# A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{MS}$ -pole quark mass relation

Fael, Matteo 1; Lange, Fabian 1,2; Schönwald, Kay 1; Steinhauser, Matthias 1
1 Institut für Theoretische Teilchenphysik (TTP), Karlsruher Institut für Technologie (KIT)
2 Institut für Astroteilchenphysik (IAP)

## Abstract:

We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter x and the dimension d, in the whole kinematic range of x. The method is based on differential equations, which, however, do not require any special form, and series expansions around singular and regular points. This method provides results well suited for fast numerical evaluation and sufficiently precise for phenomenological applications. We apply the approach to four-loop on-shell integrals and compute the coefficient function of eight colour structures in the relation between the mass of a heavy quark defined in the $\overline{MS}$ and the on-shell scheme allowing for a second non-zero quark mass. We also obtain analytic results for these eight coefficient functions in terms of harmonic polylogarithms and iterated integrals. This allows for a validation of the numerical accuracy.

 Zugehörige Institution(en) am KIT Institut für Astroteilchenphysik (IAP)Institut für Theoretische Teilchenphysik (TTP) Publikationstyp Zeitschriftenaufsatz Publikationsjahr 2021 Sprache Englisch Identifikator ISSN: 1029-8479, 1126-6708, 1127-2236 KITopen-ID: 1000138677 HGF-Programm 51.11.01 (POF IV, LK 01) Teilchenphysik Erschienen in Journal of High Energy Physics Verlag Scuola Internazionale Superiore di Studi Avanzati (SISSA) Band 2021 Heft 9 Seiten 152 Nachgewiesen in DimensionsScopusWeb of Science
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