Phenomenological analysis of charmless $B\to PV$ decays in the modified perturbative QCD approach

Abstract

We analyze the charmless two-body decays of the $B$ meson into a pseudoscalar and a vector meson, referred to as $B\to PV$ decay, within the framework of the modified perturbative QCD (PQCD) approach, which was originally developed to solve the long-standing puzzles, the so-called $\pi\pi$ and $\pi K$ puzzles. In this method, based on the conventional PQCD calculations, soft form factors and contributions arising from color-octet quark-antiquark components in the final state are introduced, which involve essentially nonperturbative dynamics. By employing the flavor SU(3) symmetry and its breaking effect, the parameters describing soft contributions are correlated and subsequently reduced into a more concise set of SU(3) parameters. Through a $\chi^2$ analysis procedure applied to the experimental data, these parameters are determined, from which the corresponding theoretical results for the branching ratios and $CP$ asymmetries in $B\to PV$ decays are derived. Within this framework, it is demonstrated that the theoretical calculations align well with experimental measurements, suggesting that the method developed for solving $\pi\pi$ and $\pi K$ puzzles can be extended to more decay modes of the $B$ meson. The numerical analysis shows that these soft contributions have a significant influence on the theoretical results. Furthermore, more precise experimental data are needed for deeper investigations of the $CP$ asymmetries.