Basing on the branching fractions of J/psi to VP from different experiments, we investigate on the properties of the coupling constants of J/psi to VP decays with a model-dependent approach. We find that the octet coupling constant, g_8, of strong in
teraction is about twice larger than that of the singlet coupling constant g_1; the electromagnetic breaking parameters g^i_E are larger than the mass breaking parameters g^i_M, moreover, the three parameters of electromagnetic effect are about equal, but the three parameters of mass effect are obviously different and their uncertainties are also large; and the phase angle between strong and electromagnetic interaction is in the range of 70^{circ} sim 80^{circ}. It deepens our understanding of the coupling constant of J/psi to VP decays.
The $W$-exchange process $B_{s}$ ${to}$ ${eta}_{c}(J/{psi})D$ is studied with the perturbative QCD approach. Three kinds of wave functions for $B_{s}$ meson and two forms of wave functions for charmonium are considered. It is estimated that branching
ratios for $B_{s}$ ${to}$ ${eta}_{c}bar{D}$, ${eta}_{c}D$, $J/{psi}bar{D}$, $J/{psi}D$ decays are the order of $10^{-7}$, $10^{-8}$, $10^{-8}$, $10^{-9}$, respectively, where the largest uncertainty is from wave functions. There is a possibility for measuring these decay in the near future.
The Bc -> BP,BV decays are studied with the QCD factorization approach (where P and V denote pseudoscalar and vector mesons, respectively). Considering the contributions of both current-current and penguin operators, the amplitudes of branching ratio
s are estimated at the leading approximation. We find that the contributions of the penguin operators are very small due to the serious suppression by the CKM elements. The most promising decay modes are Bc -> Bs Pi, Bs rho, which might be easily detected at hadron colliders.
