Describing the speed of sound peak of isospin-asymmetric cold strongly interacting matter using effective models

TL;DR

This paper models the non-monotonic speed of sound in isospin-asymmetric matter using effective models with medium-dependent couplings, aligning with lattice QCD results.

Contribution

It introduces a method to incorporate medium-dependent couplings in effective models while maintaining thermodynamic consistency, reproducing lattice QCD findings.

Findings

Successfully reproduces the lattice QCD speed of sound behavior

Determines isospin chemical potential dependence of couplings

Maintains thermodynamic identities with medium-dependent couplings

Abstract

The non-monotonic behavior of the speed of sound for isospin imbalanced strongly interacting matter, found by recent lattice QCD simulations, can be reproduced within the Nambu--Jona-Lasinio model and Linear Sigma Model with quarks when the couplings become isospin chemical potential-dependent. The introduction of medium-dependent couplings can potentially affect the equivalence between the thermodynamic relations and their definitions from statistical mechanics. We describe the procedure to compensate for the introduction of medium-dependent couplings to preserve the correct thermodynamic identities. We find the isospin chemical potential dependence for the couplings from the isospin density LQCD data and, after finding the compensating function to correctly describe the pressure, we show that the description of the square of the speed of sound reported by LQCD is well reproduced when using the found medium-dependent couplings in both models.