Figs. 2, 7(b), and 12(b). The result of our calculations for several individual final states in the MSSM, assuming the Einasto profile and 500 hours of observation, can be found in Fig. 14 of [110].
In Fig. 13(a) we show the new W + W − and bb projected sensitivities, obtained using the binned likelihood method, in the (m χ , σv) plane of the CMSSM. The W + W − final state bound provides a rough estimate of the exclusion reach for the ∼ 1 TeV higgsino region, whereas the bb bound applies to the A-resonance region. In Fig. 13(b) we show the same for the NUHM. Figure 13 shows that the binned likelihood method leads to significantly improved sensitivity relative to that of Ref. [36], which was presented in Figs. 7(b) and 12(b).
In the remainder of this appendix we show that, in light of the results of [110], under reasonable assumptions the full extent of the 95% credible region of the CMSSM will be probed by a limited number of upcoming experiments. These are, by increasing mass scale: 1. CMS and ATLAS direct SUSY searches at the LHC Run II; and 95% credible regions are shown by the inner and outer contours, respectively. Points are distributed according to the posterior probability. The projected LHC Run II 95% C.L. exclusion line from Ref. [111] is shown in red solid for reference. Blue points lie within sensitivity for direct SUSY searches, gray points are unconstrained. (b) Same as (a) except that points in magenta are sensitive to future measurements of BR Bs → µ + µ − , as described in Ref. [16]. (c) Same as (a) except that points in orange lie within sensitivity of tonne-scale underground DM detectors. (d) Same as (a) except that points in green lie within sensitivity of CTA to γ rays from DM annihilations, as calculated in Ref. [110].
The impact of each experiment's projected sensitivity on the parameter space of the CMSSM is shown in the four panels of Fig. 14. In Fig. 14(a) we show a sample of points distributed according to the posterior probability, whose 68% and 95% credible regions are shown by the inner and outer contours, respectively. The points in blue lie within the projected sensitivity of searches for squarks and gluinos at the LHC Run II calculated in Ref. [111], whereas the gray points remain unconstrained. The expected limit from the 0-1 lepton + jets + missing energy searches with 300 fb −1 at 14 TeV is shown as a red solid line. As is well known, Run II will be sensitive to most of the remaining part of the stau-coannihilation region, presently not excluded by the LHC 8 TeV run.
As was explained in Ref. [16], one will exclude the 95% credible posterior region corresponding to the A-resonance region of the CMSSM if the measurement of BR (B s → µ + µ − ) eventually converges to its SM expectation with an error of ∼ 5%, and at the same time the theoretical uncertainties reach approximately the same precision. In Fig. 14(b) we show in magenta the points that will be excluded under the projection considered in Ref. [16]: BR (B s → µ + µ − ) proj = (3.50 ± 0.17 ± 0.17) × 10 −9 , with experimental and theoretical uncertainties added in quadrature. As was mentioned in Sec. 3, it should be noted that there will be considerable overlap between the constraint from BR (B s → µ + µ − ) and searches for a heavy Higgs decaying to tau pairs.
The projected 90% C.L. sensitivity for XENON-1T in the (m χ , σ SI p ) plane of the CMSSM was shown in Fig. 7(a) as a dashed magenta line. This corresponds to the excluded points in the (m 0 , m 1/2 ) plane that are presented in orange in Fig. 14(c). XENON-1T and other tonne-scale detectors will probe the ∼ 1 TeV higgsino region in its near entirety, with the exception of the points at large m 0 and m 1/2 .
We finally come to CTA's sensitivity to γ rays from the GC. We applied the binned likelihood function constructed in [110] to the points of the CMSSM, under the assumption of the Einasto profile for the DM distribution in the GC. The points of the (m 0 , m 1/2 ) plane excluded at the 95% C.L. by the likelihood function with 500 hours of observation are shown in green in Fig. 14(d). CTA is going to provide a strong constraint in the ∼ 1 TeV higgsino region, as well as on the majority of the A-resonance region's points. The sensitivity of CTA reaches the part of the ∼ 1 TeV higgsino region that lies outside the sensitivity of tonne-scale underground DM detectors and provides complementary probe to the rest of the parameter space with the exception of the stau-coannihilation region.
To conclude, in Fig. 15 we show the combination of the constraints presented in the panels of Fig. 14. We want to point out that there is no single gray point left in the figure. Since the posterior sample shown contains approximately 20000 points, this implies that even regions well beyond the 95% credible level will be constrained. In addition, Fig. 15 highlights the considerable amount of overlapping between the parameter space probed by CTA and that of other experiments, so that for most of the parameter space detection/exclusion will not rely on a single measurement.
In this regard, we want to point out that if one adopts a flatter profile than the Einasto for the DM distribution in the halo, the above projection for CTA will inevitably be weakened. We have checked that under the NFW profile assumption most points belonging to the A-resonance region and those included in the 68% credible part of the ∼ 1 TeV higgsino region will be excluded. However, most points belonging to the 95% part of the ∼ 1 TeV higgsino region, and those characterized by even larger m 0 and m 1/2 will be beyond reach. Even so, CTA is going to provide an invaluable instrument for complementary testing of the regions of parameter space shown in Figs. 14(b) and 14(c), that will be probed at the LHC and in tonne-scale underground detectors.