The S-wave resonance contributions in the Bs0 decays into ψ(2S, 3S) plus pion pair

The three-body decays B-s(0) -> psi(2S, 3S)pi(+)pi(-) are studied based on the perturbative QCD approach. With the help of the nonperturbative two-pion distribution amplitudes, the analysis is simplified into the quasi-two-body processes. Besides the traditional factorizable and nonfactorizable diagrams at the leading order, the next-to-leading order vertex corrections are also included to cancel the scale dependence. The f(0)(980), f(0)(1500) resonance contributions as well as the nonresonant contributions are taken into account using the presently known pi pi time-like scalar form factor for the s (s) over bar component. It is found that the predicted B-s(0) -> psi(2S)pi(+)pi(-) decay spectra in the pion pair invariant mass shows a similar behavior as the experiment. The calculated S-wave contributions to the branching ratio of B-s(0) -> psi(2S)pi(+)pi(-) is 6.0 x 10(-5), which is in agreement with the LHCb data B(B-s(0) -> psi(2S)pi(+)pi(-)) = (7.2 +/- 1.2) x 10(-5) within errors. The estimate of B(B-s(0) -> psi(3S)pi(+)pi(-)) can reach the order of 10(-5), pending the corresponding measurements.