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

Inspired by the recent measurement of the ratio of Bc branching fractions to J/ψ π ⁺ and J/ψ μ ⁺ν μ final states at the LHCb detector, we study the semileptonic decays of Bc 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 Bc→ 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 Bc 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 BR(Bc⁺→ J/Ψ π ⁺)BR(Bc⁺→ J/Ψ μ ⁺ν μ) is in good agreement with the data. For Bc→ V l ν 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.