Profile likelihood maps of a 15-dimensional MSSM

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 < 1.5 TeV 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, $\sim 10^{-20}$ 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 $2.4 \times 10^{-10}$ 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.