Semileptonic decays of Bc meson to S-wave charmonium states in the perturbative QCD approach

Inspired by the recent measurement of the ratio of branching fractions to and final states at the LHCb detector, we study the semileptonic decays of meson to the S-wave ground and radially excited 2S and 3S charmonium states with the perturbative QCD approach. After evaluating the form factors for the transitions , where P and V denote pseudoscalar and vector S-wave charmonia, respectively, we calculate the branching ratios for all these semileptonic decays. The theoretical uncertainty of hadronic input parameters are reduced by utilizing the light-cone wave function for the meson. It is found that the predicted branching ratios range from up to and could be measured by the future LHCb experiment. Our prediction for the ratio of branching fractions is in good agreement with the data. For decays, the relative contributions of the longitudinal and transverse polarization are discussed in different momentum transfer squared regions. These predictions will be tested on the ongoing and forthcoming experiments.