Determining the Weak Phase $\gamma$ in the Presence of Rescattering

Abstract

We suggest a new technique to determine the CKM phase $\gamma$ {\em without} neglecting the (soft) final state rescattering effects. We use (time integrated) $B$ meson decay rates to $\pi$'s and $K$'s. A set of 5 $\Delta S = 0$ (or 1 $\Delta S =0$ and 4 $\Delta S= 1$) decay rates is used to compute the strong phases and magnitudes of the tree level and penguin contributions as functions of $\gamma$. These are used to {\em predict} a $\Delta S = 1$ $(\Delta S = 0) B_{d/s}$ decay rate as a function of $\gamma$ (using SU(3) symmetry). The measurement of this decay rate then gives $\gamma$. We illustrate this technique using different cases. Most of the decay modes we use are expected to be accessible at the B-factories (e^+ e^- or hadron machines).