Quark Matter at Four Loops: Hardships and How to Overcome Them

Knowledge of the pressure of cold and dense quark matter is known to significantly constrain the equation of state of neutron-star matter, a quantity playing a key role in deciphering the stars' internal structure. In this Letter, we make important progress toward determining the last unknown contribution to the pressure at next-to-next-to-next-to-leading order in the strong coupling constant α_{s}, available through the sum of all four-loop vacuum diagrams of dense quantum chromodynamics. We demonstrate the cancellation of both the covariant gauge parameter and all infrared divergences in the sum, showcasing the effective-field-theory paradigm in action. For the remaining infrared-finite four-loop integrals, we demonstrate the efficacy of the dense loop tree duality method-a novel numerical framework for multiloop calculations in thermal field theory. Together, our results show that completing the next-to-next-to-next-to-leading order pressure of cold quark matter is no longer merely possible but for the first time within reach.