Gluons in glueballs: Spin or helicity?

TL;DR

This paper demonstrates that using a helicity formalism for gluons in potential models accurately reproduces the observed glueball spectrum and quantum numbers, aligning well with lattice QCD results.

Contribution

It introduces a helicity-based approach to modeling gluons in glueballs, resolving issues with extra states in traditional spin-based models.

Findings

Helicity formalism reproduces lattice QCD quantum numbers.

Glueball mass spectrum matches lattice QCD predictions.

Instanton effects are important for accurate spectrum modeling.

Abstract

In the last decade, lattice QCD has been able to compute the low-lying glueball spectrum with accuracy. Like other effective approaches of QCD, potential models still have difficulties to cope with gluonic hadrons. Assuming that glueballs are bound states of valence gluons with zero current mass, it is readily understood that the use of a potential model, intrinsically non covariant, could be problematic in this case. The main challenge for this kind of model is actually to find a way to introduce properly the more relevant degree of freedom of the gluon: spin or helicity. In this work, we use the so-called helicity formalism of Jacob and Wick to describe two-gluon glueballs. We show in particular that this helicity formalism exactly reproduces the $J^{PC}$ numbers which are observed in lattice QCD when the constituent gluons have a helicity-1, without introducing extra states as it is the case in most of the potential models. These extra states appear when gluons are seen as spin-1 particles. Using a simple spinless Salpeter model with Cornell potential within the helicity formalism, we obtain a glueball mass spectrum which is in good agreement with lattice QCD predictions for helicity-1 gluons provided instanton-induced interactions are taken into account.