P-wave contributions to B(s)→ψKπ decays in perturbative QCD approach * * Supported by the National Natural Science Foundation of China (11947013, 11605060, 11775117, 11547020); Ya Li is also Supported by the Natural Science Foundation of Jiangsu Province (BK20190508) and the Research Start-up Funding of Nanjing Agricultural University; Zhou Rui is Supported in part by the Natural Science Foundation of Hebei

Abstract

We study the quasi-two-body decays by employing the perturbative QCD (PQCD) factorization approach, where the charmonia represents and . The corresponding decay channels are studied by constructing the kaon-pion distribution amplitude (DA) , which comprises important final state interactions between the kaon and pion in the resonant region. Relativistic Breit-Wigner formulas are adopted to parameterize the time-like form factor appearing in the kaon-pion DAs. The SU(3) flavor symmetry breaking effect resulting from the mass difference between the kaon and pion is taken into account, which makes significant contributions to the longitudinal polarizations. The observed branching ratios and the polarization fractions of are accommodated by tuning hadronic parameters for the kaon-pion DAs. The PQCD predictions for modes from the same set of parameters can be tested by precise data obtained in the future from LHCb and Belle II experiments.