Effective potential between two gluons from the scalar glueball

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 0.7 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.

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

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Cited by in corpus (7)

• Gluons in glueballs: Spin or helicity?
• Constituent gluon interpretation of glueballs and gluelumps
• Short-range potentials from QCD at order $g^2$
• Modelling duality between bound and resonant meson spectra by means of free quantum motions on the de Sitter space time dS4
• Wave functions of $SU(3)$ pure gauge glueballs on the lattice
• Effective potential between two transverse gluons from lattice QCD
• Handling the Cornell potential within the Lagrange-mesh method in momentum space