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

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.

arXiv comment27 pages, 12 figures, Expanded discussion, version to appear in EPJ A, contribution for the topical Issue "The QCD Phase Diagram in Strong Magnetic Fields"

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• Effects of the quark anomalous magnetic moment in the chiral symmetry restoration: magnetic catalysis and inverse magnetic catalysis
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• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Revisiting shear stress tensor evolution: Non-resistive magnetohydrodynamics with momentum-dependent relaxation time
• Quantum version of transport coefficients in Nambu--Jona-Lasinio model at finite temperature and strong magnetic field
• Collision energy dependence of the critical end point from baryon number fluctuations in the Linear Sigma Model with quarks
• Catalysis and inverse electric catalysis in a scalar theory
• Magnetized pole-mass of neutral $\rho$ meson within full RPA evaluation
• Describing the speed of sound peak of isospin-asymmetric cold strongly interacting matter using effective models
• The magnetized (2+1)-dimensional Gross-Neveu model at finite density
• Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram
• Neutral pion mass in warm magnetized medium within Linear Sigma Model coupled to Quarks $\left({\text{LSM}}_q\right)$ framework
• Thermomagnetic effects on light pseudo-scalar meson masses within the SU(3) Nambu-Jona--Lasinio model
• Darker and brighter branes: Suppression and enhancement of photon production in a strongly coupled magnetized plasma
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