# How to identify gluonium states using QCD counting rules

## TL;DR

This paper proposes using QCD counting rules to differentiate gluonium states from other hadrons by analyzing their production cross sections at high momentum transfer, providing a practical method for experimental identification.

## Contribution

It introduces a novel approach applying QCD counting rules to distinguish gluonium from quark-based hadrons based on their twist and production cross section behavior.

## Key findings

- Gluonium states have twist tau=2, leading to less suppressed production at high momentum transfer.
- Quark-containing mesons have higher twist tau=3 or 4, resulting in more suppressed cross sections.
- Experimental strategies at Belle-II and in hadroproduction are proposed to identify gluonium states.

## Abstract

Verifying the existence of bound states of gluons and distinguishing them from conventional quark-antiquark, hybrid or tetraquark states has remained a key problem in QCD. We show that QCD counting rules for the power-law fall-off of production cross sections at high momentum transfer can be used to distinguish gluonium states from conventional hadrons. The valence two-gluon contribution to a 0^+ gluonium bound state has L=0 and thus twist (dimension minus spin of their minimum interpolating operators) tau=2. The competing twist assignments for scalar f_0 mesons have twist tau = 3 for the valence |q qbar > configuration or |qqbar g> in an s-wave, and tau >= 4 for |q qbar qbar q > tetraquarks, etc. Thus, the production cross section for mesons with quark-containing valence wavefunctions relative to glueball production should be suppressed by at least a power of momentum transfer. Distinguishing these processes is feasible in exclusive e^-e^+ --> phi f_0 reactions at 9 and 11 GeV center of mass energy at Belle-II. In the case of single-particle inclusive hadroproduction A B --> C X, the cross section for scalar gluonium production at high transverse momentum p_T and fixed x_T = 2 p_T/sqrt(s) will dominate meson or tetraquark production by at least two powers of p_T.