We determine the pressure of a cold and dense electron gas to a nearly complete next-to-next-to-next-to-leading order (${\mathrm{N}}^3\mathrm{LO}$) 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 ${\mathrm{N}}^3\mathrm{LO}$ calculation for cold and dense quark matter.

• Received 23 May 2022
• Accepted 7 December 2022

DOI:https://doi.org/10.1103/PhysRevD.107.L031501

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Published by the American Physical Society