Relativistic studies of the charmonium and bottomonium systems using the Sucher equation

In this dissertation, bound states of quarks and anti-quarks (mesons) are studied with a relativistic equation known as the Sucher equation. Prior to the work in this dissertation, the Sucher equation had never been used for meson mass spectra. Furthermore, a full angular momentum analysis of the Sucher equation has never been studied. The Sucher equation is a relativistic equation with positive energy projectors imposed on the interaction. Since spin is inherent to the equation, the Sucher equation is equivalent to a relativistic Schrodinger equation with a spin-dependent effective potential. Through a complete general angular momentum analysis of the equation, we found that different angular momenta can couple through the effective potential without explicitly using tensor interaction. Next we expanded the wave functions in a complete set of basis functions and converted the Sucher equation into a matrix eigenvalue equation. As a practical application, we fit to the low lying states of the bottomonium and charmonium systems with the minimal number of input parameters, and we were able to predict the remaining spectra. We find that the Sucher equation may be used for charmonium and bottomonium spectra. However, the spin dependent interactions inherent to the Sucher equation do not produce adequate energy level splitting between singlet and triplet states.