  Many of the XYZ mesons discovered in the last decade can be identified as
bound states of a heavy quark and antiquark in Born-Oppenheimer (B-O)
potentials defined by the energy of gluon and light-quark fields in the
presence of static color sources. The mesons 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. The
deepest hybrid potentials are known from lattice QCD calculations. The deepest
tetraquark potentials can be inferred from lattice QCD calculations of static
adjoint mesons. Selection rules for hadronic transitions are derived and used
to identify XYZ mesons that are candidates for ground-state energy levels in
the B-O potentials for charmonium hybrids and tetraquarks.
