Induced magnetic moment in the magnetic catalysis of chiral symmetry breaking

Efrain J Ferrer,Vivian De La Incera

doi:10.1016/j.nuclphysbps.2015.10.041

Abstract

The chiral symmetry breaking in a Nambu-Jona-Lasinio effective model of quarks in the presence of a magnetic field is investigated. We show that new interaction tensor channels open up via Fierz identities due to the explicit breaking of the rotational symmetry by the magnetic field. We demonstrate that the magnetic catalysis of chiral symmetry breaking leads to the generation of two independent condensates, the conventional chiral condensate and a spin-one condensate. While the chiral condensate generates, as usual, a dynamical fermion mass, the new condensate enters as a dynamical anomalous magnetic moment in the dispersion of the quasiparticles. Since the pair, formed by a quark and an antiquark with opposite spins, possesses a resultant magnetic moment, an external magnetic field can align it giving rise to a net magnetic moment for the ground state. The two condensates contribute to the effective mass of the LLL quasiparticles in such a way that the critical temperature for chiral symmetry restoration becomes enhanced.

Highlights

The phases of matter under strong magnetic fields constitute an active topic of interest in light of the experimental production of large magnetic fields in heavy-ion collisions, and because of the existence of strongly magnetized astrophysical compact objects
In the presence of a magnetic field there is no magnetically catalyzed chiral condensate ψψ without the simultaneous generation of a second dynamical condensate of the form ψΣ3ψ. The genesis of this phenomenon lies in the fact that the chiral pairs possess net magnetic moments that tend to align with the external magnetic field
The collective effect of these magnetic moments leads to the ground state magnetization and manifests itself as a spin-one condensate ψΣ3ψ which enters in the quasiparticle spectrum as an anomalous magnetic moment (AMM)

Summary

Introduction

The phases of matter under strong magnetic fields constitute an active topic of interest in light of the experimental production of large magnetic fields in heavy-ion collisions, and because of the existence of strongly magnetized astrophysical compact objects. A magnetic field is known to produce the catalysis of chiral symmetry breaking (MCχSB) [3] in any system of fermions with arbitrarily weak attractive interaction This effect has been actively investigated for the last two decades [4]. It has been shown that in QED [5] the MCχSB leads to a dynamical fermion mass and inevitably to a dynamical anomalous magnetic moment (AMM). This is connected to the fact that the AMM does not break any symmetry that has not already been broken by the other condensate. The two condensates contribute to the effective dynamical mass, which is mainly determined by the quark/antiquark pairing in the lowest Landau lever (LLL), resulting in a significant increase in the critical temperature for the chiral restoration, as compared to the case where only the magnetically catalyzed chiral condensate is considered

Model and Condensates

Critical Temperature

Conclusion and Discussion