NNNLO pressure of cold quark matter: leading logarithm

At high baryon chemical potential μB, the equation of state of QCD allows a weak-coupling expansion in the QCD coupling αs. The result is currently known up to and including the full next-to-next-to-leading order αs2. Starting at this order, the computations are complicated by the modification of particle propagation in a dense medium, which necessitates nonperturbative treatment of the scale αs1/2μB. We apply a hard-thermal-loop scheme for capturing the contributions of this scale to the weak-coupling expansion, and we use it to determine the leading-logarithm contribution to next-to-next-to-next-to-leading order: αs3ln2αs. 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.