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.

Comments: 9 pages with 2 included eps figures; revised argument, taking into account the special shape of the amplitude quadrangle. An improved bound on rescattering effects is given