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 = B-0(z) over cap 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) over bar) and interinstanton distance ((R) over bar), as functions of T. In addition, we include the meson-loop corrections 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-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) approximate to (7-9)m(pi)(2), even in the presence of the explicit isospin breaking (m(u) not equal m(d)). 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. The strength of the isospin breaking between the quark condensates is also explored in detail by defining the ratio R equivalent to (< iu(dagger)u > - < id(dagger)d >)/(< iu(dagger)u > + < id(dagger)d >), which indicates the competition between the explicitly isospin-breaking effect and magnetic-catalysis effect. 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.