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

Alejandro Ayala1, Bruno El-Bennich2,3, Ricardo L. S. Farias4,5, Luis A. Hernández6, Bruno S. Lopes4,5, Luis Carlos Parra Lara1,*, and Renato Zamora7,8

  • 1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, CdMx 04510, Mexico
  • 2Departamento de Física, Universidade Federal de São Paulo, Rua São Nicolau 210, 09913-030 Diadema, São Paulo, Brazil
  • 3Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271—Bloco II, 01140-070 São Paulo, São Paulo, Brazil
  • 4Departamento de Física, Universidade Federal de Santa Maria, 97105-900 Santa Maria, Rio Grande do Sul, Brazil
  • 5Center for Nuclear Research, Department of Physics, Kent State University, Kent, Ohio 44242, USA
  • 6Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Avenida San Rafael Atlixco 186, Ciudad de México 09340, Mexico
  • 7Facultad de Ingeniería y Arquitectura, Universidad Central de Chile, Av. Sta. Isabel 1186, Santiago 8330601, Chile
  • 8Facultad de Ingeniería, Universidad San Sebastián, Bellavista 7, Recoleta, Santiago, Chile

  • *Contact author: luis.parra@correo.nucleares.unam.mx
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Phys. Rev. D 114, 036018 – Published 14 August, 2026

DOI: https://doi.org/10.1103/qzv1-qj4m

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.

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Phys. Rev. D 114, 036018– Published 14 August, 2026
  • Received 28 April 2026
  • Accepted 6 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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