Degenerate fermionic matter at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup><mml:mi>LO</mml:mi></mml:mrow></mml:math>: Quantum electrodynamics
Tyler Gorda, Aleksi Kurkela, Juuso Österman, Risto Paatelainen, Saga Säppi, Philipp Schicho, Kaapo Seppänen, Aleksi Vuorinen
Abstract
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 ${\ensuremath{\alpha}}_{e}$, 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 $O({\ensuremath{\alpha}}_{e}^{3}\mathrm{ln}{\ensuremath{\alpha}}_{e})$ 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.