Radiative $\eta'$ Decays, the Topological Susceptibility and the Witten-Veneziano Mass Formula

TL;DR

This paper derives modified formulae for radiative $ ext{eta'}$ decays in QCD, incorporating gluonic effects, and connects these to the topological susceptibility and the Witten-Veneziano mass formula.

Contribution

It provides new theoretical modifications to decay formulae and links experimental decay measurements to the topological susceptibility in QCD with massive quarks.

Findings

Derived modified decay formulae including gluonic contributions.

Generalized the Witten-Veneziano mass formula for $ ext{eta'}$.

Showed how to extract topological susceptibility from decay data.

Abstract

The formulae describing the radiative decays $\eta'(\eta)\rta\c\c$ in QCD beyond the chiral limit are derived. The modifications of the conventional PCAC formulae due to the gluonic contribution to the axial anomaly in the flavour singlet channel are precisely described. The decay constants are found to satisfy a modified Dashen formula which generalises the Witten--Veneziano formula for the mass of the $\eta'$. Combining these results, it is shown how the topological susceptibility in QCD with massive, dynamical quarks may be extracted from measurements of $\eta'(\eta)\rta\c\c$.