Three-loop QCD+QED corrections to on-shell quark renormalization

TL;DR

This paper computes three-loop mixed QCD and QED corrections to on-shell quark mass and wave-function renormalization, providing precise relations between different quark mass definitions and the anomalous dimension in the combined theory.

Contribution

It presents the first complete three-loop mixed QCD+QED corrections to on-shell quark renormalization constants and mass relations, including conversion formulas and anomalous dimensions.

Findings

Derived three-loop corrections to quark mass and wave-function renormalization constants.

Established the relation between pole mass and $ar{ ext{MS}}$ mass including mixed corrections.

Provided explicit conversion formulas between pole mass and trace-anomaly subtracted $\sigma$-mass.

Abstract

We present the three-loop QCD+QED mixed corrections to the on-shell quark mass and wave-function renormalization constants through orders $\mathcal{O}(\alpha_s^m\alpha^n)$ with $m+n=3$. We further derive the three-loop relation between the pole mass and the $\overline{\text{MS}}$ mass of a heavy quark, including the complete mixed QCD+QED contributions. The corresponding quark-mass anomalous dimension in the presence of both interactions is also extracted. Moreover, we provide the explicit conversion formulae, up to the same perturbative order, between the pole mass and the trace-anomaly subtracted $\sigma$-mass of heavy quark.