\begin{document}$B_c^- \to (\eta_c, J/\psi) l ^- \bar{\nu}_l$\end{document} using the PQCD factorization approach with the newly defined distribution amplitudes of the \begin{document}$B_c$\end{document} 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 \begin{document}$B_c \to (\eta_c,J/\psi) l \bar{\nu}$\end{document} 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 \begin{document}$R_{\eta_c}, R_{ J/\psi}$\end{document} and of the longitudinal polarization \begin{document}$P_{\tau}$\end{document} are \begin{document}$R_{\eta_c}=0.34\pm 0.01, R_{J/\psi}=0.28\pm 0.01$\end{document}, \begin{document}$P_{\tau}(\eta_c) = 0.37\pm 0.01$\end{document} and \begin{document}$P_{\tau}(J/\psi) = -0.55 \pm 0.01$\end{document}; and (c) after including the lattice results, the theoretical predictions slightly change: \begin{document}$R_{\eta_c}=0.31\pm 0.01$\end{document}, \begin{document}$ R_{ J/\psi}=0.27\pm 0.01$\end{document}, \begin{document}$P_{\tau}( \eta_c) = 0.36 \pm 0.01$\end{document} and \begin{document}$P_{\tau}( J/\psi) = -0.53\pm 0.01$\end{document}. The theoretical predictions of \begin{document}$R_{ J/\psi}$\end{document} agree with the measurements within the errors. The other predictions could be tested by the LHCb experiment in the near future."> Semileptonic decays <inline-formula><tex-math id="M1">\begin{document}${{ B}_{ c} \to (\eta_{ c},{ J}/\psi) { l} \bar{\nu}_{ l}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/c11f0e52-5df6-490a-b1f0-23586cba3380/CPC-2019-0339_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/c11f0e52-5df6-490a-b1f0-23586cba3380/CPC-2019-0339_M1.png"/></alternatives></inline-formula> in the “PQCD+Lattice” approach -
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