Gauge invariance of radiative jet functions in the position-space formulation of SCET

Journal Article · 25 March 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.109.056020 · OSTI ID:2328160

Bodwin, Geoffrey T.; Ee, June-Haak ; Kang, Daekyoung ; Wang, Xiang-Peng

In subleading powers of soft-collinear effective theory (SCET), the Lagrangian contains couplings between soft quarks and hard-collinear quarks. Matrix elements of the hard-collinear parts of these couplings are radiative jet functions. In the position-space formulation of SCET, the Lagrangians are constructed from operators that appear to be gauge invariant. Nevertheless, we find violations of gauge invariance arise in the hard-collinear sector because gauge transformations can shift the momentum of a hard-collinear quark field from the hard-collinear sector to the soft sector, where the hard-collinear fields, by definition, have no support. The violations of gauge invariance are manifested in perturbation theory in the hard-collinear sector through the absence of certain Feynman diagrams that would be present in full QCD. A consequence of the absence of these diagrams is that the radiative jet functions that follow directly from the position-space Lagrangians are not gauge invariant, and we demonstrate this through explicit calculations in lower-order perturbation theory. We obtain gauge-invariant Lagrangians by adding to existing position-space Lagrangians terms that are proportional to the soft-quark equation of motion. These gauge-invariant Lagrangians are valid for nonzero, as well as zero, quark masses. We also remark briefly on the gauge invariance of certain Lagrangians that have been constructed in the label-momentum formulation of SCET. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 2328160
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 5 Vol. 109; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English