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

TL;DR

This paper investigates the possibility that $ ext{cos}\gamma<0$ in rare $B$ decays, updating theoretical predictions with sum rule form factors and analyzing decay patterns to support this hypothesis.

Contribution

It provides updated predictions using light cone sum rule form factors and discusses decay patterns that could confirm $ ext{cos}\gamma<0$ in $B$ decays.

Findings

Pattern of decay rates supports $ ext{cos}\gamma<0$ hypothesis.

Electroweak penguin effects significantly alter certain decay rates.

Specific decay rate relations could serve as experimental tests.

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.