Magnetic susceptibility of the QCD vacuum

Hyun-Chul Kim, M. Musakhanov, M. Siddikov

Published 2004-11-12Version 1

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 $Z[V,T,\hat{m}]$ in the presence of the current quark mass $\hat{m}$ 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: $\chi_{u,d}< i\psi_{u,d}^\dagger \psi_{u,d}>_0 \sim 40\sim45 {\rm MeV}$, while $\chi_{s}< i\psi_s^\dagger \psi_s >_0 \simeq 6\sim 10 {\rm MeV}$ with the quark condensate $<i\psi^\dagger \psi>_0$.