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Using the diabatic formalism, a rigorous generalization of the Born-Oppenheimer approximation, we study the effects of introducing simple meson-meson molecular potentials to an established diquark model for tetraquark states, and calculate mixed bound states composed of both diquark-antidiquark and meson-meson molecular components.We examine the behavior of properties of the states as one varies the parameters of the dimeson potential, and find that significant regions of parameter space occur in which one may produce mass eigenstates exactly matching the specific examples of χc1 and χc0. We also find regions in which a pure dimeson molecular state emerges, and study the same state properties in such cases. 

Using the diabatic formalism, which generalizes the adiabatic approximation in the Born-Oppen-heimer formalism, we apply well-known Hamiltonian methods to calculate the effect of open di-meson thresholds that lie well below the mass of elementary $c\overline{c}q{\overline{q}}^{\prime }$, $c\overline{c}s\overline{s}$, and $c\overline{c}q\overline{s}$tetraquark bound states. We compute the resulting mass shifts for these states, as well as their decay widths to the corresponding meson pairs. Each mass eigenstate, originally produced using a bound-state approximation under the diabatic formalism, consists of an admixture of a compact diquark-antidiquark configuration (an eigenstate of the original dynamical diquark model) with an extended di-meson configuration induced by the nearest threshold. We compare our results with those from our recent work that employs a scattering formalism, and find a great deal of agreement, but also comment upon interesting discrepancies between the two approaches. Published by the American Physical Society2024