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arXiv · 2610.33164

Four-loop $\overline{\rm MS}$-pole quark mass relation with two different masses

Matteo Fael·Fabian Lange·Kay Schönwald·Matthias Steinhauser
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Abstract

We calculate the relation between heavy-quark masses defined in the on-shell and $\overline{\rm MS}$ 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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Matteo Fael, Fabian Lange, Kay Schönwald, Matthias Steinhauser. 2026-10-23. Four-loop $\overline{\rm MS}$-pole quark mass relation with two different masses. https://arxiv.org/abs/2610.33164

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