Four-body decays B(s) \u2192 (K\u03c0)S/P(K\u03c0)S/P in the perturbative QCD approach

Abstract

We investigate the four-body decays B(s) → (Kπ)S/P(Kπ)S/P in the Kπ-pair invariant mass region around the K*(892) resonance in the perturbative QCD (PQCD) approach, where (Kπ)S/P denotes a S- or P-wave Kπ configuration. The contributions from the P-wave resonance K*(892) and from possible S-wave components are included into the parametrization of the Kπ two-meson distribution amplitudes, which are the non-perturbative inputs in this formalism. We calculate the branching ratio for each resonance and observe sizable S-wave contributions to the Bs modes, well consistent with recently available LHCb data. We also deduce the polarization fractions for the {K}^{ast }{overline{K}}^{ast } final states, and compare our predictions to those in previous PQCD analyses of the corresponding two-body B → {K}^{ast }{overline{K}}^{ast } decays. The polarization puzzle associated with the two U-spin related channels B0 → {K}^{ast 0}{overline{K}}^{ast 0} and {B}_s^0to {K}^{ast 0}{overline{K}}^{ast 0} still exists. In addition to direct CP asymmetries, triple-product asymmetries and S-wave induced direct CP asymmetries originating from the interference among various helicity amplitudes, are presented. It is shown that true triple-product asymmetries are rather small, while direct CP asymmetries and S-wave-induced direct CP asymmetries are significant in some decays. Our results will be subject to stringent tests with precise data from B factories in the near future.