On a Renormalized QCD-inspired Model in the Light-cone Formulation
In the Hamiltonian light-cone approach to QCD an effective one-body equation for describing mesons with different quark and anti-quark flavor is broken down to an oversimplified model. This model serves as a platform to study explicit renormalization in a non-perturbative context. Two numerically and conceptually totally different renormalization schemes are used to demonstrate this, where at the end, both yield the same physical results. The corresponding renormalized quark potential is arbitrary for small relative distances, in the sense that there is a freedom in choosing the regulating functions for large momenta. Far beyond this region the potential is showing a universal Coulomb behaviour. Using this arbitrariness at small distances, by requiring it for example to start off as a pure harmonic oscillator potential, it inevitably forms a barrier in the scattering region in order to catch up with the asymptotic Coulomb part of the quark potential. This mechanism allows to see confinement. The renormalized model is then solved in momentum space by calculating its mass spectrum. These are then compared with the experimental measured values. A large part of this thesis is dedicated to the calculation of resonances in the stationary picture, as well as Coulomb scattering in the troublesome representation of momentum space. This difficulty is represented as a stand-alone section in the appendix.
Networked Digital Library of Theses and Dissertations