Magnetic Susceptibility of the Quark Condensate and Polarization from Chiral Models

TL;DR

This paper calculates the magnetic susceptibility of the quark condensate and quark polarization at zero temperature using chiral models, confirming saturation behavior at high magnetic fields.

Contribution

It provides a self-consistent analysis of chiral symmetry breaking effects on quark properties in magnetic fields using two established models, including analytic estimates.

Findings

Numerical results agree with recent literature.

Confirmed saturation of polarization at large magnetic fields.

Analytic estimates match numerical results in different regimes.

Abstract

We compute the magnetic susceptibility of the quark condensate and the polarization of quarks at zero temperature and in a uniform magnetic background. Our theoretical framework consists of two chiral models that allow to treat self-consistently the spontaneous breaking of chiral symmetry: the linear $\sigma-$model coupled to quarks, dubbed quark-meson model, and the Nambu-Jona-Lasinio model. We also perform analytic estimates of the same quantities within the renormalized quark-meson model, both in the regimes of weak and strong fields. Our numerical results are in agreement with the recent literature; moreover, we confirm previous Lattice findings, related to the saturation of the polarization at large fields.