The Role of $B_s \to K π$ in Determining the Weak Phase $γ$

Abstract

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