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

Abstract

In this work, we calculate the $CP$-averaged branching ratios and direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P ρ^\prime(1450), Pρ^{\prime\prime}(1700)\to P ππ$ by employing the perturbative QCD (PQCD) factorization approach, where $P$ is a light pseudoscalar meson $K, π, η$ and $η^{\prime}$. The considered decay modes are studied in the quasi-two-body framework by parameterizing the two-pion distribution amplitude $Φ_{ππ}^{\rm P}$. The $P$-wave time-like form factor $F_π$ in the resonant regions associated with the $ρ^\prime(1450)$ and $ρ^{\prime\prime}(1700)$ is estimated based on available experimental data. The PQCD predictions for the $CP$-averaged branching ratios of the decays $B_{(s)}\to Pρ^\prime(1450), Pρ^{\prime\prime}(1700)\to Pππ$ are in the order of $10^{-7} \sim 10^{-9}$. The branching ratios of the two-body decays $B_{(s)}\to Pρ^\prime(1450), Pρ^{\prime\prime}(1700)$ are extracted from the corresponding quasi-two-body decay modes. The whole pattern of the pion form factor-squared $|F_π|^2$ 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.

8 pages, 1 figure