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200938 https://hdl.handle.net/2286/R.2.N.200938 http://rightsstatements.org/vocab/InC/1.0/ All Rights Reserved 2025 173 pages Doctoral Dissertation Academic theses en Martinez, Steven Lebed, Richard F Lunardini, Cecilia Keeler, Cynthia Baumgart, Matthew Arizona State University Partial requirement for: Ph.D., Arizona State University, 2025 Field of study: Physics In this dissertation, I will present recent works on generalizing the dynamical diquark model for exotic hadrons with the incorporation of the diabatic formalism. The diabatic formalism, which is a rigorous generalization of the Born-Oppenheimer approximation present in the original dynamical diquark, allows for the explicit inclusion of mixing between the fundamental diquark anti-diquark configuration and di-meson configurations. I first present calculated $J^{PC}$- and flavor-specific mass eigenvalues using a bound-state approximation, and find, as a specific example, that the state associated with the $\chi_{c1}(3872)$ emerges with a dominant $D^0 \bar D^{*0}$ component, while still maintaining a significant diquark-antidiquark component. I then show the application of two methods for lifting this bound-state approximation: Hamiltonian methods that incorporate the open thresholds as corrections to the mass eigenvalue, and a scattering formalism, which allows for the states with open di-meson thresholds to emerge as resonances in a cross section profile. In the former, it is found that the corrections to the mass eigenvalues are generally nominal, while also calculating the associated strong decay widths. In the latter, elastic open-charm di-meson cross sections are calculated as functions of center-of-mass energy, and observe that all relevant states have a corresponding resonant profile, while also commenting on interesting effects that arise such as threshold cusps. The diabatic dynamical diquark model is then employed in order to study the $T^{+}_{cc}$ state, using it (and its unique threshold structure) as a laboratory to study isospin symmetry breaking and threshold-specific spin effects. Finally, the inclusion of the di-meson configurations is completed by introducing an explicit attractive, short-distance correction (di-meson potential) to the di-meson energies. It is found that, in some cases, this causes the emergence of a new, pure di-meson bound state, while in others, it is possible to adjust model parameters to retrieve exact fits to experimental state masses. Physics Particle Physics Exotic Hadrons Phenomenology QCD Quarks A Diabatic Framework for Exotic Hadrons: Generalizing the Dynamical Diquark Model