Critical chiral hypersurface of the magnetized NJL model

Angelo Martínez,Alfredo Raya

doi:10.1016/j.nuclphysb.2018.07.008

Angelo Martínez, Alfredo Raya

Open Access

https://doi.org/10.1016/j.nuclphysb.2018.07.008

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Abstract

In pursuit of sketching the effective magnetized QCD phase diagram, we find conditions on the critical coupling for chiral symmetry breaking in the Nambu–Jona-Lasinio model in a nontrivial thermo-magnetic environment. Critical values for the plasma parameters, namely, temperature and magnetic field strength for this to happen are hence found in the mean field limit. The magnetized phase diagram is drawn from the criticality condition for different models of the effective coupling describing the inverse magnetic catalysis effect.

Highlights

Understanding the behavior of quantum chromodynamics (QCD) in a nontrivial thermo-magnetic environment of quarks and gluons is both a very hot topic and a hard nut to crack
These extreme conditions are met, for instance, in compact stars and in peripheral relativistic heavy ion collisions, which give rise to magnetic fields of around m2π at RHIC and 15m2π at LHC [2]. These fields are short-lived [3], in order to study its effect on the chiral transition, a common starting point is to regard them as uniform in space and time in such a manner that the scenario for the said transition is impacted by the magnetic field strength in a non-trivial manner as the heat bath temperature is increased
In an attempt to sketch the magnetized QCD phase diagram, after neglecting density effects, lattice QCD simulations available in Refs. [4,5,6] reveal, on the one hand, that the chiral condensate grows with the magnetic field strength for temperatures below T0, the pseudocritical temperature for the chiral transition in absence of the magnetic field, in accordance with the universal phenomenon of magnetic catalysis (MC)

Summary

INTRODUCTION

Understanding the behavior of quantum chromodynamics (QCD) in a nontrivial thermo-magnetic environment of quarks and gluons is both a very hot topic and a hard nut to crack (a recent review on the sketch of the magnetized QCD phase diagram can be found in Ref. [1]). These extreme conditions are met, for instance, in compact stars and in peripheral relativistic heavy ion collisions, which give rise to magnetic fields of around m2π at RHIC and 15m2π at LHC [2] These fields are short-lived [3], in order to study its effect on the chiral transition, a common starting point is to regard them as uniform in space and time in such a manner that the scenario for the said transition is impacted by the magnetic field strength in a non-trivial manner as the heat bath temperature is increased. Within the Linear Sigma models (LSM), the full thermomagnetic dependence of the self-coupling [11] as well as the quadratic and quartic couplings [12] have been obtained including the medium screening effects properly These findings capture the basic traits of the IMC effect, namely, decreasing of the couplings with increasing magnetic field for T > T0 as well as the critical temperatures for chiral symmetry restoration.

GAP EQUATION

CRITICAL CURVES

INVERSE MAGNETIC CATALYSIS MODELS OF THE COUPLING CONSTANT

CONCLUDING REMARKS