# Quasi-two-body decays $B_{(s)}\to P\rho^\prime(1450), P\rho^{\prime\prime}(1700)\to P\pi\pi$ in the perturbative QCD approach

## TL;DR

This paper calculates branching ratios and CP asymmetries for specific B meson decays involving rho prime resonances using perturbative QCD, providing predictions testable by current and future experiments.

## Contribution

It introduces a perturbative QCD approach to analyze quasi-two-body B decays involving rho prime resonances, incorporating experimental data for form factors.

## Key findings

- Branching ratios estimated between 10^{-7} and 10^{-9}.
- Predictions align with existing pion form factor measurements.
- Results will be tested by LHCb and Belle II.

## Abstract

In this work, we calculate the $CP$-averaged branching ratios and direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P \rho^\prime(1450), P\rho^{\prime\prime}(1700)\to P \pi\pi$ by employing the perturbative QCD (PQCD) factorization approach, where $P$ is a light pseudoscalar meson $K, \pi, \eta$ and $\eta^{\prime}$. The considered decay modes are studied in the quasi-two-body framework by parameterizing the two-pion distribution amplitude $\Phi_{\pi\pi}^{\rm P}$. The $P$-wave time-like form factor $F_{\pi}$ in the resonant regions associated with the $\rho^\prime(1450)$ and $\rho^{\prime\prime}(1700)$ is estimated based on available experimental data. The PQCD predictions for the $CP$-averaged branching ratios of the decays $B_{(s)}\to P\rho^\prime(1450), P\rho^{\prime\prime}(1700)\to P\pi\pi$ are in the order of $10^{-7} \sim 10^{-9}$. The branching ratios of the two-body decays $B_{(s)}\to P\rho^\prime(1450), P\rho^{\prime\prime}(1700)$ are extracted from the corresponding quasi-two-body decay modes. The whole pattern of the pion form factor-squared $|F_\pi|^2$ measured by {\it BABAR} Collaboration could also be understood based on our studies. Our PQCD predictions will be tested by the precise data from the LHCb and the future Belle II experiments.