QCD Chiral restoration at finite $T$ under the Magnetic field: Studies based on the instanton vacuum model

Abstract

We investigate the chiral restoration at finite temperature $(T)$ under the strong external magnetic field $\vec{B}=B_{0}\hat{z}$ of the SU(2) light-flavor QCD matter. We employ the instanton-liquid QCD vacuum configuration accompanied with the linear Schwinger method for inducing the magnetic field. The Harrington-Shepard caloron solution is used to modify the instanton parameters, i.e. the average instanton size $(\bar{\rho})$ and inter-instanton distance $(\bar{R})$, as functions of $T$. In addition, we include the meson-loop corrections (MLC) as the large-$N_{c}$ corrections because they are critical for reproducing the universal chiral restoration pattern. We present the numerical results for the constituent-quark mass as well as chiral condensate which signal the spontaneous breakdown of chiral-symmetry (SB$\chi$S), as functions of $T$ and $B$. Besides we find that the changes for the $F_\pi$ and $m_\pi$ due to the magnetic field is relatively small, in comparison to those caused by the finite $T$ effect.