Matching heavy-quark fields in QCD and HQET at three loops

TL;DR

This paper derives the three-loop relation between heavy-quark fields in QCD and HQET, and explores gauge invariance properties of related QED fields, advancing precision in quantum field theory calculations.

Contribution

It provides the first three-loop derivation of the heavy-quark field relation in QCD and extends gauge invariance analysis to all orders in QED.

Findings

Derived three-loop relation between QCD and HQET heavy-quark fields.

Proved gauge invariance of the QED electron field relation to all orders.

Showed the gauge dependence of the QED electron field's anomalous dimension at one loop.

Abstract

The relation between the heavy-quark field in QCD and the corresponding field in HQET is derived up to three loops, and to all orders in the large-$\beta_0$ limit. The corresponding relation between the QED electron field and the Bloch--Nordsieck one is gauge invariant to all orders. We also prove that the $\bar{\text{MS}}$ anomalous dimension of the QED electron field depends on the gauge parameter only at one loop.