Quasi-two-body B(s)→Vππ decays with resonance f0(980) in the PQCD approach.

Motivated by the measurements of the branching fractions of the quasi-two-body decays B0→K*0(f0(980)→)π+π- and B0→ρ0(f0(980)→)π+π-, we study the charmless B→V(f0(980)→)π+π- decays in the perturbative QCD approach. Supposing that f0(980) is a two-quark state and mixture of n̄n=(ūu+d̄d)/√2 and s̄s with the mixing angle θ, we calculate the branching fractions of these decays with the new introduced s-wave π+π--pair wave function. When the mixing angle θ lies in the range [135°,155°], the calculated branching fractions of the B0→K*0f0(980)→K*0π+π- and B0→ρ0f0(980)→ρ0π+π- decays are in agreement with the experimental data. The branching fractions of other decays could be measured in the current LHCb and Belle II experiments. Considering the isospin symmetry, we also estimate the branching fractions of the quasi-two-body decays B→Vf0(980)→Vπ0π0, which are half of the corresponding decays B→Vf0(980)→Vπ+π-. Moreover, the direct CP asymmetries of these decays are also calculated, and some of them can be tested in the current experiments. [ABSTRACT FROM AUTHOR]