Degenerate fermionic matter at N${}^3$LO: Quantum Electrodynamics

Abstract

We determine the pressure of a cold and dense electron gas to a nearly complete next-to-next-to-next-to-leading order (N${}^3$LO) in the fine-structure constant ${\alpha }_e$, utilizing a new result for the two-loop photon self-energy from a companion paper. Our result contains all infrared-sensitive contributions to the pressure at this order, including the coefficient of the $O({\alpha }_e^3\ln {\alpha }_e^{})$ term, and leaves only a single coefficient associated with the contributions of unresummed hard momenta undetermined. Moreover, we explicitly demonstrate the complete cancellation of infrared divergences according to the effective field theory paradigm by determining part of the hard contributions at this order. Our calculation provides the first improvement to a 45-year-old milestone result and demonstrates the feasibility of the corresponding N${}^3$LO calculation for cold and dense quark matter.

6 pages (main text), 6 pages (supplemental material) and 3 figures

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Cited by in corpus (6)

• Equation of State of Cold Quark Matter to $O({\alpha }_s^3\ln {\alpha }_s)$
• Soft photon propagation in a hot and dense medium to next-to-leading order
• Soft gluon self-energy at finite temperature and density: hard NLO corrections in general covariant gauge
• Integrating by parts at finite density
• Power corrections to the photon polarization tensor in a hot and dense medium of massive fermions
• Momentum expansions in finite-density perturbative calculations