Quark deconfinement and gluon condensate in a weak magnetic field

TL;DR

This paper investigates how a weak magnetic field influences QCD sum rules, revealing that both the deconfinement parameter and gluon condensate increase with magnetic field strength, indicating magnetic catalysis of confinement and chiral symmetry breaking.

Contribution

It provides the first analysis of magnetic field effects on QCD sum rules, showing explicit quadratic corrections and linking magnetic dependence of deconfinement and gluon condensate.

Findings

Deconfinement parameter s_0 increases with magnetic field.

Gluon condensate increases with magnetic field.

Magnetic field acts as a catalyst for confinement and chiral symmetry breaking.

Abstract

We study QCD finite energy sum rules (FESR) for the axial-vector current correlator in the presence of a magnetic field, in the weak field limit and at zero temperature. We find that the perturbative QCD as well as the hadronic contribution to the sum rules get explicit magnetic field-dependent corrections and that these in turn induce a magnetic field dependence on the deconfinement phenomenological parameter s_0 and on the gluon condensate. The leading corrections turn out to be quadratic in the field strength. We find from the dimension d=2 first FESR that the magnetic field dependence of s_0 is proportional to the absolute value of the light-quark condensate. Hence, it increases with increasing field strength. This implies that the parameters describing chiral symmetry restoration and deconfinement behave similarly as functions of the magnetic filed. Thus, at zero temperature the magnetic field is a catalysing agent of both chiral symmetry breaking and confinement. From the dimension d=4 second FESR we obtain the behavior of the gluon condensate in the presence of the external magnetic field. This condensate also increases with increasing field strength.