(a) Static-quark potentials and radial probability densities against quark-antiquark separation r for r0-1=450 MeV. (b) Spin-averaged b-bar b spectrum in the leading Born-Oppenheimer approximation (light quarks neglected). Solid lines indicate experimental measurements. Short dashed lines indicate the conventional S and P state masses obtained from the Schrodinger equation with the Sigmag+ potential for quark mass Mb=4.58 GeV. Dashed-dotted lines indicate the hybrid quarkonium states obtained from the Piu (L=1,2,3) and Sigmau- (L=0,1,2) potentials. Repeating the same analysis in the charmonium system, we find the lowest Piu hybrid 1.19 GeV above the spin averaged ground state. Note that the inclusion of light quark loops will dramatically change this spectrum.