Visible and Invisible Pseudoscalar Meson Decays from Anomaly Sum Rules

TL;DR

This paper investigates pseudoscalar meson decays involving photons and neutrinos using anomaly sum rules, revealing a nontrivial gluon form factor structure that hints at a pseudoscalar glueball and aligning with historical decay data.

Contribution

It introduces a systematic analysis of the gluon form factor B(q^2) in meson decays, suggesting the existence of a pseudoscalar glueball around 1.5-2 GeV and refining decay rate predictions.

Findings

B(q^2) exhibits complex structure near 1 GeV^2

Decay predictions align with historical data when mixing effects are considered

Enhanced pion decay branching ratio by a factor of 3

Abstract

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.