Improved perturbative QCD formalism for $B_c$ meson decays

We derive the $k_T$ resummation for doubly heavy-flavored $B_c$ meson decays by including the charm quark mass effect into the known formula for a heavy-light system. The resultant Sudakov factor is employed in the perutrbative QCD study of the “golden channel” $B_c^{+}\to J\mathrm{/}\psi {\pi }^{+}$. With a reasonable model for the $B_c$ meson distribution amplitude, which maintains approximate on-shell conditions of both the partonic bottom and charm quarks, it is observed that the imaginary piece of the $B_c\to J\mathrm{/}\psi$ transition form factor appears to be power suppressed, and the $B_c^{+}\to J\mathrm{/}\psi {\pi }^{+}$ branching ratio is not lower than ${10}^{-3}$. The above improved perutrbative QCD formalism is applicable to $B_c$ meson decays to other charmonia and charmed mesons.