Quark matter at four loops: hardships and how to overcome them

TL;DR

This paper advances the calculation of the pressure of cold, dense quark matter to the four-loop level in QCD, overcoming significant technical challenges and demonstrating the effectiveness of new numerical methods, bringing us closer to precise neutron star models.

Contribution

It provides the first concrete progress towards calculating the N3LO pressure of dense quark matter, including handling infrared divergences and applying the dense Loop Tree Duality method.

Findings

Successful cancellation of gauge parameter and IR divergences.

Validation of the dense Loop Tree Duality method for four-loop integrals.

Progress towards complete N3LO pressure calculation.

Abstract

Knowledge of the pressure of cold and dense quark matter (QM) 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 work, we make important progress towards determining the last unknown contribution to the pressure at Next-to-Next-to-Next-to-Leading Order (N3LO) in the strong coupling constant $\alpha_s$, 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 (IR) divergences in the sum, showcasing the effective-field-theory paradigm in action. For the remaining IR-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 N3LO pressure of cold QM is no longer merely possible but for the first time concretely within reach.