Heavy Quark Effective Theory at one-loop order: An explicit example

TL;DR

This paper analyzes one-loop order correlation functions involving axial currents with heavy and light quarks in lattice QCD, highlighting the asymptotic nature of the 1/m expansion and the impact of quark mass on discretization errors.

Contribution

It provides an explicit one-loop perturbative comparison between full QCD and the static effective theory on the lattice, revealing non-analytic terms and mass-dependent discretization effects.

Findings

Deviations from the m→∞ limit are small for quark masses 2-3 times above the external scale.

The 1/m expansion exhibits non-analytic behavior, indicating its asymptotic nature.

Discretization errors depend strongly on quark mass at finite lattice spacing.

Abstract

We consider correlation functions containing the axial current of one light and one heavy quark in the static approximation as well as in full QCD, using the lattice regularization. Up to one-loop order of perturbation theory, we study the difference between the full and the effective theory in the continuum limit. In the full theory we find a term non-analytic in 1/m, revealing the asymptotic character of the 1/m-expansion. In general, deviations from the m-to-infinity limit turn out to be small and are well described by the first non-trivial terms when m is a factor 2-3 above the external scale. We also investigate the mass dependence of discretization errors, and find that the behaviour of the correlation functions at finite lattice spacing differs significantly from that in the continuum limit when the quark mass is large.