Matching the heavy-quark fields in QCD and HQET at four loops

TL;DR

This paper computes the four-loop matching coefficient for heavy-quark fields in QCD and HQET, providing analytical results and extending understanding of on-shell integrals with two masses, with applications to QED.

Contribution

It presents the first four-loop calculation of the QCD/HQET heavy-quark field matching coefficient, including analytical results and mass effects.

Findings

Four-loop matching coefficient computed analytically.

On-shell integrals with two masses analyzed in detail.

Relation between electron and Bloch-Nordsieck fields derived at four loops.

Abstract

The QCD/HQET matching coefficient for the heavy-quark field is calculated up to four loops. It must be finite; this requirement produces analytical results for some terms in the four-loop on-shell heavy-quark field renormalization constant which were previously only known numerically. The effect of a non-zero lighter-flavor mass is calculated up to three loops. A class of on-shell integrals with two masses is analyzed in detail. By specifying our result to QED, we obtain the relation between the electron field and the Bloch--Nordsieck field with four-loop accuracy.