Examination of Flavor Symmetry in $B,B_s\to K\pi$ Decays

Abstract

We study a relation between the weak phase $\gamma$ and the rates and CP asymmetries of several $K\pi$ decays of $B^{+}$, $B^0$, and $B_s$, emphasizing the impact of the latter measurements. Current data indicate large SU(3) breaking in the strong phases or failure of factorization (including its application to penguin amplitudes) in $K\pi$ modes of $B^0$ and $B_s$. SU(3) and factorization only remain approximately valid if the branching ratio for $B_s\to K^{-}{\pi }^{+}$ exceeds its current value of $(5.27\pm 1.17)\times 10^{-6}$ by at least 42%, or if a parameter $\xi$ describing ratios of form factors and decay constants is shifted from its nominal value by more than twice its estimated error.

Comments: 10 pages, 4 figures. Misprints in some exponents corrected; one experimental value and some discussion updated