Bayesian implications of current LHC and XENON100 search limits for the CMSSM

The CMS Collaboration has released the results of its search for supersymmetry, by applying an ${\ensuremath{\alpha}}_{T}$ method to $1.1/\mathrm{fb}$ of data at 7 TeV. The null result excludes (at 95% C.L.) 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% C.L.) values of the spin-independent scattering cross sections ${\ensuremath{\sigma}}_{p}^{\mathrm{SI}}$ as low as ${10}^{\ensuremath{-}8}\text{ }\text{ }\mathrm{pb}$. 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 ${\ensuremath{\alpha}}_{T}$ limit, we simulate detector efficiency for the CMS ${\ensuremath{\alpha}}_{T}1.1/\mathrm{fb}$ analysis and validate our method against the official 95% C.L. 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 ${\ensuremath{\alpha}}_{T}$ is included, in particular, the narrow light Higgs resonance region becomes excluded, but the focus point/horizontal branch region remains allowed at the $1\ensuremath{\sigma}$ level. Adding the limit from XENON100 has a weaker additional effect, in part due to large uncertainties in evaluating ${\ensuremath{\sigma}}_{p}^{\mathrm{SI}}$, which we include in a conservative way, although we find that it reduces the posterior probability of the focus point region to the $2\ensuremath{\sigma}$ 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 $250\text{ }\text{ }\mathrm{GeV}\ensuremath{\lesssim}{m}_{\ensuremath{\chi}}\ensuremath{\lesssim}343\text{ }\text{ }\mathrm{GeV}$ (at $1\ensuremath{\sigma}$) while, as the result of improved limits from the LHC, the favored range of ${\ensuremath{\sigma}}_{p}^{\mathrm{SI}}$ is pushed down to values below ${10}^{\ensuremath{-}9}\text{ }\text{ }\mathrm{pb}$. We highlight tension between $\ensuremath{\delta}(g\ensuremath{-}2{)}_{\ensuremath{\mu}}^{\mathrm{SUSY}}$ and $\mathcal{B}\mathcal{R}(\overline{B}\ensuremath{\rightarrow}{X}_{s}\ensuremath{\gamma})$, which is exacerbated by including the ${\ensuremath{\alpha}}_{T}$ limit; each constraint favors a different region of the CMSSM's mass parameters.