Quasi-two-body decays B P f₀ (500) P^+^- in the perturbative QCD approach

In this paper, we study the quasi-two-body decays B P f₀ (500) P^+^- (with P= (, K, , ^) ) within framework of perturbative QCD (PQCD) factorization approach. With the help of - distribution amplitude and scalar form factor F_ (²), we calculate the CP averaged branching fraction and the CP asymmetry for the quasi-two-body decays B P f₀ (500) P^+^-. Taking the quasi-two-body decay B^+ ^+ f₀ (500) ^+ ^+ ^- as an explicit example, we present the behaviour of differential branching fraction and direct CP violation versus the - invariant mass. The total branching fraction and direct CP violation are B (B^+ ^+ ^+^-) = (1. 78 0. 41 0. 51) 10^-6 and A ₂₏ (B^+ ^+ ^+^-) = (29. 8 11. 1 13. 0) \% respectively. Our results could be tested by further experiments.