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

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arxiv 2106.05296 v1 pith:AE2YLIJT submitted 2021-06-09 hep-ph

Matteo Fael , Fabian Lange , Kay Schönwald , Matthias Steinhauser This is my paper · ORCID
classification hep-ph
keywords integralsmethodcomputemassquarkcoefficienteightfour-loop
verification ladder T0 review T1 audit T2 compute T3 formal
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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 $\overline{\rm MS}$ 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.

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Cited by 5 Pith papers

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