Abstract

The NJL model of one-flavor quark is employed to study the properties of QCD mater with finite temperature, external magnetic field, and chiral chemical potential. Through the mean-field approximation and a self-consistent method, a non-perturbative quark propagator is proposed to deduce the gap equations, and it can be proved that besides the classic vacuum condensate, there are non-zero statistical averages of a quark current and quark magnetic moment. Through a rigorous algebraic method, the quark current leads to a modified chiral magnetic effect. Through a numerical method, the quark magnetic moment is non-zero in the chiral breaking phase, and its relation with chiral chemical potential is studied.

Highlights

  • This effect is highly relative to the magnetic field and chiral chemical potential

  • In our previous work [35], we proposed a self-consistent method to prove that, with external magnetic field and chemical potential, there is a non-zero axial vector current, which leads to the ‘Chiral Separation Effect’ and a non-zero quark magnetic moment

  • We studied the one-flavor NJL model of the quark with finite temperature, chiral chemical potential, and external magnetic field

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Summary

Introduction

Effects on QCD Matter in NJL Model with a Self-Consistent Method. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. One of the most intriguing properties induced by a magnetic field in the QCD matter is the ‘Chiral Magnetic Effect’ (CME), which has been widely studied in recent decades [26–30] This effect is highly relative to the magnetic field and chiral chemical potential. In our previous work [35], we proposed a self-consistent method to prove that, with external magnetic field and chemical potential, there is a non-zero axial vector current, which leads to the ‘Chiral Separation Effect’ and a non-zero quark magnetic moment. We employ the same method to study the NJL model of QCD matter with an external magnetic field and chiral chemical potential and try to find out new properties of the classic.

Basic Formulae and the Inconsistency
The Minimal Consistency Ansatz
Solve the Gap Equations
The Chiral Symmetry Restoring Phase
The Chiral Symmetry Breaking Phase
The Modified CME in Chiral Symmetry Breaking Phase—A Rigorous Proof
Discussion and Conclusions
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