Probing New Physics via the $B_s^0\to {\mu }^{+}{\mu }^{-}$ Effective Lifetime

Abstract

We have recently seen new upper bounds for $B_s^0\to {\mu }^{+}{\mu }^{-}$, a key decay to search for physics beyond the Standard Model. Furthermore a non-vanishing decay width difference $\Delta {\Gamma }_s$ of the $B_s$ system has been measured. We show that $\Delta {\Gamma }_s$ affects the extraction of the $B_s^0\to {\mu }^{+}{\mu }^{-}$ branching ratio and the resulting constraints on the New Physics parameter space, and give formulae for including this effect. Moreover, we point out that $\Delta {\Gamma }_s$ provides a new observable, the effective $B_s^0\to {\mu }^{+}{\mu }^{-}$ lifetime ${\tau }_{{\mu }^{+}{\mu }^{-}}$, which offers a theoretically clean probe for New Physics searches that is complementary to the branching ratio. Should the $B_s^0\to {\mu }^{+}{\mu }^{-}$ branching ratio agree with the Standard Model, the measurement of ${\tau }_{{\mu }^{+}{\mu }^{-}}$, which appears feasible at upgrades of the LHC experiments, may still reveal large New Physics effects.

6 pages, 2 figures, title matches published version in Physical Review Letters

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