Title: Semileptonic decays of $$B_c$$ B c meson to S-wave charmonium states in the perturbative QCD approach
Abstract: Inspired by the recent measurement of the ratio of $$B_c$$ branching fractions to $$J/\psi \pi ^+$$ and $$J/\psi \mu ^+\nu _{\mu }$$ final states at the LHCb detector, we study the semileptonic decays of $$B_c$$ 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 $$B_c\rightarrow P,V$$ , 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 $$B_c$$ meson. It is found that the predicted branching ratios range from $$10^{-7}$$ up to $$10^{-2}$$ and could be measured by the future LHCb experiment. Our prediction for the ratio of branching fractions $$\frac{\mathcal {BR}(B_c^+\rightarrow J/\Psi \pi ^+)}{\mathcal {BR}(B_c^+\rightarrow J/\Psi \mu ^+\nu _{\mu })}$$ is in good agreement with the data. For $$B_c\rightarrow V l \nu _l$$ 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.