Equation of state of cold quark matter to $O(\alpha_s^3 \ln \alpha_s)$

Accurately understanding the equation of state (EOS) of high-density, zero-temperature quark matter plays an essential role in constraining the behavior of dense strongly interacting matter inside the cores of neutron stars. In this Letter, we study the weak-coupling expansion of the EOS of cold quark matter and derive the complete, gauge-invariant contributions from the long-wavelength, dynamically screened gluonic sector at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant $\alpha_s$. This elevates the EOS result to the $O(\alpha_s^3 \ln \alpha_s)$ level, leaving only one unknown constant from the unscreened sector at N3LO, and places it on par with its high-temperature counterpart from 2003. This is achieved by generalizing next-to-leading order gluon self-energies within the hard-thermal-loop limit from high temperatures and densities to zero temperature. We find that including these screened gluonic contributions at N3LO yields a remarkably well-converged EOS, with essentially no renormalization-scale dependence. Finally, we perform a Bayesian estimation of the remaining unscreened contribution at N3LO and find that the full EOS of cold quark matter at this order may show markedly improved convergence over the lower-order results.