Hot and dense QED at N3LO: infrared sector
Abstract
We determine the infrared-sensitive contribution to the pressure of hot and dense massless quantum electrodynamics (QED) at O(e6) in the electric charge e, obtaining a representation valid across the crossover between the thermally dominated and degenerate regimes. This contribution arises from a hard-thermal-loop (HTL) resummed soft photon dressed by either the one-loop power correction or the two-loop next-to-leading-order photon self-energy. After separating the static and nonstatic sectors, we obtain the static contribution in closed form and perform the nonstatic Matsubara sum analytically in terms of the digamma function, reducing the remaining finite coefficient to a one-dimensional numerical integral. The finite-temperature HTL counterterm cancels the factorization divergence before expansion; at strictly zero temperature T, this divergence instead cancels against the hard four-loop contribution. At vanishing chemical potential, the static sector reproduces the complete known O(e5) pressure. Taking the cold limit of the dimensionally regulated, unsubtracted nonstatic contribution reproduces the correct cold mixed result. Crucially, at any fixed T>0, the nonstatic result remains analytic in e2. The zero-temperature O(e6ln e) term in QED arises only in the nonuniform limit T/mE→0 where mE is the electric screening mass, demonstrating that the weak-coupling and zero-temperature limits do not commute.
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BibTeX
@misc{gorda2026dense,
title = {{Hot and dense QED at N$^3$LO: infrared sector}},
author = {Tyler Gorda and Swastik Majumder},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10771},
eprint = {2610.10771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10771},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hot and dense QED at N^3LO: infrared sector
AU - Tyler Gorda
AU - Swastik Majumder
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10771
UR - https://arxiv.org/abs/2610.10771
AB - We determine the infrared-sensitive contribution to the pressure of hot and dense massless quantum electrodynamics (QED) at O(e^6) in the electric charge e, obtaining a representation valid across the crossover between the thermally dominated and degenerate regimes. This contribution arises from a hard-thermal-loop (HTL) resummed soft photon dressed by either the one-loop power correction or the two-loop next-to-leading-order photon self-energy. After separating the static and nonstatic sectors, we obtain the static contribution in closed form and perform the nonstatic Matsubara sum analytically in terms of the digamma function, reducing the remaining finite coefficient to a one-dimensional numerical integral. The finite-temperature HTL counterterm cancels the factorization divergence before expansion; at strictly zero temperature T, this divergence instead cancels against the hard four-loop contribution. At vanishing chemical potential, the static sector reproduces the complete known O(e^5) pressure. Taking the cold limit of the dimensionally regulated, unsubtracted nonstatic contribution reproduces the correct cold mixed result. Crucially, at any fixed T>0, the nonstatic result remains analytic in e^2. The zero-temperature O(e^6ln e) term in QED arises only in the nonuniform limit T/m_E→0 where m_E is the electric screening mass, demonstrating that the weak-coupling and zero-temperature limits do not commute.
ER -