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Four-loop MS̅-pole quark mass relation with two different masses
Abstract
We calculate the relation between heavy-quark masses defined in the on-shell and MS̅ renormalization schemes up to four-loop order in Quantum Chromodynamics, accounting for a second, non-zero quark mass. We employ a semi-analytical method that yields precise results valid for all values of the mass ratio. In particular, our approach enables generalized expansions for small and large values of the second quark mass, incorporating all logarithmic contributions. For the limiting cases of a vanishing or equal second quark mass, we significantly improve upon the precision of known results for 18 of the 23 colour structures.
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BibTeX
@misc{fael2026fourloop,
title = {{Four-loop $\overline\rm MS$-pole quark mass relation with two different masses}},
author = {Matteo Fael and Fabian Lange and Kay Schönwald and Matthias Steinhauser},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33164},
eprint = {2610.33164},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33164},
}
RIS
TY - UNPB
TI - Four-loop MS̅-pole quark mass relation with two different masses
AU - Matteo Fael
AU - Fabian Lange
AU - Kay Schönwald
AU - Matthias Steinhauser
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33164
UR - https://arxiv.org/abs/2610.33164
AB - We calculate the relation between heavy-quark masses defined in the on-shell and MS̅ renormalization schemes up to four-loop order in Quantum Chromodynamics, accounting for a second, non-zero quark mass. We employ a semi-analytical method that yields precise results valid for all values of the mass ratio. In particular, our approach enables generalized expansions for small and large values of the second quark mass, incorporating all logarithmic contributions. For the limiting cases of a vanishing or equal second quark mass, we significantly improve upon the precision of known results for 18 of the 23 colour structures.
ER -