Peculiar features of the relations between pole and running heavy quark masses and estimates of the O(\alpha_s^4) contributions

TL;DR

This paper investigates the perturbative relations between pole and running heavy quark masses, focusing on kinematic effects and providing estimates for four-loop QCD corrections.

Contribution

It offers new insights into the $ heta$-function effects in mass relations and provides estimates for O(α_s^4) contributions in QCD.

Findings

Identification of $ heta$-function effects in mass relations

Estimates of four-loop QCD corrections

Analysis of kinematic $ heta$-effects in series coefficients

Abstract

Perturbative relations between pole and running heavy quark masses, defined in the Minkowski regions, are considered. Special attention is paid to the appearance of the kinematic $\pi^2$-effects, which exist in the coefficients of these series. The estimates of order $O(\alpha_s^4)$ QCD corrections are presented.