  New lattice data for the Pi_u and Sigma_u^- potentials at short distances are
presented. We compare perturbation theory to the lower static hybrid potentials
and find good agreement at short distances, once the renormalon ambiguities are
accounted for. We use the non-perturbatively determined continuum-limit static
hybrid and ground state potentials at short distances to determine the gluelump
energies. The result is consistent with an estimate obtained from the gluelump
data at finite lattice spacings. For the lightest gluelump, we obtain
Lambda_B^{RS}(nu_f=2.5/r_0)=[2.25\pm 0.10(latt.)\pm 0.21 (th.)\pm 0.08
(Lambda_{MS})]/r_0 in the quenched approximation with r_0^{-1} approx 400 MeV.
We show that, to quote sensible numbers for the absolute values of the gluelump
energies, it is necessary to handle the singularities of the singlet and octet
potentials in the Borel plane. We propose to subtract the renormalons of the
short-distance matching coefficients, the potentials in this case. For the
singlet potential the leading renormalon is already known and related to that
of the pole mass, for the octet potential a new renormalon appears, which we
approximately evaluate. We also apply our methods to heavy light mesons in the
static limit and from the lattice simulations available in the literature we
obtain the quenched result \bar{Lambda}^{RS}(nu_f=2.5/r_0)=[1.17\pm
0.08(latt.)\pm 0.13 (th.) \pm 0.09 (Lambda_{MS})]/r_0.
  We calculate m_{b,MS}(m_{b,MS}) and apply our methods to gluinonia whose
dynamics are governed by the singlet potential between adjoint sources. We can
exclude non-standard linear short-distance contributions to the static
potentials, with good accuracy.
