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 $\mathit{\sigma }·\mathit{B}$ 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.

• Received 27 May 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.112002