# $P$-wave contributions to $B_{(s)}\to\psi K\pi$ decays in perturbative QCD approach

## TL;DR

This paper analyzes $B_{(s)}$ decays into charmonium and kaon-pion pairs via $K^*$ resonances using perturbative QCD, modeling final state interactions and SU(3) symmetry breaking to match observed data.

## Contribution

It introduces a novel approach to modeling $K ext{-} ext{pion}$ interactions in $B$ decays within PQCD, including resonance effects and SU(3) breaking, providing predictions for multiple decay channels.

## Key findings

- Successfully reproduces branching ratios and polarization fractions for $B_{(s)} o ext{J/}\psi K^*$ decays.
- Provides predictions for higher $K^*$ resonances that can be tested by future experiments.
- Highlights the importance of SU(3) breaking in polarization outcomes.

## Abstract

In this work, we studied the quasi-two-body decays $B_{(s)} \to \psi [K^*(892), K^*(1410),$ $K^*(1680)] \to \psi K\pi$ by employing the perturbative QCD (PQCD) factorization approach, where the charmonia $\psi$ represents $J/\psi$ and $\psi(2S)$. The corresponding decay channels are studied by constructing the kaon-pion distribution amplitude (DA) $\Phi_{K \pi}^{\rm P}$, which contained the important final state interactions between the kaon and pion in the resonant region. The relativistic Breit-Wigner formulas are adopted to parameterize the time-like form factor $F_{K\pi}$ appeared in the kaon-pion DAs. The SU(3) flavor symmetry breaking effect resulting from the mass difference between kaon and pion is taken into account, which makes significant contributions to the longitudinal polarizations. We accommodate well the observed branching ratios and the polarization fractions of the $B_{(s)} \to \psi K^*(892) \to \psi K\pi$ by tuning the hadronic parameters for the kaon-pion DAs. The PQCD predictions for the $B_{(s)} \to \psi [K^*(1410), K^*(1680)] \to \psi K\pi$ modes from the same set of parameters can be tested by the future precise data from the LHCb and the Belle II experiments.