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Using the QCD factorization approach, we reexamine the two-body hadroniccharmless $B$-meson decays to final states involving a pseudoscalar~($P$) and avector~($V$) meson, with inclusion of the penguin contractions ofspectator-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 areof order $\alpha_s^2$. Their impacts on the CP-averaged branching ratios andCP-violating asymmetries are examined. We find that these higher order penguincontraction contributions have significant impacts on some specific decaymodes. Since $B\to \pi K^{\ast}$, $K \rho$ decays involve the same electro-weakphysics as $B\to \pi K$ puzzles, we present a detailed analysis of these decaysand find that the five R-ratios for $B\to \pi K^{\ast}$, $K \rho$ system are inagreement with experimental data except for $R(\pi K^*)$. Generally, these newcontributions are found to be important for penguin-dominated $B\to PV$ decays.Comment: 45 pages, 12 figures. Theoretical uncertainties considered. Gauge  invariance proved. Version to appear in PR

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Reexamining charmless<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>P</mml:mi><mml:mi>V</mml:mi></mml:math>decays in the QCD factorization approach

Reexamining charmlessB→PVdecays in the QCD factorization approach