Exact results for ZmOS and Z2OS with two mass scales and up to three loops

Abstract

We consider the on-shell mass and wave function renormalization constants ZmOS and Z2OS 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 1−τ2 and 1−τ2/τ which extends the findings from ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order O(ϵ2) and 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.