Chiral restoration at finite T under the magnetic field with the meson-loop corrections

We investigate the (partial) chiral restoration at finite temperature (T) under the strong external magnetic field B_0 of the SU(2) light-flavor QCD matter. To this end, 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 (rho) and inter-instanton distance (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 SBCS, as functions of T and B_0. From our results we observe that the strengths of those chiral order parameters are enhanced with respect to B_0 due to the magnetic catalysis effect. We also find that there appears a region where the u and d-quark constituent masses coincide with each other at eB_0 = (7 ~ 9) m^2_pi, even in the presence of the explicit isospin breaking. The critical T for the chiral restoration T_c tends to shift to the higher temperature in the presence of the B_0 for the chiral limit but keeps almost stationary for the physical quark mass case. We also compute the pion weak-decay constant F_pi and pion mass m_pi below T_c, varying the strength of the magnetic field, showing correct partial chiral restoration behaviors. 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.