Weak Phase $\gamma$ from $B_s(t)\to K^{+}{K}^{-}$

Abstract

We re-examine the time-dependent rates of $\text{bs}(t)\to K^{+}{K}^{-}$ and $\text{obs}(t)\to K^{+}{K}^{-}$, including a lifetime difference between neutral $\text{bs}$ mass eigenstates. The two rates, normalized by the rate of $\text{bs}\to \text{ko}\text{ok}$, are used to obtain ambiguity-free information on a strong phase and on the weak phase $\gamma$. We discuss the sensitivity of extracting $\gamma$ to the measured quantities, and find that an error of $\pm 10^{\circ }$ in $\gamma$ is possible for a sample of several thousand $\text{bs}(t)\to K^{+}{K}^{-}$ decays. This study is complementary to a recent similar analysis of the U-spin related decays $\text{bo}(t)\to {\pi }^{+}{\pi }^{-}$ and $\text{ob}(t)\to {\pi }^{+}{\pi }^{-}$.

Comments: 12 pages, LaTeX, 3 figures, revised version submitted to Phys. Rev. D