Exact results for Z m OS $$ {Z}_m^{\mathrm{OS}} $$ and Z 2 OS $$ {Z}_2^{\mathrm{OS}} $$ with two mass scales and up to three loops

• Main Authors: Matteo Fael, Kay Schönwald, Matthias Steinhauser
• Format: Article
• Language: English
• Published: SpringerOpen 2020-10-01
• Series: Journal of High Energy Physics
• Subjects: NLO Computations
• Online Access: http://link.springer.com/article/10.1007/JHEP10(2020)087

Abstract We consider the on-shell mass and wave function renormalization constants Z m OS $$ {Z}_m^{\mathrm{OS}} $$ and Z 2 OS $$ {Z}_2^{\mathrm{OS}} $$ 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 1 − τ 2 $$ \sqrt{1-{\tau}^2} $$ and 1 − τ 2 / τ $$ \sqrt{1-{\tau}^2}/\tau $$ which extends the findings from ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order O $$ \mathcal{O} $$ (ϵ 2) and O $$ \mathcal{O} $$ (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.