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 $\gamma \equiv \arg (V_{ub}^{\ast })$. 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 $K^{\ast }\eta$ modes. Finding the pattern of ${\rho }^{+}{\omega }^0<{\rho }^{+}{\rho }^0$, $K^{\ast +}{\rho }^{-,0}>K^{\ast 0}{\rho }^{+}$, $K^{\ast +}{\omega }^0>K^{\ast 0}{\omega }^0$ and $K^{\ast +}\eta >K^{\ast 0}\eta$ would strengthen the support for $\cos \gamma <0$. The electroweak penguin enhances (suppresses) the $K^{\ast +}{\rho }^0$ ($K^{\ast 0}{\rho }^0$) rate by a factor of 2, and finding $K^{\ast +}{\rho }^0\simeq K^{\ast +}{\rho }^{-}$ would be strong evidence for the electroweak penguin.

Comments: 22 pages, Latex, 14 eps figures included