Matching the heavy-quark fields in QCD and HQET 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.

20 pages. v2: ref. [48] added, small changes in the text, corresponds to the journal version

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Cited by in corpus (3)

• A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{\mathrm{MS}}$-pole quark mass relation
• QCD cusp anomalous dimension: current status
• Charm-quark mass effects in NRQCD matching coefficients and the leptonic decay of the ${\rm Y}(1S)$ meson