Electroweak penguin amplitudes and constraints on $\gamma$ in charmless $B\to VP$ decays

Abstract

Electroweak penguin (EWP) amplitudes are studied model-independently in $B$ meson decays to charmless final states consisting of a vector meson ($V$) and a pseudoscalar meson ($P$). A set of SU(3) relations is derived between EWP contributions and tree amplitudes, in the approximation of retaining only the dominant EWP operators $Q_9$ and $Q_{10}$ . Two applications are described for constraining the weak phase $\gamma$, in $B^{\pm}\to \rho^{\pm} K^0$ and $B^{\pm}\to \rho^0 K^{\pm}$ (or $B^{\pm}\to K^{*\pm}\pi^0$ and $B^{\pm}\to K^{*0}\pi^{\pm}$), and in $B^0\to K^{*\pm}\pi^{\mp}$ and $B^{\pm}\to\phi K^{\pm}$. Theoretical uncertainties are discussed.