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

Supersymmetry confronts Bs -> mu+mu-: Present and future status