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

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 ${\varphi }_s$ of $B_s^0$-${\bar{B}}_s^0$ mixing. We point out that the dependence of the effective lifetime on non-linear terms in $\Delta {\Gamma }_s$ allows for a determination of ${\varphi }_s$ and $\Delta {\Gamma }_s$ given a pair of $B_s$ decays into CP-even and CP-odd final states. Using recent lifetime measurements of $B_s^0\to K^{+}{K}^{-}$ and $B_s^0\to J/\psi f_0(980)$ decays, we illustrate this method and show how it complements the constraints in the ${\varphi }_s$-$\Delta {\Gamma }_s$ plane from other observables.

16 pages, 4 figures

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