Constrained MSSM favoring new territories: The impact of new LHC limits and a 125 GeV Higgs boson

Abstract

We present an updated and extended global analysis of the constrained MSSM (CMSSM) taking into account new limits on supersymmetry from $\ensuremath{\sim}5/\mathrm{fb}$ data sets at the LHC. In particular, in the case of the razor limit obtained by the CMS Collaboration we simulate detector efficiency for the experimental analysis and derive an approximate but accurate likelihood function. We discuss the impact on the global fit of a possible Higgs boson with mass near 125 GeV, as implied by recent data, and of a new improved limit on $\mathrm{BR}({\mathrm{B}}_{\mathrm{s}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$. We identify high posterior probability regions of the CMSSM parameters as the stau-coannihilation and the $A$-funnel region, with the importance of the latter now being much larger due to the combined effect of the above three LHC results and of dark matter relic density. We also find that the focus point region is now disfavored. Ensuing implications for superpartner masses favor even larger values than before, and even lower ranges for dark matter spin-independent cross section, ${\ensuremath{\sigma}}_{p}^{\mathrm{SI}}\ensuremath{\lesssim}{10}^{\ensuremath{-}9}\text{ }\text{ }\mathrm{pb}$. We also find that relatively minor variations in applying experimental constraints can induce a large shift in the location of the best-fit point. This puts into question the robustness of applying the usual ${\ensuremath{\chi}}^{2}$ approach to the CMSSM. We discuss the goodness-of-fit and find that, while it is difficult to calculate a $p$-value, the $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ constraint makes, nevertheless, the overall fit of the CMSSM poor. We consider a scan without this constraint, and we allow $\ensuremath{\mu}$ to be either positive or negative. We find that the global fit improves enormously for both signs of $\ensuremath{\mu}$, with a slight preference for $\ensuremath{\mu}<0$ caused by a better fit to $\mathrm{BR}(\mathrm{b}\ensuremath{\rightarrow}s\ensuremath{\gamma})$ and $\mathrm{BR}({\mathrm{B}}_{\mathrm{s}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$.