Meson-Meson Molecular Binding Potentials in the Diabatic Dynamical Diquark Model

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 di-meson potential, and find that significant regions of parameter space occur in which one may produce mass eigenstates exactly matching the specific examples of ${\chi }_{c1}(3872)$ and ${\chi }_{c0}(3915)$. We also find regions in which a pure di-meson molecular state emerges, and study the same state properties in such cases.