Infrared Renormalization Group Flow for Heavy Quark Masses

TL;DR

This paper introduces a renormalization group approach for heavy quark masses that depends on two scales, improving scheme conversions and providing a new way to study infrared renormalons.

Contribution

It develops a novel R-dependent renormalization group flow for heavy quark masses, enhancing stability and offering a new method to analyze IR renormalons without bubble chains.

Findings

Flow in R improves mass scheme conversions.

Determines the LambdaQCD renormalon ambiguity coefficient.

Provides a convergent sum-rule for IR renormalons.

Abstract

A short-distance heavy quark mass depends on two parameters, the renormalization scale mu controlling the absorption of ultraviolet fluctuations into the mass, and a scale R controlling the absorption of infrared fluctuations. 1/R can be thought of as the radius for perturbative corrections that build up the mass beyond its point-like definition in the pole scheme. Treating R as a variable gives a renormalization group equation. We argue that the sign of this anomalous dimension is universal: increasing R to add IR modes decreases m(R). The flow improves the stability of conversions between mass schemes, allowing us to avoid large logs and the renormalon. The flow in R can be used to study IR renormalons without using bubble chains, and we use it to determine the coefficient of the LambdaQCD renormalon ambiguity of the pole mass with a convergent sum-rule.