NNNLO pressure of cold quark matter: leading logarithm

TL;DR

This paper computes the leading logarithmic correction at NNNLO for the pressure of cold quark matter, improving the theoretical understanding of QCD at high density and confirming the weak-coupling expansion's reliability.

Contribution

It introduces a novel application of the Hard-Thermal-Loop scheme to determine the leading-logarithm term at NNNLO in cold quark matter, the first such advancement in 40 years.

Findings

The leading-logarithm NNNLO correction is negligibly small.

The result enhances confidence in the weak-coupling expansion for cold quark matter.

First such correction computed in four decades.

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.