Analysis of $B \to K\pi$ decays with small elastic final state interactions

Abstract

An analysis of $B \to K\pi$ decays is given, assuming a small elastic $\pi K $ rescattering phase difference.Using factorization model only for the tree-level and electroweak penguin amplitudes, we show that the strong penguin amplitude, its absorptive part and the CP-violation weak phase $\gamma$ can be obtained from the measured $B \to K\pi$ branching ratios. The strength of the strong penguin and its absorptive part thus obtained from the CLEO data, are found to be very close to factorization model values and suggests a current $s$ quark mass around $m_{s} = 106 \rm MeV$. The central value of $\gamma$ is found to be around $76.10^{\circ}$, with a possible value in the range $50^{\circ}-100^{\circ}$.