Perturbative QCD meets phase quenching: The pressure of cold Quark Matter

Nonperturbative inequalities constrain the 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 αₛ, one of these inequalities manifests as an O(αₛ³) difference between the phase-quenched and QCD pressures at large baryon chemical potential μB. In this work, we generalize state-of-the-art algorithmic techniques in vacuum quantum field theory to address large-scale multiloop computations at finite chemical potential. Using this approach, we evaluate this O(αₛ³) 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 phase-quenched lattice simulations can provide a complementary nonperturbative method for accurately determining the pressure of cold and dense quark matter at O(αₛ³).