Four-loop relation between the $\bar{\rm MS}$ and on-shell quark mass

TL;DR

This paper calculates the four-loop relation between the on-shell and ar{ m MS} heavy quark masses, providing precise conversions for top, bottom, and charm quarks, and discusses uncertainties at high perturbative orders.

Contribution

It presents the four-loop relation between on-shell and ar{ m MS} quark masses, including relations to threshold masses and uncertainty analysis at NNNLO.

Findings

Precise four-loop relation between on-shell and ar{ m MS} masses for heavy quarks.

Relations established between ar{ m MS} and various threshold mass definitions.

Analysis of theoretical uncertainties at NNNLO.

Abstract

In this contribution we discuss the four-loop relation between the on-shell and $\bar{\rm MS}$ definition of heavy quark masses which is applied to the top, bottom and charm case. We also present relations between the $\bar{\rm MS}$ quark mass and various threshold mass definitions and discuss the uncertainty at next-to-next-to-next-to-leading order.