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

Abstract

In this paper, we study the non-leptonic $B_c\to J/\psi V$ 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 by 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 $B_c\to J/\psi V$ 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 $(80\sim 90)\%$. 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 for test the consistence between theoretical prediction and data because their theoretical uncertainties can be well-controlled.

Comments: 21 pages, 5 figures; To be published in Journal of Physics G