Chiral restoration at finiteTunder the magnetic field with the meson-loop corrections

Abstract

We investigate the (partial) chiral restoration at finite temperature ðTÞ under the strong external magnetic field B ¼ B 0ẑ of the SU(2) light-flavor QCD matter. To this end, we employ the instantonliquid 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 ð " Þ and interinstanton distance ð " RÞ, 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 (SBS), 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 % ð7-9Þm 2 , even in the presence of the explicit isospin breaking (m u Þ 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 ðhiu y ui À hid y diÞ=ðhiu y ui þ hid y diÞ, which indicates the competition between the explicitly isospin-breaking effect and magnetic-catalysis effect. We also compute the pion weak-decay constant F and pion mass m 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 and m due to the magnetic field is relatively small, in comparison to those caused by the finite T effect.

Deconfinement, chiral symmetry restoration and thermodynamics of (2+1)-flavor hot QCD matter in an external magnetic field

“…This pattern was also found in the context of the instanton-liquid model, modified by the HarringtonShepard caloron solution at finite T in the chiral limit [48], or in the Sakai-Sugimoto model [49].…”

QCD topological susceptibility from the nonlocal chiral quark model

“…Moreover, χ t reveals rich information on the QCD phase diagram as an order parameter of U A (1) symmetry and its relation with SχSB is also studied [21]. As already explored in our previous works [35,36], the present model has provided successful descriptions for various QCD properties at finite T as well as quark chemical potential µ q . It is based on the instanton QCD-vacuum configuration which is responsible for the nontrivial mechanisms of SχSB and its (partial) restoration.…”

Shear viscosity of quark matter at finite temperature under an external magnetic field

“…iD ¼ i@ þ ie q A . By doing this, the momentumdependent effective quark mass can be expanded in terms of the electric charge of the quark, which gives us the following expression for Oðe q Þ [42]:…”