Semileptonic decays ${{ B}_{ c} \to (\eta_{ c},{ J}/\psi) { l} \bar{\nu}_{ l}}$ in the “PQCD+Lattice” approach

Abstract：

We study the semileptonic decays $B_c^- \to (\eta_c, J/\psi) l ^- \bar{\nu}_l$ using the PQCD factorization approach with the newly defined distribution amplitudes of the $B_c$ meson and a new kind of parametrization for extrapolating the form factors which takes into account the recent lattice QCD results. We find the following main results: (a) the PQCD predictions of the branching ratios of the $B_c \to (\eta_c,J/\psi) l \bar{\nu}$ decays are smaller by about 5%-16% when the lattice results are taken into account in the extrapolation of the relevant form factors; (b) the PQCD predictions of the ratio $R_{\eta_c}, R_{ J/\psi}$ and of 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 including the lattice results, the theoretical predictions slightly change: $R_{\eta_c}=0.31\pm 0.01$ , $ 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 of $R_{ J/\psi}$ agree with the measurements within the errors. The other predictions could be tested by the LHCb experiment in the near future.