Dispersive Approach to Abelian Axial Anomaly, Mixing of Pseudoscalar Mesons and Symmetries

Abstract

We suggest a rigorous generalization of the pseudoscalar mesons mixing description in SU(3) basis. It is shown that the appearance of extra massive state nicknamed in the paper as glueball is unavoidable in any scheme with more than one angle. In this framework we develop the dispersive approach to Abelian axial anomaly of isoscalar non-singlet current. Combining it with the analysis of experimental data of charmonium radiative decays ratio we get the number of quite strict constraints for mixing parameters. Our analysis favors the equal values of axial currents coupling constants which may be considered as a manifestation of SU(3) symmetry and possible violation of chiral symmetry based predictions.