# Quasi-two-body decays $B \to D K^*(892) \to D K \pi$ in the perturbative QCD approach

## TL;DR

This paper analyzes $B o D K^*(892) o D K \pi$ decays using perturbative QCD, employing two-meson distribution amplitudes and Breit-Wigner resonance shapes, with predictions aligning with experimental data.

## Contribution

It introduces a perturbative QCD framework with two-meson distribution amplitudes for quasi-two-body decays involving $K^*(892)$ resonance.

## Key findings

- Predicted branching ratios agree with experimental measurements.
- Provided ratios of branching fractions for related decay modes.
- Predictions await testing with future LHCb and Belle-II data.

## Abstract

We study the quasi-two-body decays $B\to D K^*(892) \to D K\pi$ by employing the perturbative QCD approach. The two-meson distribution amplitudes $\Phi_{K\pi}^{\text{$P$-wave}}$ are adopted to describe the final state interactions of the kaon-pion pair in the resonance region. The resonance line shape for the $P$-wave $K\pi$ component $K^*(892)$ in the time-like form factor $F_{K\pi}(s)$ is parameterized by the relativistic Breit-Wigner function. For most considered decay modes, the theoretical predictions for their branching ratios are consistent with currently available experimental measurements within errors. We also disscuss some ratios of the branching fractions of the concerned decay processes. More precise data from LHCb and Belle-II are expected to test our predictions.