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 ${\varphi }_3$ 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 ${\varphi }_2$ from the $B\to \pi \pi$ data may suffer theoretical uncertainty more than the expected one of $O({\lambda }^2)\sim 5$.

Comments: 11 pages, 4 figures