Quark mass relations to four-loop order

TL;DR

This paper computes the relation between on-shell and -bar heavy quark masses at four-loop order, improving the precision of quark mass determinations in quantum chromodynamics.

Contribution

It provides the first four-loop order calculation of the heavy quark mass relation, enhancing the accuracy of -bar mass extractions from experimental data.

Findings

Established four-loop relation between on-shell and -bar masses

Improved the precision of -bar heavy quark mass determinations

Enabled next-to-next-to-next-to-leading order accuracy in mass relations

Abstract

We present results for the relation between a heavy quark mass defined in the on-shell and $\bar{\rm MS}$ scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the $\bar{\rm MS}$ quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the $\bar{\rm MS}$ heavy quark masses.