Eur. Phys. J. A (2021) 57: 234
https://doi.org/10.1140/epja/s10050-021-00534-4

Review

QCD phase diagram in a magnetized medium from the chiral symmetry perspective: the linear sigma model with quarks and the Nambu–Jona-Lasinio model effective descriptions

¹ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510, CdMx, Mexico
² Department of Physics, Centre for Theoretical and Mathematical Physics, University of Cape Town, Rondebosch, 7700, Cape Town, South Africa
³ Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, 09340, CdMx, Mexico
⁴ Instituto de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile
⁵ Centro Científico Tecnológico de Valparaíso-CCTVAL, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile
⁶ Centro de Ciencias Exactas and Departamento de Ciencias Básicas, Universidad del Bío-Bío, Casilla 447, Chillán, Chile

^a ayala@nucleares.unam.mx

Received: 11 April 2021
Accepted: 17 June 2021
Published online: 15 July 2021

Abstract

We review the main features of the QCD phase diagram description, at finite temperature, baryon density and in the presence of a magnetic field, from the point of view of effective models, whose main ingredient is chiral symmetry. We concentrate our attention on two of these models: The linear sigma model with quarks and the Nambu–Jona-Lasinio model. We show that a main ingredient to understand the characteristics of the phase transitions is the inclusion of plasma screening effects that capture the physics of collective, long-wave modes, and thus describe a prime property of plasmas near transition lines, namely, long distance correlations. Inclusion of plasma screening makes possible to understand the inverse magnetic catalysis phenomenon even without the need to consider magnetic field-dependent coupling constants. Screening is also responsible for the emergence of a critical end point in the phase diagram even for small magnetic field strengths. Although versatile, the NJL model is also a more limited approach since, being a non-renormalizable model, a clear separation between pure vacuum and medium effects is not always possible. The model cannot describe inverse magnetic catalysis unless a magnetic field dependent coupling is included. The location of the critical end point strongly depends on the choice of the type of interaction and on the magnetic field dependence of the corresponding coupling. Overall, both models provide sensible tools to explore the properties of magnetized, strongly interacting matter. However, a cross talk among them as well as a consistent physical approach to determine the model parameters is much needed.