The Effect of Logarithmic Mesonic Potential on the Magnetic Catalysis in the Chiral Quark-Sigma Model

TL;DR

This paper investigates how a logarithmic mesonic potential influences magnetic catalysis in the chiral quark-sigma model, showing enhanced chiral symmetry breaking compared to the original model, with implications for understanding QCD under magnetic fields.

Contribution

It introduces a logarithmic mesonic potential into the chiral quark-sigma model and demonstrates its effect on magnetic catalysis, comparing results with other models like NJL and Schwinger-Dyson.

Findings

Logarithmic potential enhances chiral symmetry breaking.

Increasing coupling constant further promotes symmetry breaking.

Higher sigma mass inhibits the broken vacuum state.

Abstract

The chiral symmetry breaking in the presence of external magnetic field is studied in the framework of logarithmic quark-sigma model. The effective logarithmic mesonic potential is employed and is numerically solved in the mean-field approximation. We find that the chiral symmetry breaking enhances in comparison with the original sigma model. Two sets of parameterization are investigated in the present model. We find that increasing coupling constant enhances the breaking symmetry while increasing sigma mass inhibits enhancing chiral broken vacuum state. A comparison with the Numbu-Jona-Lasinio model and the Schwinger-Dyson equation is discussed. We conclude that the logarithmic sigma model enhances the magnetic catalysis in comparison with the original sigma model and other models.