Visible and Invisible Pseudoscalar Meson Decays from Anomaly Sum Rules

The decays of pseudoscalar mesons to real and virtual photons as well as neutrino-antineutrino pairs are considered in the framework of the dispersive method based on Anomaly Sum Rules. The contribution of singlet channel involving the new non-perturbative gluon form factor of virtual photon $B(q^2)$ is systematically taken into account. The detailed analysis of its dependence on photon virtuality $q^2$ relying on the available data for meson transition fomfactors is performed. It is shown that B has quite a nontrivial structure at $q^2 \sim 1 GeV^2$ which may be a signal of the existence of pseudoscalar glueball with a mass about 1.5-2 GeV. The calculation of the decay to $\nu \bar \nu$ pairs leads to the compatibility with the result of Arnellos, Marciano and Parsa of 1982, when pion decay is considered neglecting the mixing effects. The account for these effects results, however, in the enhancement of pion branching ratio by a factor of 3, while that for eta decay is larger by several orders of magnitude. It is stressed, that dependence on the pair invariant mass is entirely defined by QCD and coincides with that of the meson transition form factor. The role of obtained results for the physics at HHaS detector at HIAF is discussed.