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

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