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

Abstract

We have recently seen new upper bounds for \(B^0_s\to \mu^+\mu^-\), 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 \(B^0_s\to \mu^+\mu^-\) 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 \(B^0_s\to \mu^+\mu^-\) lifetime \(\tau_{\mu^+\mu^-}\), which offers a theoretically clean probe for New Physics searches that is complementary to the branching ratio. Should the \(B^0_s\to \mu^+\mu^-\) 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.