Magnetization of the QCD vacuum at large fields

The response of the QCD vacuum to very large static external magnetic fields (q B >> Lambda_QCD^2) is studied. In this regime, the magnetization of the QCD vacuum is naturally described via perturbative QCD. Combining pQCD and the Schwinger proper time formalism, we calculate the magnetization of the QCD vacuum due to a strong magnetic field at leading order (one-loop) to be proportional to B log B. We show that the leading perturbative correction (two-loop) vanishes.