Confronting effective models for deconfinement in dense quark matter with lattice data

TL;DR

This paper compares lattice data for dense quark matter with an extended Nambu-Jona-Lasinio model, introducing novel elements like chiral twist and Polyakov loop renormalization to improve qualitative agreement.

Contribution

It introduces two new modifications to the effective model—chiral twist and Polyakov loop renormalization—and determines the Polyakov loop dependence on chemical potential from lattice data.

Findings

Qualitative agreement with lattice data achieved

Chiral twist improves chiral symmetry breaking modeling

Polyakov loop renormalization aligns model with lattice results

Abstract

Ab initio numerical simulations of the thermodynamics of dense quark matter remain a challenge. Apart from the infamous sign problem, lattice methods have to deal with finite volume and discretization effects as well as with the necessity to introduce sources for symmetry-breaking order parameters. We study these artifacts in the Polyakov-loop-extended Nambu-Jona-Lasinio model, and compare its predictions to existing lattice data for cold and dense two-color matter with two flavors of Wilson quarks. To achieve even qualitative agreement with lattice data requires the introduction of two novel elements in the model: (i) explicit chiral symmetry breaking in the effective contact four-fermion interaction, referred to as the chiral twist, and (ii) renormalization of the Polyakov loop. The feedback of the dense medium to the gauge sector is modeled by a chemical-potential-dependent scale in the Polyakov-loop potential. In contrast to previously used analytical ansaetze, we determine its dependence on the chemical potential from lattice data for the expectation value of the Polyakov loop. Finally, we propose to add a two-derivative operator to our effective model. This term acts as an additional source of explicit chiral symmetry breaking, mimicking an analogous term in the lattice Wilson action.