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

TL;DR

This study examines how strong magnetic fields influence chiral symmetry restoration at finite temperature in SU(2) QCD matter, incorporating meson-loop corrections to accurately model the phenomena.

Contribution

It introduces a comprehensive approach combining instanton-liquid models, Schwinger method, and meson-loop corrections to analyze chiral restoration under magnetic fields.

Findings

Magnetic catalysis enhances chiral order parameters.

Critical temperature for chiral restoration shifts higher with magnetic field.

Pion properties show partial restoration behaviors with small magnetic field effects.

Abstract

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.