Analysis of CKM-favored quasi-two-body B → D (R→ ) K π decays in PQCD approach

LHCb Collaboration studied the resonant structure of B_s→D^0K^-π ^+ decays using the Dalitz plot analysis technique, based on a data sample corresponding to an integrated luminosity of 3.0fb^-1 of pp collision. The K^-π ^+ components have been analyzed in the amplitude model, where the decay amplitude is modeled to be the resonant contributions with respect to the intermediate resonances K^*(892) , K_0^*(1430) and K_2^*(1430) . Motivated by the experimental results, we investigate the CKM-favored quasi-two-body B →D^0Kπ decays in the framework of the perturbative QCD (PQCD) approach. We calculate the the branching fractions by introducing the appropriate wave functions of Kπ pair. Our results are in agreement well the available data, and others can be tested in LHCb and Belle-II experiments. Using the narrow-width-approximation, we also extract the branching fractions of the corresponding two-body B→D R decays, which agree to the previous theoretical calculations and the experimental data within the errors. There are no CP asymmetries in these decays in the standard model, because these decays are all governed by only the tree operators.