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

Abstract

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.

Comments: 18 pages, 4 figures and 4 tables. Some important modifications to the text, new parametrization for extrapolation of the form factors, new numerical results, new figure, several new references added