The QCD radiative corrections to the leptonic decay rate of the ${\mathit{B}}_{\mathit{c}}$ meson are calculated using the formalism of nonrelativistic QCD (NRQCD) to separate short-distance and long-distance effects. The ${\mathit{B}}_{\mathit{c}}$ 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 ${\mathrm{\alpha }}_{\mathit{s}}$ 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%.

• Received 16 January 1995

DOI:https://doi.org/10.1103/PhysRevD.52.181