Effective potential between two gluons from the scalar glueball

Physics – High Energy Physics – High Energy Physics - Phenomenology

Scientific paper

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4 figures; Comments added, one typo corrected in v2. V3 accepted for publication in EPJA : major changes, content enlarged, in

Scientific paper

10.1140/epja/i2007-10441-3

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 0.7 GeV. 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.

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