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The B_s to mu+ mu- decay plays an outstanding role in tests of the StandardModel and physics beyond it. The LHCb collaboration has recently reported thefirst evidence for this decay at the 3.5 sigma level, with a branching ratio inthe ballpark of the Standard Model prediction. Thanks to the recentlyestablished sizable decay width difference of the B_s system, anotherobservable, A^mumu_DeltaGamma, is available, which can be extracted from thetime-dependent untagged B_s to mu+ mu- rate. If tagging information isavailable, a CP-violating asymmetry, S_mumu, can also be determined. These twoobservables exhibit sensitivity to New Physics that is complementary to thebranching ratio. We define and analyse scenarios in which these quantitiesallow us to discriminate between model-independent effective operators andtheir CP-violating phases. In this context we classify a selection of popularNew Physics models into the considered scenarios. Furthermore, we considerspecific models with tree-level FCNCs mediated by a heavy neutral gauge boson,pseudoscalar or scalar, finding striking differences in the predictions ofthese scenarios for the observables considered and the correlations among them.We update the Standard Model prediction for the time-integrated branching ratiotaking the subtle decay width difference effects into account. We find (3.56+/- 0.18) x 10^-9, and discuss the error budget.

Probing New Physics with the B_s to {\mu}+ {\mu}- Time-Dependent Rate