Infrared Renormalization Group Flow for Heavy Quark Masses

TL;DR

R evolution improves the stability of conversion between short-distance mass schemes, allowing us to avoid large logs and the renormalon, and to study IR renormalons without using bubble chains.

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.

Figures (2)

• Figure 1: Convergence of the sum-rule for $P_{1/2}$ for $m_{\rm pole}$ .
• Figure 2: Top-mass scheme conversion from $R_0=3\,{\rm GeV}$ to $R=163\,{\rm GeV}$. Shown are fixed order results (LO,NLO,NNLO) and RGE results (LL,NLL,NNLL), both in the MSR scheme.