  Many of the XYZ mesons discovered in the last decade can be identified as
bound states in Born-Oppenheimer (B-O) potentials for a heavy quark and
antiquark. They include quarkonium hybrids, which are bound states in excited
flavor-singlet B-O potentials, and quarkonium tetraquarks, which are bound
states in flavor-nonsinglet B-O potentials. We present simple parameterizations
of the deepest flavor-singlet B-O potentials. We infer the deepest
flavor-nonsinglet B-O potentials from lattice QCD calculations of static
adjoint mesons. Selection rules for hadronic transitions are used to identify
XYZ mesons that are candidates for ground-state energy levels in the B-O
potentials for charmonium hybrids and tetraquarks. The energies of the
lowest-energy charmonium hybrids are predicted by using the results of lattice
QCD calculations to calculate the energy splittings between the ground states
of different B-O potentials and using the Schroedinger equation to determine
the splittings between energy levels within a B-O potential.
