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

Abstract

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 N_f. It is shown that this model does satisfy the low-energy theorems with an accuracy of $\sim 17$. We estimate also the contribution of the nonperturbative conversion of gluons into photons to the decay ${\eta }^{\prime }\to 2\gamma$ and compare with experimental data.

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