Radiative improvement of the lattice NRQCD action using the background field method with applications to quarkonium spectroscopy

TL;DR

This paper applies the background field method to lattice NRQCD to compute one-loop radiative corrections for improved quarkonium spectroscopy predictions, achieving better agreement with experimental data.

Contribution

It introduces a gauge-covariant background field approach to calculate radiative corrections in lattice NRQCD, enhancing the accuracy of quarkonium spectroscopy.

Findings

Radiative corrections improve hyperfine splitting predictions.

Corrected lattice results align with experimental measurements.

First application of background field method in this context.

Abstract

We apply the background field (BF) 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 by matching the NRQCD prediction for particular on-shell processes with those of relativistic continuum QCD. We explain how the BF method is implemented in automated perturbation theory and discuss the technique for matching the relativistic and non-relativistic theories. We compute the one-loop radiative corrections to the sigma.B and Darwin terms for the NRQCD action currently used in simulations, as well as the one-loop coefficients of the spin-dependent O(alpha^2) four-fermion contact terms. The effect of the corrections on the hyperfine splitting of bottomonium is estimated using earlier simulation results; the corrected lattice prediction is found to be in agreement with experiment. Agreement of the hyperfine splitting of bottomonium and the B-meson system is confirmed by recent simulation studies (Dowdall et al.) which include our NRQCD radiative corrections for the first time.