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We have recently seen new upper bounds for $B^0_s\to \mu^+\mu^-$, a key decayto search for physics beyond the Standard Model. Furthermore a non-vanishingdecay width difference $\Delta\Gamma_s$ of the $B_s$ system has been measured.We show that $\Delta\Gamma_s$ affects the extraction of the $B^0_s\to\mu^+\mu^-$ branching ratio and the resulting constraints on the New Physicsparameter space, and give formulae for including this effect. Moreover, wepoint out that $\Delta\Gamma_s$ provides a new observable, the effective$B^0_s\to \mu^+\mu^-$ lifetime $\tau_{\mu^+\mu^-}$, which offers atheoretically clean probe for New Physics searches that is complementary to thebranching ratio. Should the $B^0_s\to \mu^+\mu^-$ branching ratio agree withthe Standard Model, the measurement of $\tau_{\mu^+\mu^-}$, which appearsfeasible at upgrades of the LHC experiments, may still reveal large New Physicseffects.

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