A test of the instanton vacuum chiral quark model with axial anomaly low-energy theorems

The QCD+QED axial anomaly low-energy theorems are applied to estimate the accuracy of an instanton vacuum — based chiral quark model. The low-energy theorems give an exact relation between the matrix elements of the gluon and photon parts of the QCD+QED axial anomaly operator equation. The matrix elements between vacuum and two photon states and between vacuum and two gluon states are calculated for arbitrary Nf. It is shown that this model does satisfy the low-energy theorems with an accuracy of ∼ 17%. We estimate also the contribution of the nonperturbative conversion of gluons into photons to the decay η′ → 2γ and compare with experimental data.