The rho-pi puzzle and vector glueball mixing

TL;DR

This paper investigates how mixing between the $ ho ext{-} ext{pi}$ puzzle and vector glueball states can explain deviations from the expected 13% decay rule in charmonium states, using the extended Linear Sigma Model.

Contribution

It introduces a model incorporating vector glueball mixing to explain the $ ho ext{-} ext{pi}$ puzzle and provides insights into glueball decay widths.

Findings

Mixing can suppress $ ho ext{-} ext{pi}$ decay channels to match observations.

A simple model shows potential for explaining the $ ho ext{-} ext{pi}$ puzzle.

Data fitting constrains glueball decay widths.

Abstract

The $\psi(3686)$ is identified as the radial excitation of the $J/\psi$. Based on perturbative QCD, the branching ratio of the $\psi(3686)$ into some final hadron state should be approximately 13% of the branching ratio of the $J/\psi$ to that same hadron final state. This is called the "13\% rule". However, certain decay channels such as the $\rho\pi$ severely violate this 13% rule. Using the extended Linear Sigma Model, we study the effect a small mixing angle between the $\psi(3686)$ and the vector glueball can have on the 13% rule. We show that in a simple model the mixing can already suppress $\psi(3686)$ decays sufficiently to match the $\rho\pi$ observation, but to fully describe the data a more sophisticated model is necessary. We also show that matching to data can tell us about the magnitude of glueball decay widths.