Model-independent predictions for decays of hidden-heavy hadrons into pairs of heavy hadrons

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 $6j$ and $9j$ 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.