SU(3) Flavor Symmetry and CP Violating Rate Differences for Charmless $B\to PV$ 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 $B\to PV$ 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 $\Delta (B\to {\pi }^{+}{\rho }^{-})=-\Delta (B\to {\pi }^{+}{K}^{\ast -})$, $\Delta (B\to {\pi }^{-}{\rho }^{+})=-\Delta (K^{-}{\rho }^{+})$. SU(3) breaking effects are also estimated using factorization approximation. These relations can be tested at B factories in the near future.

Comments: Latex 18 pages. New references and comments added