Study of B_c → J/ψV and $B_c^{\ast }\to {\eta }_{c}V$ decays within the QCD factorization

In this paper, we study the non-leptonic B _c → J/ψV and $B_c^{\ast }\to {\eta }_{c}V$ $(V=\rho ,K^{\ast })$ weak decays in the framework of QCD factorization. In the evaluation, the form factors are calculated using the Bauer–Stech–Wirbel model and the light-front quark model, respectively. Besides the longitudinal amplitude, the power-suppressed transverse contributions are also evaluated at next-to-leading order. The predictions for the observables of B _c → J/ψV and $B_c^{\ast }\to {\eta }_{c}V$ decays are presented. We find that the NLO QCD contribution presents about 8% correction to the branching ratios, and the longitudinal polarization fractions of these decays are at the level of (80 ∼ 90)%. In addition, we suggest direct measurements on some useful ratios, $R_{K^{\ast }/\rho }^{(\lambda =0)}$ and ${\tilde{R}}_{K^{\ast }/\rho }^{(\lambda =0)}$, which are very suitable to test the consistence between theoretical prediction and data because their theoretical uncertainties can be well controlled. (paper)