Bayesian Implications of Current LHC and XENON100 Search Limits for the Constrained MSSM

The CMS Collaboration has released the results of its search for supersymmetry, by applying an alphaT method to 1.1/fb of data at 7 TeV. The null result excludes (at 95% CL) a low-mass region of the Constrained MSSM's parameter space that was previously favored by other experiments. Additionally, the negative result of the XENON100 dark matter search has excluded (at 90% CL) values of the spin-independent scattering cross sections sigma^SI_p as low as 10^-8 pb. We incorporate these improved experimental constraints into a global Bayesian fit of the Constrained MSSM by constructing approximate likelihood functions. In the case of the alphaT limit, we simulate detector efficiency for the CMS alphaT 1.1/fb and validate our method against the official 95% CL contour. We identify the 68% and 95% credible posterior regions of the CMSSM parameters, and also find the best-fit point. We find that the credible regions change considerably once a likelihood from alphaT is included, in particular the narrow light Higgs resonance region becomes excluded, but the focus point/horizontal branch region remains allowed at the 1sigma level. Adding the limit from XENON100 has a weaker additional effect, in part due to large uncertainties in evaluating sigma^SI_p, which we include in a conservative way, although we find that it reduces the posterior probability of the focus point region to the 2sigma level. The new regions of high posterior favor squarks lighter than the gluino and all but one Higgs bosons heavy. The dark matter neutralino mass is found in the range 250 GeV <~ m_Chi1 <~ 343 GeV (at 1sigma) while, as the result of improved limits from the LHC, the favored range of sigma^SI_p is pushed down to values below 10^{-9} pb. We highlight tension between (g-2)_mu and BR(b->sg), which is exacerbated by including the alphaT limit; each constraint favors a different region of the CMSSM's mass parameters.Comment: Accepted by PRD. Added discussions on prior dependence and the p-value. Main conclusions unchanged. 21 pages, 12 figure

Simple and statistically sound recommendations for analysing physical theories

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at Zenodo