Magnetic susceptibility of the QCD vacuum

We investigate the magnetic susceptibility of the QCD vacuum, based on the instanton vacuum. Starting from the instanton liquid model for the instanton vacuum, we derive the light-quark partition function Z[V,T,mˆ] in the presence of the current quark mass mˆ as well as the external Abelian vector and tensor fields. We calculate a two-point correlation function relevant for the magnetic susceptibility and derive it beyond the chiral limit. We obtain for the different flavors the following magnetic susceptibility: χu,d〈iψu,d†ψu,d〉0∼40-45MeV, while χs〈iψs†ψs〉0≃6-10MeV with the quark condensate 〈iψ†ψ〉0.