Supersymmetry confronts $B_s → μ^+μ^-$ : Present and future status

The purely leptonic rare decay Bs -> mu+mu- is very sensitive to supersymmetric contributions which are free from the helicity suppression of its Standard Model diagrams. The recent observation of the decay by the LHCb experiment and the first determination of its branching fraction motivate a review of their impact on the viable parameter space of supersymmetry. In this paper we discuss the implications of the present and expected future accuracy on BR(Bs -> mu+mu-) for constrained and unconstrained MSSM scenarios, in relation to the results from direct SUSY searches and the Higgs data at the LHC. While the constraints from BR(Bs -> mu+mu-) can be very important in specific SUSY regions, we show that the current result, and even foreseen future improvements in its accuracy, will leave a major fraction of the SUSY parameter space, compatible with the results of direct searches, unconstrained. We also highlight the complementarity of the Bs -> mu+mu- decay with direct SUSY searches.