Radiative Improvement of the Lattice Nonrelativistic QCD Action Using the Background Field Method and Application to the Hyperfine Splitting of Quarkonium States

We present the first application of the background field method to nonrelativistic 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 coefficients of the $\mathbit{\ensuremath{\sigma}}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{B}$ term in the NRQCD action and the four-fermion spin-spin interaction are 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.