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.

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

References in corpus (13)

• Heavy Quark Symmetry
• The three-loop QCD $\beta$-function and anomalous dimensions
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• Reparameterisation Invariance Constraints on Heavy Particle Effective Field Theories
• Matching QCD and HQET heavy--light currents at two loops and beyond
• The three loop on-shell renormalization of QCD and QED
• Three-loop anomalous dimension of the heavy-light quark current in HQET
• Cancellation of Renormalon Ambiguities in the Heavy Quark Effective Theory
• Three-Loop Chromomagnetic Interaction in HQET
• Light quark mass effects in the on-shell renormalization constants
• Heavy Quark Effective Theory at Large Orders in $1/m$
• Matching QCD and HQET heavy-light currents at three loops
• Decoupling of heavy quarks in HQET

Cited by in corpus (8)

• On the Casimir scaling violation in the cusp anomalous dimension at small angle
• Four-loop cusp anomalous dimension in QED
• Four-loop wave function renormalization in QCD and QED
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Matching the heavy-quark fields in QCD and HQET at four loops
• QCD cusp anomalous dimension: current status
• Introduction to effective field theories. 3. Bloch--Nordsieck effective theory, HQET
• Matching QCD and HQET at three loops