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

TL;DR

This work addresses charmless two-body $B$ decays to a pseudoscalar and a vector meson ($B\to PV$) by extending the PQCD framework to include soft form factors and color-octet quark-antiquark components, thereby capturing essential nonperturbative dynamics. The authors employ flavor SU(3) symmetry and its breaking to reduce the parameter space and perform a $\chi^2$ fit to 32 decay channels and 62 observables, achieving overall good agreement with experimental data for branching ratios and many $CP$ asymmetries. Key findings are that soft contributions and color-octet effects significantly influence predictions, particularly in channels challenging for previous approaches (e.g., $\pi^0\rho^0$, $\eta'\rho^+$), and that more precise CP-violation data are needed to further test the framework. The approach extends prior successes in $B\to PP$ decays to $B\to PV$, highlighting the role of nonperturbative inputs and SU(3) relations in improving predictive power across a broader class of two-body $B$ decays.

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. Based on the conventional PQCD calculations, soft form factors and contributions arising from color-octet quark-antiquark components in the final state are introduced in this study, which involves 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 $χ^2$ analysis procedure applied to the experimental data, these parameters are determined, for 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, thereby offering a solution to several long-standing puzzles. The numerical analysis shows that these soft contributions have significant influence on the theoretical results. Furthermore, more precise experimental data are needed for deeper investigations of the $CP$ asymmetries.

Figures (2)

• Figure 1: Topological diagrams which contribute to the $B\to PV$ decays. The diagrams are grouped into four distinct categories: factorizable emission diagrams (a) and (b), nonfactorizable emission diagrams (c) and (d), nonfactorizable annihilation diagrams (e) and (f), and factorizable annihilation diagrams (g) and (h).
• Figure 2: Diagrams of NLO QCD corrections: the diagrams (a), (b), (c) and (d) represent the vertex corrections, diagram (e) illustrates the quark-loop corrections, and diagram (f) depicts the chromomagnetic penguin corrections.