Renormalization group invariant mean-field model for QCD at finite isospin density

TL;DR

This paper develops a renormalization-group invariant mean-field model for QCD at finite isospin density, accurately matching lattice data and providing insights into the phase diagram and speed of sound in dense strongly interacting matter.

Contribution

It introduces a novel renormalization-group invariant mean-field formulation of the quark-meson model for QCD at finite isospin density, aligning with lattice and perturbative results.

Findings

Model's phase diagram agrees with lattice QCD data.

Speed of sound exceeds conformal bound at small/intermediate isospin chemical potentials.

Speed approaches conformal limit at large isospin chemical potentials.

Abstract

QCD at nonzero isospin chemical potentials has phenomenological relevance for a series of physical systems and provides an ideal testground for the modeling of dense strongly interacting matter. The two-flavor quark-meson model is known to effectively describe the condensation of charged pions in QCD that occurs in this setting. In this paper, we derive a renormalization-group invariant mean-field formulation of the model and demonstrate that the resulting phase diagram and equation of state are in quantitative agreement with data from lattice QCD simulations at small and intermediate isospin chemical potentials. In particular, the speed of sound from the model shows an excess over the conformal bound as previously seen in lattice computations in agreement with chiral perturbation theory. We then consider the speed of sound in the limit of large isospin chemical potentials and see that it approaches the conformal limit from above, in qualitative agreement with recent lattice results and in quantitative agreement with perturbation theory in the presence of a BCS gap. Finally, we consider the phase diagram in the approach to the chiral limit. We find that within the model the chiral phase transition connects to the pion condensation phase boundary in the chiral limit and we discuss the implications for the properties of the chiral transition point.