Year: 2026
Type: preprint
Abstract: 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 $O\left(e^5\right)$ 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 $O(e^6\ln e)$ term in QED arises only in the nonuniform limit ${T}/{m_{\rm{E}}}\to0$ where $m_{\rm{E}}$ is the electric screening mass, demonstrating that the weak-coupling and zero-temperature limits do not commute.
Source: arXiv (Cornell University)
Authors: Gorda, Tyler, Majumder, Swastik
Institution: The Ohio State University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221094553