Weak phases $\gamma$ and $\alpha$ from $B^+$, or $B^0$ and $B_s$ decays

Abstract

An improved flavor SU(3) method is presented for determining the weak angle $\gamma$ of the unitarity triangle using decay rates for $B^+\to K\pi, B^+\to K^+\bar K^0$ and $B^+\to \pi^+\eta$ (or $B^0\to K\pi$ and $B_s\to K \pi$), their CP-conjugate modes and the CP-averaged rate for $B^\pm\to\pi^\pm\pi^{0}$. Rescattering (color-suppressed) contribution in $B^+(B^0)\to K\pi$, for which an improved bound is obtained, is subtracted away. The only significant SU(3) breaking effects are accounted for in the factorization approximation of tree amplitudes. The weak angle $\alpha$ is obtained as a byproduct.