Probing New Physics via the $B^0_s\to μ^+μ^-$ Effective Lifetime

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

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