Baryons as Relativistic Bound States of Quark and Diquark

Abstract

In this thesis a model framework for describing baryons as diquark-quark bound states is presented which is formulated in an explicitly covariant manner. The relativistic bound state problem for three quarks is considered. Diquarks are introduced as separable correlations in the two-quark correlation function and thereby baryons are described by a Bethe-Salpeter equation for bound states of quark and diquark which interact by quark exchange. In analogy to the meson spectrum, scalar and axialvector diquarks are considered to be the most important two-quark configurations within baryons. The numerical solutions of the covariant Bethe-Salpeter equation are subsequently employed in the calculation of electromagnetic, strong and axial form factors of the nucleons. The construction of the electromagnetic current operator in the diquark-quark model respects gauge invariance. Invariance under chiral symmetry transformations is slightly violated for vector diquarks have been neglected, leading to a modest violation of the Goldberger-Treiman relation. The possibility of an effective parametrization of confinement by suitable modifications of the quark and diquark propagators is investigated. It is shown that the modelling of confinement chosen here is suitable for the calculation of the octet and devuplet spectrum and spacelike nucleon properties, but its applicability breaks down for processes where large energies are transferred to the nucleon as it is the case in certain meson production processes. Model solutions for nucleon wave functions and observables are compared between the full relativistic treatment and a widely used semi-relativistic approximation. The considerable deviations in the results illustrate the inadequacy of employing the semi-relativistic treatment.