The effect of antisymmetrization in diquark models of baryons.

Abstract

In this thesis the effect of antisymmetrization in diquark models of baryons composed of light (u and d) quarks is investigated. The diquark in this study is considered alternately as a pointlike and as a composite particle. The wave functions for both diquark and diquark-quark systems have been determined in a non-relativistic approximation by using the radial Schrodinger equation and a range ofcentral potentials. The ground state masses ofthe diquarkquark system have been calculated in three distinct ways: (1) The ground state energy eigenvalues and the wave functions for thediquark and diquarkquark, each being treated as a two-body system, have been calculated by using the generalized Runge-Kutta and search methods. (2) The expectation values for the potential energy and kinetic energy have been calculated by using the wave functions derived in (1) for the two-body system without antisymmetrization. These results have been checked by applying the virial theorem in parallel calculations. (3) The potential and kinetic energy expectation values have also been determined by taking antisymmetrization into account via operator kernels namely, norm, potential and kinetic energy which have been derived by using the non-local Generator Coordinate Method (GCM). The expectation values of these operator kernels have been calculated with respect to the wave functions produced in (1). For the purpose of performing the integrations the wave functions , expanded in terms of cubic splines, and Gaussian quadrature have been employed. Lastly the diquark and diquark-quark ground state masses were calculated for each approach, (1) - (3), and compared with (a) each other, (b) the results for a two-body system, (c) the results for a full three-body treatment and, (d) the average mass of N- b:. . The form factors and root mean square radii ofthe baryon for the four central potentials have been calculated with antisymmetrization for each approach (1) - (3) and compared with (a) each other, (b) the results for the baryon without antisymmetrization (c) the results for the baryon with antisymmetrization including the meson cloud (d) the experimental data. The trends found are striking and it can be concluded that there is a strong dynamical effect due to the presence of antisymmetrization in diquark models of baryons.