Radiative improvement of the lattice NRQCD action using the background field method and application to the hyperfine splitting of quarkonium states

TL;DR

This paper applies the background field method to lattice NRQCD to compute one-loop radiative corrections, improving the accuracy of hyperfine splitting predictions for bottomonium and aligning them with experimental results.

Contribution

It introduces the first use of the background field method in lattice NRQCD for gauge-covariant one-loop corrections, specifically for the $\sigma ext{ extperiodcentered} B$ term.

Findings

The $\sigma ext{ extperiodcentered} B$ coefficient is computed at one-loop level.

The correction shifts the hyperfine splitting of bottomonium to match experimental data.

The method enhances the precision of lattice NRQCD calculations.

Abstract

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.