# $\chi_c$ decays and the gluon content of the $\eta'$, $\eta$ mesons

## TL;DR

This paper investigates the gluon content of the $\

## Contribution

It introduces a model that accounts for interference effects and quark mass influences to explain decay rates, revealing the gluon component in $\

## Key findings

- Decay rates can be explained by destructive interference effects.
- A reasonable gluon component in $\
- Interference effects are crucial in understanding meson decay behaviors.

## Abstract

The large mass of the $\eta'$ meson indicates that a sizeable gluon component is present in the meson wave function. However, the $\chi_{c0}$ and $\chi_{c2}$ decays to $\eta'$ mesons, which proceed via a purely gluonic intermediate state and we would therefore na\"{i}vely expect to be enhanced by such a component, are in fact relatively suppressed. We argue that this apparent contradiction may be resolved by a proper treatment of interference effects in the decay. In particular, by accounting for the destructive interference between the quark and gluon components of the $\eta'$ distribution function, in combination with a model for strange quark mass effects, we demonstrate that the observed $\chi_{c(0,2)}\to\eta(')\eta(')$ branching ratios can be reproduced for a reasonable gluon component of the $\eta'$, $\eta$ mesons.