How Constrained is the cMSSM?

Abstract: We study the allowed parameter space of the constrained minimal supersymmetric Standard Model (cMSSM) in the light of direct searches, constraints from $B$-physics (including the recent measurement of the branching ratio for $B_s \to \mu^+\mu^-$) and the dark matter relic density. For low or moderate values of $\tan\beta$, the strongest constraints are those imposed by direct searches, and therefore, large areas of the parameter space are still allowed. In the large $\tan \beta$ limit, however, the $B$-physics constraints are more restrictive, effectively forcing the squark and gluino masses to lie close to or above a TeV. A light Higgs boson could dramatically change the allowed parameter space, but we need to know its mass precisely for this to be effective. We emphasize that it is still too early to write off the cMSSM, even in the large $\tan\beta$ limit. Finally we explore strategies to extend the LHC search for cMSSM signals beyond the present reach of the ATLAS and CMS Collaborations.