Radiative Corrections to the Kinetic Couplings in Nonrelativistic Lattice QCD

TL;DR

This paper calculates radiative corrections to kinetic couplings in nonrelativistic lattice QCD, revealing significant mass-dependent effects and emphasizing the need for higher-order computations for precision.

Contribution

It provides leading-order perturbative calculations of mass and wave function renormalizations, energy shifts, and kinetic coupling corrections in nonrelativistic lattice QCD.

Findings

Kinetic coupling corrections are about 10% for heavy quarks

Corrections increase rapidly as quark mass decreases

Two-loop corrections are necessary for improved accuracy

Abstract

The heavy-quark mass and wave function renormalizations, energy shift, and radiative corrections to two important couplings, the so-called kinetic couplings, in nonrelativistic lattice QCD are determined to leading order in tadpole-improved perturbation theory. The scales at which to evaluate the running QCD coupling for these quantities, except the wave function renormalization, are obtained using the Lepage-Mackenzie prescription. When the bare quark mass is greater than the inverse lattice spacing, the kinetic coupling corrections are roughly 10\% of the tree-level coupling strengths; these corrections grow quickly as the bare quark mass becomes small. A need for computing the two-loop corrections to the energy shift and mass renormalization is demonstrated.