  Hidden-heavy hadrons can decay into pairs of heavy hadrons through
transitions from confining Born-Oppenheimer potentials to hadron-pair
potentials with the same Born-Oppenheimer quantum numbers. The transitions are
also constrained by conservation of angular momentum and parity. From these
constraints, we derive model-independent selection rules for decays of
hidden-heavy hadrons into pairs of heavy hadrons. The coupling potentials are
expressed as sums of products of Born-Oppenheimer transition amplitudes and
angular-momentum coefficients. If there is a single dominant Born-Oppenheimer
transition amplitude, it factors out of the coupling potentials between
hidden-heavy hadrons in the same Born-Oppenheimer multiplet and pairs of heavy
hadrons in specific heavy-quark-spin-symmetry doublets. If furthermore the
kinetic energies of the heavy hadrons are much larger than their spin
splittings, we obtain analytic expressions for the relative partial decay rates
in terms of Wigner 6-j and 9-j symbols. We consider in detail the decays of
quarkonia and quarkonium hybrids into the lightest heavy-meson pairs. For
quarkonia, our model-independent selection rules and relative partial decay
rates agree with previous results from quark-pair-creation models in simple
cases and give stronger results in other cases. For quarkonium hybrids, we find
disagreement even in simple cases.
