SU(3) Flavor Symmetry and CP Violating Rate Differences for Charmless $B\to P V$ Decays

Abstract

We derive several relations between CP violating rate differences $\Delta(B\to PV) = \Gamma(B\to PV) - \Gamma(\bar B \to \bar P \bar V)$ for charmless $B\to P V$ decays in the Standard Model using SU(3) flavor symmetry. It is found that although the relations between branching ratios of $\Delta S = 0$ and $\Delta S = -1$ processes are complicated, there are simple relations independent of hadronic models between some of the $\Delta S =0$ and $\Delta S = -1$ rate differences due to the unitarity property of the Kobayashi-Maskawa matrix, such as $ \Delta(B\to \pi^+ \rho^-) = -\Delta(B\to \pi^+ K^{*-})$, $\Delta(B\to \pi^- \rho^+) = - \Delta(K^- \rho^+)$. SU(3) breaking effects are also estimated using factorization approximation. These relations can be tested at B factories in the near future.