NNNLO pressure of cold quark matter: leading logarithm

Abstract

At high baryon chemical potential ${\mu }_B$, the equation of state of QCD allows a weak-coupling expansion in the QCD coupling ${\alpha }_s$. The result is currently known up to and including the full next-to-next-to-leading order (NNLO) ${\alpha }_s^2$. Starting at this order, the computations are complicated by the modification of particle propagation in a dense medium, which necessitates non-perturbative treatment of the scale ${\alpha }_s^{1/2}{\mu }_B$. In this work, we apply a Hard-Thermal-Loop scheme for capturing the contributions of this scale to the weak-coupling expansion, and use it to determine the leading-logarithm contribution to NNNLO: ${\alpha }_s^3{\ln }^2{\alpha }_s$. This result is the first improvement to the equation of state of massless cold quark matter in 40 years. The new term is negligibly small, and thus significantly increases our confidence in the applicability of the weak-coupling expansion.

8 pages with appendix, 2 figures; v3: Added footnote to point out minus sign error in final result

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• New constraints on radii and tidal deformabilities of neutron stars from GW170817
• Cold Quark Matter
• The lattice QCD phase diagram in and away from the strong coupling limit
• The pressure of deconfined QCD for all temperatures and quark chemical potentials

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