Eur. Phys. J. A (2007) 33: 87-93
https://doi.org/10.1140/epja/i2007-10441-3

Regular Article - Hadron Physics

Effective potential between two gluons from the scalar glueball

¹ Groupe de Physique Nucléaire Théorique, Université de Mons-Hainaut, Place du Parc 20, BE-7000, Mons, Belgium
² Académie universitaire Wallonie-Bruxelles, Place du Parc 20, BE-7000, Mons, Belgium

^* e-mail: fabien.buisseret@umh.ac.be.

Received: 23 May 2007
Accepted: 16 July 2007
Published online: 31 July 2007

Abstract

Starting from the 0⁺⁺ glueball mass and wave function computed from lattice QCD, we compute the local potential between two constituent gluons. Since the properties of constituent gluons are still a matter of research, we allow for them to be either massless, or massive with a mass around 0.7GeV. Both pictures are actually used in the literature. When the gluons are massless, the corresponding local potential is shown to be compatible with a Cornell form, that is a linear confinement plus a short-range Coulomb part, with standard values for the flux tube energy density and for the strong coupling constant. When the gluons are massive, the confining potential is a saturating one, commonly used to simulate string-breaking effects. These results fill a gap between lattice QCD and phenomenological models: The picture of the scalar glueball as a bound state of two constituent gluons interacting via a phenomenological potential is shown to emerge from pure gauge lattice QCD computations. Moreover, we show that the allowed potential shape is constrained by the mass of the constituent gluons.