Interpreting the time-dependent CP asymmetry in $B^0\to {\pi }^0{K}_S$

Abstract

Flavor SU(3) is used for studying the time-dependent CP asymmetry in $B^0\to {\pi }^0{K}_S$ by relating this process to $B^0\to {\pi }^0{\pi }^0$ and $B^0\to K^{+}{K}^{-}$. We calculate correlated bounds on $S_{\pi K}-\sin 2\beta$ and $C_{\pi K}$, with maximal magnitudes of 0.2 and 0.3, where $S_{\pi K}$ and $C_{\pi K}$ are coefficients of $\sin \Delta mt$ and $\cos \Delta mt$ in the asymmetry. Stronger upper limits on $B^0\to K^{+}{K}^{-}$ are expected to reduce these bounds and to imply nonzero lower limits on these observables. The asymmetry is studied as a function of a strong phase and the weak phase $\gamma$.

Comments: 11 pages, 2 figures, to be published in Phys. Lett. B. Some equations corrected leading to small changes in figures