Effective Lifetimes of $B_s$ Decays and their Constraints on the $B_s^0$-$\bar B_s^0$ Mixing Parameters

TL;DR

This paper discusses how measurements of effective lifetimes of $B_s$ meson decays can be used to constrain the $B_s^0$-$ar B_s^0$ mixing parameters, specifically $ riangle ext{Gamma}_s$ and $ ext{phi}_s$, providing a complementary approach to existing methods.

Contribution

It introduces a method to determine $ ext{phi}_s$ and $ riangle ext{Gamma}_s$ from effective lifetime measurements of specific $B_s$ decay modes, enhancing the analysis of $B_s$ mixing.

Findings

Effective lifetime measurements can probe $ riangle ext{Gamma}_s$ and $ ext{phi}_s$.

The method complements existing constraints from other observables.

Recent measurements of $B_s$ decays support the proposed approach.

Abstract

Measurements of the effective lifetimes of $B_s$-meson decays, which only require untagged rate analyses, allow us to probe the width difference $\Delta\Gamma_s$ and the CP-violating phase $\phi_s$ of $B^0_s$-$\bar B^0_s$ mixing. We point out that the dependence of the effective lifetime on non-linear terms in $\Delta\Gamma_s$ allows for a determination of $\phi_s$ and $\Delta\Gamma_s$ given a pair of $B_s$ decays into CP-even and CP-odd final states. Using recent lifetime measurements of $B^0_s\to K^+K^-$ and $B^0_s\to J/\psi f_0(980)$ decays, we illustrate this method and show how it complements the constraints in the $\phi_s$-$\Delta\Gamma_s$ plane from other observables.