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

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