Abstract
We consider the on-shell mass and wave function renormalization constants \( {Z}_m^{\mathrm{OS}} \) and \( {Z}_2^{\mathrm{OS}} \) up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters \( \sqrt{1-{\tau}^2} \) and \( \sqrt{1-{\tau}^2}/\tau \) which extends the findings from ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order \( \mathcal{O} \)(ϵ2) and \( \mathcal{O} \)(ϵ) at two- and three-loop order which are crucial ingredients for a future four-loop calculation. Compact results for the expansions around the zero-mass, equal-mass and large-mass cases allow for a fast high-precision numerical evaluation.
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Fael, M., Schönwald, K. & Steinhauser, M. Exact results for \( {Z}_m^{\mathrm{OS}} \) and \( {Z}_2^{\mathrm{OS}} \) with two mass scales and up to three loops. J. High Energ. Phys. 2020, 87 (2020). https://doi.org/10.1007/JHEP10(2020)087
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DOI: https://doi.org/10.1007/JHEP10(2020)087