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 $B^{\pm }\to K^{\ast \pm }{\pi }^0$ and $B^{\pm }\to K^{\ast 0}{\pi }^{\pm }$), and in $B^0\to K^{\ast \pm }{\pi }^{\mp }$ and $B^{\pm }\to \varphi K^{\pm }$. Theoretical uncertainties are discussed.

Comments: 19 pages, additional comments on factorization, to appear in Physical Review D