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

TL;DR

This paper discusses how the $B^0_s o \mu^+\mu^-$ decay's effective lifetime can serve as a clean, complementary observable for detecting new physics beyond the Standard Model, especially considering the effects of the decay width difference $\Delta\Gamma_s$.

Contribution

It introduces the effective $B^0_s o \mu^+\mu^-$ lifetime as a new observable for new physics searches and provides formulae to incorporate $\Delta\Gamma_s$ effects in analyses.

Findings

$\Delta\Gamma_s$ impacts the extraction of the branching ratio.

The effective lifetime $ au_{\mu^+\mu^-}$ offers a theoretically clean probe for new physics.

Measurement of $ au_{\mu^+\mu^-}$ is feasible at upgraded LHC experiments.

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.