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

Abstract

We revisit $B\to K^{\ast }\pi$ 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 $B\to K^{\ast }\pi$, $K\rho$ decays are calculated. With appropriate parameter inputs, the theoretical results can be in good agreement with experimental data.

Comments: 16 pages, 1 figure