Chiral first order phase transition at finite baryon density and zero temperature from self-consistent pole masses in the linear sigma model with quarks

TL;DR

This paper investigates the chiral phase transition at finite baryon density and zero temperature using a two-flavor Linear Sigma Model with quarks, revealing a first order transition with distinct thermodynamic signatures.

Contribution

It introduces a self-consistent one-loop approach that extends beyond ring-diagram approximation to analyze the phase transition at arbitrary chemical potentials.

Findings

The phase transition is of first order at a critical chemical potential equal to the vacuum quark mass.

Discontinuous behavior observed in chiral condensate, masses, and couplings at the transition.

Speed of sound squared shows a discontinuity and approaches the conformal limit smoothly.

Abstract

We use the two-flavor Linear Sigma Model with quarks as an effective description of QCD to investigate the nature of the chiral phase transition at finite baryon chemical potential and zero temperature. We work at one-loop order to set up and solve the system of self-consistent coupled equations for the particle pole masses. The chemical potential-dependent value of the chiral order parameter is obtained by minimizing the one-loop effective potential. This treatment goes beyond the conventional ring-diagram approximation and provides a description valid for arbitrary values of the chemical potential. We find that the phase transition is of first order, and occurs when the quark chemical potential reaches the value of the vacuum quark mass for the chosen set of parameters. The first order nature of the transition is signaled by the discontinuous behavior of the chiral condensate, the masses and the couplings. The thermodynamics of the system is readily implemented and in particular, we find that the square of the speed of sound exhibits a discontinuity at the phase transition and then smoothly approaches the conformal limit from below.