Composition of the Pseudoscalar Eta and Eta' Mesons

TL;DR

This paper investigates the internal composition and mixing of eta and eta' mesons using various decay processes, constraining their mixing angle, assessing gluonic components, and proposing tests and predictions for future experiments.

Contribution

It provides a comprehensive analysis of eta-eta' mixing, constrains the mixing angle, estimates gluonic content, and suggests experimental tests and decay mode analyses for better understanding.

Findings

Eta-eta' mixing angle approximately 42 degrees.

Gluonic component in eta' less than 5%.

Predicted branching ratios for specific decays.

Abstract

The composition of the eta and eta' mesons has long been a source of discussion and is of current interest with new experimental results appearing. We investigate what can be learnt from a number of different processes: V to P gamma and P to V gamma (V and P are light vector and pseudoscalar mesons respectively), P to gamma gamma, J/psi,psi' to P gamma, J/psi,psi' to P V, and chi_{c0,2} to PP. These constrain the eta-eta' mixing angle to a consistent value, phi approx 42 degrees; we find that the c cbar components are lesssim 5% in amplitude. We also find that, while the data hint at a small gluonic component in the eta', the conclusions depend sensitively on unknown form factors associated with exclusive dynamics. In addition, we predict BR(psi' to eta' gamma) approx 1 10^{-5} and BR(chi_{c0} to eta eta') approx 2 10^{-5} - 1 10^{-4}. We provide a method to test the mixing using chi_{c2} to eta eta, eta' eta', and eta eta' modes and make some general observations on chi_{c0,2} decays. We also survey the semileptonic and hadronic decays of bottom and charmed mesons and find some modes where the mixing angle can be extracted cleanly with the current experimental data, some where more data will allow this, and some where a more detailed knowledge of the different amplitudes is required.