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.