Abstract: We present new global fits of the constrained Minimal Supersymmetric Standard Model (cMSSM), including LHC 1/fb integrated luminosity SUSY exclusion limits, recent LHC 5/fb constraints on the mass of the Higgs boson and XENON100 direct detection data. Our analysis fully takes into account astrophysical and hadronic uncertainties that enter the analysis when translating direct detection limits into constraints on the cMSSM parameter space. We provide results for both a Bayesian and a Frequentist statistical analysis. We find that LHC 2011 constraints in combination with XENON100 data can rule out a significant portion of the cMSSM parameter space. Our results further emphasise the complementarity of collider experiments and direct detection searches in constraining extensions of Standard Model physics. The LHC 2011 exclusion limit strongly impacts on low-mass regions of cMSSM parameter space, such as the stau co-annihilation region, while direct detection data can rule out regions of high SUSY masses, such as the Focus-Point region, which is unreachable for the LHC in the near future. We show that, in addition to XENON100 data, the experimental constraint on the anomalous magnetic moment of the muon plays a dominant role in disfavouring large scalar and gaugino masses. We find that, should the LHC 2011 excess hinting towards a Higgs boson at 126 GeV be confirmed, currently favoured regions of the cMSSM parameter space will be robustly ruled out from both a Bayesian and a profile likelihood statistical perspective.

Abstract: Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling techniques are geared towards Bayesian inference, they have also been used to estimate frequentist confidence intervals based on the profile likelihood ratio. We investigate the performance and appropriate configuration of MULTINEST, a nested sampling based algorithm, when used for profile likelihood-based analyses both on toy models and on the parameter space of the Constrained MSSM. We find that while the standard configuration previously used in the literarture is appropriate for an accurate reconstruction of the Bayesian posterior, the profile likelihood is poorly approximated. We identify a more appropriate MULTINEST configuration for profile likelihood analyses, which gives an excellent exploration of the profile likelihood (albeit at a larger computational cost), including the identification of the global maximum likelihood value. We conclude that with the appropriate configuration MULTINEST is a suitable tool for profile likelihood studies, indicating previous claims to the contrary are not well founded.

Abstract: We present statistically convergent profile likelihood maps obtained via global fits of a phenomenological Minimal Supersymmetric Standard Model with 15 free parameters (the MSSM-15), based on over 250M points. We derive constraints on the model parameters from direct detection limits on dark matter, the Planck relic density measurement and data from accelerator searches. We provide a detailed analysis of the rich phenomenology of this model, and determine the SUSY mass spectrum and dark matter properties that are preferred by current experimental constraints. We evaluate the impact of the measurement of the anomalous magnetic moment of the muon (g – 2) on our results, and provide an analysis of scenarios in which the lightest neutralino is a subdominant component of the dark matter. The MSSM-15 parameters are relatively weakly constrained by current data sets, with the exception of the parameters related to dark matter phenomenology (M-1, M-2, mu), which are restricted to the sub-TeV regime, mainly due to the relic density constraint. The mass of the lightest neutralino is found to be < 1.5TeV at 99% C.L., but can extend up to 3 TeV when excluding the g – 2 constraint from the analysis. Low-mass bino-like neutralinos are strongly favoured, with spin-independent scattering cross-sections extending to very small values, similar to 10(-20) pb. ATLAS SUSY null searches strongly impact on this mass range, and thus rule out a region of parameter space that is outside the reach of any current or future direct detection experiment. The best-fit point obtained after inclusion of all data corresponds to a squark mass of 2.3 TeV, a gluino mass of 2.1 TeV and a 130 GeV neutralino with a spin-independent cross-section of 2.4 x 10(-10) pb, which is within the reach of future multi-ton scale direct detection experiments and of the upcoming LHC run at increased centre-of-mass energy.