$B \to K\pi$ decays and the weak phase angle $\gamma$

Abstract

The large branching ratios for $B \to K\pi$ decays as observed by the CLEO Collaboration indicate that penguin interactions contribute a major part to the decay rates and provide an interference between the Cabibbo-suppressed tree and penguin contributions resulting in a CP-asymmetry between the $B \to K\pi$ and its charge conjugate mode. The CP-averaged decay rates depend also on the weak phase $\gamma$ and give us a determination of this phase. In this talk, I would like to report on a recent analysis of $B \to K\pi$ decays using factorisation model with final state interaction phase shift included. We find that factorisation seems to describe qualitatively the latest CLEO data. We also obtain a relation for the branching ratios independent of the strength of the strong penguin interactions. This relation gives a central value of $0.60 \times 10^{-5}$ for ${\mathcal B}(\bar{B}^{0} \to \bar{K}^{0}\pi^{0})$, somewhat smaller than the latest CLEO measurement. We also find that a ratio obtained from the CP-averaged $B \to K\pi$ decay rates could be used to test the factorisation model and to determine the weak angle $\gamma$ with more precise data, though the latest CLEO data seem to favor $\gamma$ in the range $90^{\circ}-120^{\circ}$.