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

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 $\overline{\text{MS}}$ anomalous dimension of the QED electron field depends on the gauge parameter only at one loop.

Comments: 9 pages, no figures. v2: discussion of gauge invariance in QED extended, references added; v3: QED gauge invariance completely proved; v4: 1 reference added; v5: several typos in the Appendix fixed