Anomaly sum rules for the case of a singlet current and their features

Abstract

Using the dispersion approach to the axial anomaly by A.D. Dolgov and V.I. Zakharov, the non-Abelian case was considered for arbitrary virtualities of photon. Anomalous sum rules for the singlet current and transition form-factors π0, η, η′ → γγ(*) are derived. Using them, the behaviour of the non-perturbative gluon matrix element 〈0|GG˜|γγ(*)〉 was established both for the case of two real photons and for the case of one virtual photon in time-like and space-like domains. The possibility of a light pseudoscalar glueball-like state is conjectured.