Quark deconfinement and gluon condensate in a weak magnetic field

Understand

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.