QCD magnetic susceptibility at finite temperature beyond the chiral limit

TL;DR

This paper studies the temperature dependence of QCD magnetic susceptibility beyond the chiral limit using the instanton model, finding a smooth decrease with temperature and agreement with lattice results.

Contribution

It introduces a finite-temperature analysis of QCD magnetic susceptibility beyond the chiral limit within the instanton model framework.

Findings

Chi_q decreases by about 20% at the chiral transition temperature.

The susceptibility decreases almost linearly beyond T_0 for non-zero quark mass.

Results are qualitatively consistent with lattice QCD simulations.

Abstract

We investigate the QCD magnetic susceptibility chi_q for flavor SU(2) at finite temperature (T) beyond the chiral limit, using the liquid instanton model, defined in Euclidean space and modified by the T-dependent caloron solution. The background electromagnetic fields are induced to the QCD vacuum, employing the Schwinger method. We first compute the scalar (chiral) and tensor condensates as functions of T as well the current-quark mass m, signaling the correct universal chiral restoration patterns. It turns out that chi_q, given by the ratio of the two condensates, is a smoothly decreasing function of T, showing about 20% reduction of its strength at the chiral transition T = T_0, in comparison to that at T = 0, and decreases almost linearly beyond T_0 for m > 0. We observe that the present numerical results are in qualitatively good agreement with other theoretical results, including the lattice simulations. Finally, we examine the effects of the external magnetic field on the tensor-polarization VEV, resulting in that it plays the role of the chiral order parameter.