Determining the Weak Phase $γ$ in the Presence of Rescattering

Abstract

We suggest a new technique to determine the CKM phase $γ$ {\em without} neglecting the (soft) final state rescattering effects. We use (time integrated) $B$ meson decay rates to $π$'s and $K$'s. A set of 5 $ΔS = 0$ (or 1 $ΔS =0$ and 4 $ΔS= 1$) decay rates is used to compute the strong phases and magnitudes of the tree level and penguin contributions as functions of $γ$. These are used to {\em predict} a $ΔS = 1$ $(ΔS = 0) B_{d/s}$ decay rate as a function of $γ$ (using SU(3) symmetry). The measurement of this decay rate then gives $γ$. 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).