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Semileptonic decays $B_c \to (η_c,J/ψ) l \barν_l $ in the "PQCD + Lattice" approach

In this paper, we studied the semileptonic decays $B_c^- \to (η_c, J/ψ) l ^- \barν_l$ 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 $B_c \to (η_c,J/ψ) l \barν$ 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 $R_{η_c, J/ψ}$ and the longitudinal polarization $P_τ$ are $R_{η_c}=0.34\pm 0.01 , R_{J/ψ}=0.28\pm 0.01$, $P_τ(η_c) = 0.37\pm 0.01$ and $P_τ(J/ψ) = -0.55 \pm 0.01$ ; and (c) after the inclusion of the lattice input the theoretical predictions changed slightly: $R_{η_c}=0.31\pm 0.01$, $ R_{ J/ψ}=0.27\pm 0.01$, $P_τ( η_c) = 0.36 \pm 0.01$ and $P_τ( J/ψ) = -0.53\pm 0.01$. The theoretical predictions for $R_{ J/ψ}$ agree with the measured one within errors, and other predictions could be tested in the near future LHCb experiments.