Reexamining charmless B\to PV decays in QCD factorization approach

Abstract

Using the QCD factorization approach, we reexamine the two-body hadronic charmless $B$-meson decays to final states involving a pseudoscalar~($P$) and a vector~($V$) meson, with inclusion of the penguin contractions of spectator-scattering amplitudes induced by the $b\to D{g}^{\ast }{g}^{\ast }$~(where $D=d$ or $s$, and $g^{\ast }$ denotes an off-shell gluon) transitions, which are of order ${\alpha }_s^2$. Their impacts on the CP-averaged branching ratios and CP-violating asymmetries are examined. We find that these higher order penguin contraction contributions have significant impacts on some specific decay modes. Since $B\to \pi K^{\ast }$, $K\rho$ decays involve the same electro-weak physics as $B\to \pi K$ puzzles, we present a detailed analysis of these decays and find that the five R-ratios for $B\to \pi K^{\ast }$, $K\rho$ system are in agreement with experimental data except for $R(\pi K^{\ast })$. Generally, these new contributions are found to be important for penguin-dominated $B\to PV$ decays.

Comments: 45 pages, 12 figures. Theoretical uncertainties considered. Gauge invariance proved. Version to appear in PRD