The nonleptonic charmless decays of $B_c$ meson

In this paper, with the framework of (p)NRQCD and SCET, the processes $B_c\to M_1 M_2$areinvestigated\mathrm{.}Here$M_{1(2)}$ denotes the light charmless meson, such as $\pi$, $\rho$, $K$ or $K^{\ast }$. Based on the SCET power counting rules, the leading transition amplitudes are picked out, which include $A_{wA}^2$, $A_{wB}^2$, $A_{wC}^2$, $A_{wD}^2$ and $A_c^0$. From SCET, their factorization formulae are proven. Based on the obtained factorization formulae, in particular, the numerical calculation on $A_{wB}^2$ is performed.