The S-wave resonance contributions in the B^{0}_{s} decays into psi (2S,3S) plus pion pair

Abstract

The three-body decays B^0_s rightarrow 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 sbar{s} component. It is found that the predicted B^0_s rightarrow 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^0_s rightarrow psi (2S) pi ^+ pi ^- is 6.0times 10^{-5}, which is in agreement with the LHCb data mathcal {B}(B^0_s rightarrow psi (2S) pi ^+ pi ^-)=(7.2pm 1.2)times 10^{-5} within errors. The estimate of mathcal {B}(B^0_s rightarrow psi (3S) pi ^+ pi ^-) can reach the order of 10^{-5}, pending the corresponding measurements.