  We present the first application of the background field method to
Non-Relativistic QCD (NRQCD) on the lattice in order to determine the one-loop
radiative corrections to the coefficients of the NRQCD action in a manifestly
gauge-covariant manner. The coefficient of the $\sigma\cdot B$ term in the
NRQCD action is computed at the one-loop level; the resulting shift of the
hyperfine splitting of bottomonium is found to bring the lattice predictions in
line with experiment.
