Gauge invariance of radiative jet functions in the position-space formulation of SCET
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
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- German Research Foundation (DFG); National Key Research and Development Program of China; National Natural Science Foundation of China (NSFC); USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), High Energy Physics (HEP)
- Grant/Contract Number:
- 89233218CNA000001; AC02-06CH11357
- OSTI ID:
- 2328160
- Report Number(s):
- LA-UR--24-25925; 056020
- 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
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