$B_c$ Exclusive Decays to Charmonium and a Light Meson at Next-to-Leading Order Accuracy

In this paper the next-to-leading order (NLO) corrections to $B_c$ meson exclusive decays to S-wave charmonia and light pseudoscalar or vector mesons, i.e. $\pi$, $K$, $\rho$, and $K^{\ast }$, are performed within non-relativistic (NR) QCD approach. The non-factorizable contribution is included, which is absent in traditional naive factorization (NF). And the theoretical uncertainties for their branching ratios are reduced compared with that of direct tree level calculation. Numerical results show that NLO QCD corrections markedly enhance the branching ratio with a K factor of 1.75 for $B_{c}^{\pm}\to \eta_{c} \pi^{\pm}$and1.31for$B_{c}^{\pm}\to J/\psi \pi^{\pm}$. In order to investigate the asymptotic behavior, the analytic form is obtained in the heavy quark limit, i.e. $m_b\to \mathrm{\infty }$. We note that annihilation topologies contribute trivia in this limit, and the corrections at leading order in $z= m_c/m_b$ expansion come from form factors and hard spectator interactions. At last, some related phenomenologies are also discussed.