Contributions of {K}_0^{ast } (1430) and {K}_0^{ast } (1950) in the three-body decays B \u2192 K\u03c0h

Abstract

We study the contributions of the resonant states {K}_0^{ast } (1430) and {K}_0^{ast } (1950) in the three-body decays B → Kπh (with h = π, K) in the perturbative QCD approach. The crucial nonperturbative input FKπ(s) in the distribution amplitudes of the S-wave Kπ system is derived from the matrix element of vacuum to Kπ pair. The C P averaged branching fraction of the quasi-two-body decay process B → {K}_0^{ast } (1950) h → Kπh is about one order smaller than that of the corresponding decay B → {K}_0^{ast } (1430)h → Kπh. In view of the important contribution from the S-wave Kπ system for the B → Kπh decays, it is not appropriate to neglect the {K}_0^{ast } (1950) in the theoretical or experimental studies for the relevant three-body B meson decays. The predictions in this work for the relevant decays are consistent with the existing experimental data.