Determining the Weak Phase $γ$ 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).
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