QCD Radiative Corrections to the Leptonic Decay Rate of the B_c Meson

The QCD radiative corrections to the leptonic decay rate of the $B_c$ meson are calculated using the formalism of nonrelativistic QCD (NRQCD) to separate short-distance and long-distance effects. The $B_c$ decay constant is factored into a sum of NRQCD matrix elements each multiplied by a short-distance coefficient. The short-distance coefficient for the leading matrix element is calculated to order ${\alpha }_s$ by matching a perturbative calculation in full QCD with the corresponding perturbative calculation in NRQCD. This short-distance correction decreases the leptonic decay rate by approximately $15\mathrm{\%}$.