Tree-Penguin Interference and Tests for $\cos\gamma < 0$ in Rare $B\to PP$, $PV$ and $VV$ Decays

Abstract

Recent rare $B \to PP$, $PV$ decay data suggest that factorization holds well if, contrary to current fits, one has $\cos\gamma < 0$ where $\gamma \equiv {\rm arg}(V_{ub}^*)$. We update previous results with light cone sum rule form factors, which seem to work better. We then discuss various $B\to VV$ modes as well as the $K^{*} \eta$ modes. Finding the pattern of $\rho^+\omega^0 < \rho^+\rho^0$, $K^{*+}\rho^{-,0} > K^{*0}\rho^+$, $K^{*+}\omega^0 > K^{*0}\omega^0$ and $K^{*+}\eta > K^{*0}\eta$ would strengthen the support for $\cos\gamma < 0$. The electroweak penguin enhances (suppresses) the $K^{*+}\rho^{0}$ ($K^{*0}\rho^{0}$) rate by a factor of 2, and finding $K^{*+}\rho^{0} \simeq K^{*+}\rho^{-}$ would be strong evidence for the electroweak penguin.