On the relation between pole and running heavy quark masses beyond the four-loop approximation

TL;DR

This paper investigates the relation between pole and running heavy quark masses beyond four loops using an effective charges approach, estimating higher-order corrections and analyzing their behavior in perturbative QCD.

Contribution

It introduces an effective charges motivated method to study high-order corrections in the pole and MS-bar heavy quark mass relation, including estimates for five- and six-loop coefficients.

Findings

Predicted sign-alternating expansion in powers of light flavors $n_l$ for higher-order terms.

Coefficients contain $\pi^2$ effects from analytical continuation from Euclidean to Minkowskian regions.

Asymptotic nature of the perturbative mass relation varies between $t$-quark and $b$-quark at six loops.

Abstract

The effective charges motivated method is applied to the relation between pole and $\rm{\overline{MS}}$-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors $n_l$, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to $\pi^2$ effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the $t$-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the $b$-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.