Semileptonic decays $B_c \to (\eta_c,J/\psi) l \bar{\nu}_l $ in the "PQCD + Lattice" approach

In this paper, we studied the semileptonic decays $B_c^- \to (\eta_c, J/\psi) l ^- \bar{\nu}_l$ by employing the PQCD factorization approach, using the newly defined distribution amplitudes of the $B_c$ meson and the new kind of parametrization for extrapolation of the form factors , and also taking into account the lattice QCD results about the relevant form factors at several points. We found the following main results: (a) the PQCD predictions for the branching ratios of $B_c \to (\eta_c,J/\psi) l \bar{\nu}$ decays will become a little smaller by about $(5-16)\%$ when the lattice input are taken into account in the extrapolation of the relevant form factors; (b) the PQCD predictions for the ratio $R_{\eta_c, J/\psi}$ and the longitudinal polarization $P_{\tau}$ are $R_{\eta_c}=0.34\pm 0.01 , R_{J/\psi}=0.28\pm 0.01$, $P_{\tau}(\eta_c) = 0.37\pm 0.01$ and $P_{\tau}(J/\psi) = -0.55 \pm 0.01$ ; and (c) after the inclusion of the lattice input the theoretical predictions changed slightly: $R_{\eta_c}=0.31\pm 0.01$, $ R_{ J/\psi}=0.27\pm 0.01$, $P_{\tau}( \eta_c) = 0.36 \pm 0.01$ and $P_{\tau}( J/\psi) = -0.53\pm 0.01$. The theoretical predictions for $R_{ J/\psi}$ agree with the measured one within errors, and other predictions could be tested in the near future LHCb experiments.