Renormalization of bilinears in nonrelativistic QCD

We calculate the $O\left({\alpha }_s\right)$ corrections to bilinear lattice vertex operators in nonrelativistic QCD (NRQCD) on the lattice. We use the lowest-order (in $\frac{1}{M}$) NRQCD action which includes the time derivative and kinetic energy terms, but we ignore spin effects. We give the correction required to convert a lattice calculation of the pseudoscalar heavy-light meson decay constant into a value appropriate for the continuum. For the light fermion we have used ordinary Wilson fermions, improved Wilson fermions, and naive fermions. We also give the correction required for a calculation of the vector heavy-heavy meson leptonic width. This is unfortunately large.