Revisiting $B\to K^*\pi$ and $B\to K\rho$ decays using the modified perturbative QCD approach

TL;DR

This paper applies a modified perturbative QCD approach with an infrared cutoff to analyze $B o K^* ext{pi}$ and $B o K ho$ decays, achieving good agreement with experimental data.

Contribution

It introduces a critical infrared cutoff scale and considers color-octet contributions within the modified perturbative QCD framework for these decays.

Findings

Calculated branching fractions match experimental data.

Predicted CP violations are consistent with observations.

The approach effectively separates hard and soft contributions.

Abstract

We revisit $B\to K^*\pi$ and $B\to K\rho$ decay processes using the modified perturbative QCD approach, which is developed based on the perturbative QCD approach with a few improvements. A critical infrared cutoff scale $\mu_c$ is introduced to separate hard and soft contributions in the decay process. Hard contributions with scale $\mu$ larger than $\mu_c$ are calculated with perturbative QCD, and soft contributions with $\mu<\mu_c$ are described in terms of soft transition and production form factors. In addition, color-octet contributions are considered phenomenologically. The branching fractions and $CP$ violations of $B\to K^*\pi$, $K\rho$ decays are calculated. With appropriate parameter inputs, the theoretical results can be in good agreement with experimental data.