The Role of $B_s\to K\pi$ in Determining the Weak Phase $\gamma$

Abstract

The decay rates for $B^0\to K^{+}{\pi }^{-}$, $B^{+}\to K^0{\pi }^{+}$, and the charge-conjugate processes were found to provide information on the weak phase $\gamma \equiv \mathrm{Arg}(V_{ub}^{\ast })$ when the ratio $r$ of weak tree and penguin amplitudes was taken from data on $B\to \pi \pi$ or semileptonic $B\to \pi$ decays. We show here that the rates for $B_s\to K^{-}{\pi }^{+}$ and ${\bar{B}}_s\to K^{+}{\pi }^{-}$ can provide the necessary information on $r$, and estimate the statistical accuracy of forthcoming measurements at the Fermilab Tevatron.

Comments: 8 pages, LaTeX, no figures, submitted to Physics Letters B, corrections to discussion of SU(3) breaking added