Weak phases from topological-amplitude parametrization

Abstract

We propose a parametrization for two-body nonleptonic $B$ meson decays, in which the various topologies of amplitudes are counted in terms of powers of the Wolfenstein parameter $\lambda\sim 0.22$. The weak phases and the amplitudes are determined by comparing this parametrization with available measurements. It is possible to obtain the phase $\phi_3$ from the $B\to K\pi$ data up to theoretical uncertainty of $O(\lambda^3)\sim 1%$. The recently measured $B_d^0\to\pi^0\pi^0$ branching ratio implies a large color-suppressed or penguin amplitude, and that the extraction of the phase $\phi_2$ from the $B\to\pi\pi$ data may suffer theoretical uncertainty more than the expected one of $O(\lambda^2)\sim 5%$.