Hard-Region Fermion Self-Energy and Fermion--Photon Vertex in Thermal QED through Two Loops
Abstract
We compute hard-region contributions to the fermion self-energy and the off-shell fermion--photon vertex in massless thermal QED in a covariant Rξ gauge. The calculation includes the one-loop next-to-leading-power and two-loop leading-power terms in the expansion in soft external momenta, together with the zero-temperature counterterms required to remove ultraviolet subdivergences. In the real-time formalism, we first derive symmetry constraints on the two-fermion--N-photon amplitudes, which lead to distinct selection rules in the soft-momentum expansion. The fermion--photon vertex is decomposed into Dirac-vector and axial-vector coefficients. The former satisfies the Ward--Takahashi identity, while the latter is transverse to the photon momentum. These relations are verified at the integrand level. The hard self-energy corrections computed here produce no finite contribution to the fermion damping rate. Our results provide previously unavailable two- and three-point hard-region data for higher-order analyses of fermion mass shifts and inclusive rates, as well as for the construction of a next-to-leading-order fermionic effective action.
Versions
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BibTeX
@misc{hataei2026hardregion,
title = {{Hard-Region Fermion Self-Energy and Fermion--Photon Vertex in Thermal QED through Two Loops}},
author = {Ali Hataei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.27137},
eprint = {2606.27137},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.27137},
}
RIS
TY - UNPB
TI - Hard-Region Fermion Self-Energy and Fermion--Photon Vertex in Thermal QED through Two Loops
AU - Ali Hataei
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2606.27137
UR - https://arxiv.org/abs/2606.27137
AB - We compute hard-region contributions to the fermion self-energy and the off-shell fermion--photon vertex in massless thermal QED in a covariant R_ξ gauge. The calculation includes the one-loop next-to-leading-power and two-loop leading-power terms in the expansion in soft external momenta, together with the zero-temperature counterterms required to remove ultraviolet subdivergences. In the real-time formalism, we first derive symmetry constraints on the two-fermion--N-photon amplitudes, which lead to distinct selection rules in the soft-momentum expansion. The fermion--photon vertex is decomposed into Dirac-vector and axial-vector coefficients. The former satisfies the Ward--Takahashi identity, while the latter is transverse to the photon momentum. These relations are verified at the integrand level. The hard self-energy corrections computed here produce no finite contribution to the fermion damping rate. Our results provide previously unavailable two- and three-point hard-region data for higher-order analyses of fermion mass shifts and inclusive rates, as well as for the construction of a next-to-leading-order fermionic effective action.
ER -