Perturbative QCD meets phase quenching: The pressure of cold quark matter

Nonperturbative inequalities constrain the thermodynamic pressure of Quantum Chromodynamics (QCD) with its phase-quenched version, a Sign-Problem-free theory amenable to lattice treatment. In the perturbative regime with a small QCD coupling constant ${\alpha }_s$, one of these inequalities manifests as an $O({\alpha }_s^3)$ difference between the phase-quenched and QCD pressures at large baryon chemical potential. In this work, we generalize state-of-the-art algorithmic techniques used in collider physics in vacuum quantum field theory to address large-scale multiloop computations at finite chemical potential, by direct numerical integration of Feynman diagrams in momentum space. Using this novel approach, we evaluate this $O({\alpha }_s^3)$ difference and show that it is a gauge-independent and small positive number compared to the known perturbative coefficients at this order. This implies that at high baryon densities, phase-quenched lattice simulations can provide a complementary nonperturbative method for accurately determining the pressure of cold quark matter at $O({\alpha }_s^3)$.