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

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We investigate the (partial) chiral restoration at finite temperature (T) under the strong external magnetic field B₀ 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-Nc 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 B₀. From our results we observe that the strengths of those chiral order parameters are enhanced with respect to B₀ 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 eB₀ = (7 9) m²ₚi, even in the presence of the explicit isospin breaking. The critical T for the chiral restoration Tc tends to shift to the higher temperature in the presence of the B₀ for the chiral limit but keeps almost stationary for the physical quark mass case. We also compute the pion weak-decay constant Fₚi and pion mass mₚi below Tc, varying the strength of the magnetic field, showing correct partial chiral restoration behaviors. Besides we find that the changes for the Fₚi and mₚi due to the magnetic field is relatively small, in comparison to those caused by the finite T effect.