On-shell renormalisation constants including two different nonzero masses

TL;DR

This paper calculates the impact of a second massive quark on the relation between pole and minimal subtracted quark mass, including wave function renormalisation, at three-loop order, relevant for bottom quark physics.

Contribution

It provides new three-loop level results for the effect of a second massive quark on mass renormalisation constants, including technical details of the calculation.

Findings

Quantifies the effect of a second massive quark on mass relations

Includes wave function renormalisation effects

Relevant for phenomenology of bottom quark with virtual charm effects

Abstract

We present results for the effect of a second massive quark in the relation between the pole and the minimal subtracted quark mass at the three loop level. We also consider the analogous effect for the wave function renormalisation constant. Some technical details of the calculation are given. Our result is phenomenologically relevant for the bottom quark including virtual charm effects.