QCD magnetic susceptibility at finite temperature beyond the chiral limit
Abstract
We investigate QCD magnetic susceptibility ${\ensuremath{\chi}}_{q}$ for light-flavor SU(2) at finite temperature ($T$) beyond the chiral limit, using the liquid instanton model for ${N}_{c}=3$, defined in Euclidean space and modified by the $T$-dependent caloron solution. The background electromagnetic fields are included in the QCD vacuum, employing the Schwinger method. We first compute the scalar (chiral) and tensor condensates as functions of $T$ and the current-quark mass $m$, signaling the correct universal chiral restoration patterns. It turns out that ${\ensuremath{\chi}}_{q}$, 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 $T\ensuremath{\equiv}{T}_{0}$, in comparison to that at $T=0$, and decreases almost linearly beyond ${T}_{0}$ for $m\ensuremath{\ne}0$. 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, which plays the role of the chiral order parameter.