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New Physics Contribution to $B_s \to μ^+ μ^-$ within R-Parity Violating Supersymmetric Models

We re-visit the problem of New Physics (NP) contribution to the branching ratio of the $B_s \to μ^+ μ^-$ decay in light of the recent observation of this decay by LHCb. We consider R-parity violating (RPV) supersymmetric models as a primary example - recently one has reported stringent constraints on the products of the RPV coupling constants that account for the $B_s \to μ^+ μ^-$ transition at the tree level. We argue that despite the LHCb measurement of the $B(B_s \to μ^+ μ^-)$ is in a remarkable agreement with the Standard Model (SM) prediction, there is still room for a significant New Physics contribution to the $B(B_s \to μ^+ μ^-)$, as the sign of the $B_s \to μ^+ μ^-$ transition amplitude may be opposite to that of the Standard Model; alternatively the amplitude may have a large phase. We conduct our analysis mainly for the case of real RPV couplings. We find that taking into account the scenario with the sign flip of the $B_s \to μ^+ μ^-$ amplitude (as compared to that of the SM) makes the bounds on the RPV coupling products significantly weaker. Also, we discuss briefly how our results are modified if the RPV couplings have large phases. In particular, we examine the dependence of the derived bounds on the phase of the NP amplitude.