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 $Δ(B\to PV) = Γ(B\to PV) - Γ(\bar B \to \bar P \bar V)$ 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 $ΔS = 0$ and $ΔS = -1$ processes are complicated, there are simple relations independent of hadronic models between some of the $ΔS =0$ and $ΔS = -1$ rate differences due to the unitarity property of the Kobayashi-Maskawa matrix, such as $ Δ(B\to π^+ ρ^-) = -Δ(B\to π^+ K^{*-})$, $Δ(B\to π^- ρ^+) = - Δ(K^- ρ^+)$. SU(3) breaking effects are also estimated using factorization approximation. These relations can be tested at B factories in the near future.