Abelian Decomposition and Glueball-Quarkonium Mixing in QCD

TL;DR

This paper explores an Abelian decomposition of QCD that introduces a quark and chromon model, providing a framework to understand glueball-quarkonium mixing and identifying specific mesons as predominantly glueball states.

Contribution

It generalizes the quark model to include chromons, analyzes glueball-quarkonium mixing, and identifies candidate glueball states in various meson sectors.

Findings

Identification of $f_0(500)$ and $f_0(1500)$ as glueball-dominant in the $0^{++}$ sector

Identification of $f_2(1950)$ as a glueball candidate in the $2^{++}$ sector

Identification of $ ext{eta}(1405)$ and $ ext{eta}(1475)$ as glueball states in the $0^{-+}$ sector

Abstract

The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons (the neurons) and the colored valence gluons (the chromons) gauge independently naturally generalizes the quark model to the quark and chromon model which could play the central role in hadron spectroscopy. We discuss the color reflection symmetry, the fundamental symmetry of the quark and chromon model, and explain how it describes the glueballs and the glueball-quarkonium mixing in QCD. We present the numerical analysis of glueball-quarkonium mixing in $0^{++}$, $2^{++}$, and $0^{-+}$ sectors below 2 GeV, and show that in the $0^{++}$ sector $f_0(500)$ and $f_0(1500)$, in the $2^{++}$ sector $f_2(1950)$, and in the $0^{-+}$ sector $\eta(1405)$ and $\eta(1475)$ could be identified as predominantly the glueball states. We discuss the physical implications of our result.