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.

Abstract: We present a Bayesian analysis of the NUGHM, a supersymmetric scenario with non-universal gaugino masses and Higgs masses, including all the relevant experimental observables and dark matter constraints. The main merit of the NUGHM is that it essentially includes all the possibilities for dark matter (DM) candidates within the MSSM, since the neutralino and chargino spectrum -and composition- are as free as they can be in the general MSSM. We identify the most probable regions in the NUHGM parameter space, and study the associated phenomenology at the LHC and the prospects for DM direct detection. Requiring that the neutralino makes all of the DM in the Universe, we identify two preferred regions around m(chi 10) = 1 TeV, 3 TeV, which correspond to the (almost) pure Higgsino and wino case. There exist other marginal regions (e.g. Higgs-funnel), but with much less statistical weight. The prospects for detection at the LHC in this case are quite pessimistic, but future direct detection experiments like LUX and XENON1T, will be able to probe this scenario. In contrast, when allowing other DM components, the prospects for detection at the LHC become more encouraging – the most promising signals being, beside the production of gluinos and squarks, the production of the heavier chargino and neutralino states, which lead to WZ and same-sign WW final states – and direct detection remains a complementary, and even more powerful, way to probe the scenario.

Abstract: There exists a vast literature examining the electroweak (EW) fine-tuning problem in supersymmetric scenarios, but little concerned with the dark matter (DM) one, which should be combined with the former. In this paper, we study this problem in an, as much as possible, exhaustive and rigorous way. We have considered the MSSM framework, assuming that the LSP is the lightest neutralino, chi(0)(1), and exploring the various possibilities for the mass and composition of chi(0)(1), as well as different mechanisms for annihilation of the DM particles in the early Universe (well-tempered neutralinos, funnels and co-annihilation scenarios). We also present a discussion about the statistical meaning of the fine-tuning and how it should be computed for the DM abundance, and combined with the EW fine-tuning. The results are very robust and model-independent and favour some scenarios (like the h-funnel when M-chi 10 is not too close to m(h)/2) with respect to others (such as the pure wino case). These features should be taken into account when one explores “natural SUSY” scenarios and their possible signatures at the LHC and in DM detection experiments.

Abstract: In this paper, we minimize and compare two different fine-tuning measures in four high-scale supersymmetric models that are embedded in the MSSM. In addition, we determine the impact of current and future dark matter direct detection and collider experiments on the fine-tuning. We then compare the low-scale electroweak measure with the high-scale Barbieri-Giudice measure. We find that they reduce to the same value when the higgsino parameter drives the degree of fine-tuning. We also find spectra where the high-scale measure turns out to be lower than the low-scale measure. Depending on the high-scale model and fine-tuning definition, we find a minimal fine-tuning of 3-38 (corresponding to O(10-1)%) for the low-scale measure, and 63-571 (corresponding to O(1-0.1)%) for the high-scale measure. We stress that it is too early to conclude on the fate of supersymmetry, based only on the fine-tuning paradigm.