  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.
