Functional Methods for Heavy Quark Effective Theory

TL;DR

This paper introduces a systematic functional method for calculating one-loop effects in Heavy Quark Effective Theory, enabling efficient derivation of matching coefficients and RG equations for non-relativistic systems.

Contribution

It demonstrates the algebraic evaluation of path integrals in effective field theories with non-trivial mode decompositions, including derivations involving open covariant derivatives.

Findings

First algebraic calculation of contributions from open covariant derivatives

Systematic approach for higher-order corrections in heavy mass expansion

Framework applicable to precision QCD predictions and lattice QCD connections

Abstract

We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations. This paper provides the first demonstration that such calculations can be performed through the algebraic evaluation of the path integral for the class of effective field theories that are (i) constructed using a non-trivial one-to-many mode decomposition of the UV theory, and (ii) valid for non-relativistic kinematics. We discuss the interplay between operators that appear at intermediate steps and the constraints imposed by the residual Lorentz symmetry that is encoded as reparameterization invariance within the effective description. The tools presented here provide a systematic approach for computing corrections to higher order in the heavy mass expansion; precision applications include predictions for experimental data and connections to theoretical tests via lattice QCD. A set of pedagogical appendices comprehensively reviews modern approaches to performing functional calculations algebraically, and derives contributions from a term with open covariant derivatives for the first time.