Branching Fractions and CP Asymmetries of the Quasi-Two-Body Decays in $B_s\to K^0({\overline{K}}^0)K^{\pm }{\pi }^{\mp }$ within PQCD Approach

Abstract

Motivated by the first untagged decay-time-integrated amplitude analysis of $B_s\to K_S{K}^{\mp }{\pi }^{\pm }$ decays performed by LHCb collaboration, where the decay amplitudes are modeled to contain the resonant contributions from intermediate resonances $K^{\ast }(892)$, $K_0^{\ast }(1430)$ and $K_2^{\ast }(1430)$, we comprehensively investigate the quasi-two-body $B_s\to K^0/{\overline{K}}^0{K}^{\pm }{\pi }^{\mp }$ decays, and calculate the branching fractions and the time-dependent $CP$ asymmetries within the perturbative QCD approach based on the $k_T$ factorization. In the quasi-two-body space region the calculated branching fractions with the considered intermediate resonances are in good agreement with the experimental results of LHCb by adopting proper $K\pi$ pair wave function, describing the interaction between the kaon and pion in the $K\pi$ pair. Furthermore,within the obtained branching fractions of the quasi-two-body decays, we also calculate the branching fractions of corresponding two-body decays, and the results consist with the LHCb measurements and the earlier studies with errors. For these considered decays, since the final states are not flavour-specific, the time-dependent $CP$ could be measured. We calculate six $CP$-violation observables, which can be tested in the ongoing LHCb experiment.

Comments: 20 pages