Abstract
We extend our recent works on the P-wave two-pion resonant contributions to the kaon-pion cases in the hadronic charmless B meson decays by employing the perturbative QCD approach. The concerned decay modes are analysed in the quasi-two-body framework by parameterizing the kaon-pion distribution amplitude Phi _{K pi }^mathrm{P}, which contains the final state interactions between the kaon and pion in the resonant region. The relativistic Breit–Wigner formula for the P-wave resonant state K^*(892) is adopted to parameterize the time-like form factor F_{Kpi }. We calculate the CP-averaged branching ratios and direct CP-violating asymmetries of the quasi-two-body decays B_{(s)}rightarrow K^*(892) hrightarrow Kpi h, with h=(pi , K), in this work. It is shown that the agreement of theoretical results with the experimental data can be achieved, through which Gegenbauer moments of the P-wave kaon-pion distribution amplitudes are determined. The predictions in this work will be tested by the precise data from the LHCb and the future Belle II experiments.
Highlights
On the theoretical side, no proof of factorization has been done for the decays of the B meson into three final state mesons
The three-body interactions are expected to be suppressed strongly due to power counting rules [14]. In such quasi-two-body region of phase space, the obvious generalization of the factorization theorem for two-body decays applies, and in the region where all invariant masses are large, factorization has been explicitly shown at the leading non-trivial order in Refs. [15,16]
The perturbative QCD (PQCD) factorization approach has been employed in Refs. [34,35,36,37,38], where the strong dynamics between the two final state hadrons in resonant regions are factorized into a new non-perturbative input, the twohadron distribution amplitudes (DAs) h1h2 [39,40,41,42,43,44,45]
Summary
No proof of factorization has been done for the decays of the B meson into three final state mesons. We can restrict ourselves to the specific kinematical configurations, in which two energetic final state mesons almost collimating to each other. For such topologies, the three-body interactions are expected to be suppressed strongly due to power counting rules [14]. The three-body interactions are expected to be suppressed strongly due to power counting rules [14] In such quasi-two-body region of phase space, the obvious generalization of the factorization theorem for two-body decays applies, and in the region where all invariant masses are large, factorization has been explicitly shown at the leading non-trivial order in Refs. The QCDimproved factorization [15] has been widely applied to the studies of the three-body hadronic B meson decays in
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