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Hard-region fermion self-energy and fermion-photon vertex in thermal QED through two loops

Ali Hataei*

  • *Contact author: a.hataei@alumni.sbu.ac.ir; Hataeiali76@gmail.com
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Phys. Rev. D 114, 076016 – Published 13 October, 2026

DOI: https://doi.org/10.1103/zxnj-1vtz

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.

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Phys. Rev. D 114, 076016– Published 13 October, 2026
  • Received 26 June 2026
  • Accepted 1 September 2026
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