Analytical properties of the quark propagator : QED3, QCD and Kaon photoproduction

Abstract

Confinement and chiral symmetry breaking are the basic phenomena of strong interactions. However, these fundamental issues are not understood in a satisfactory way. Neither dynamical chiral symmetry breaking nor confinement can be explained within perturbation theory. Therefore it is necessary to employ genuin non-perturbative methods. The Dyson-Schwinger approach proves to be well suited since it yields the basic Greens functions: ghe gluon- and quark propagators. In the first chapter the electron propagator in (2+1)-dimensional QED (QED3) is investigated within the Dyson-Schwinger approach. It is demonstrated that QED3 has a confined phase. This allows to compare the results for QED3 in this confined phase to the corresponding results for Quantum Chromodynamics (QCD). In the main part the coupled system of Dyson-Schwinger equations for gluons, ghosts and quarks in Landau gauge QCD is investigated. The solutions are discussed for various numbers of fermion flavours and for different current quark masses. The pattern and strength of chiral symmetry breaking is discussed and the positivity properties of the gluon- and quark propagators are examined. The last part focusses on phenomenological constraints on the quark propagator. It will be shown that meson production processes like kaon photoproduction are especially well suited to give constraints on the quark propagator in the timelike region. This complements the Dyson-Schwinger studies which are set up for spacelike momenta.

Confinement and chiral symmetry breaking are the basic phenomena of strong interactions. However, these fundamental issues are not understood in a satisfactory way. Neither dynamical chiral symmetry breaking nor confinement can be explained within perturbation theory. Therefore it is necessary to employ genuin non-perturbative methods. The Dyson-Schwinger approach proves to be well suited since it yields the basic Greens functions: ghe gluon- and quark propagators. In the first chapter the electron propagator in (2+1)-dimensional QED (QED3) is investigated within the Dyson-Schwinger approach. It is demonstrated that QED3 has a confined phase. This allows to compare the results for QED3 in this confined phase to the corresponding results for Quantum Chromodynamics (QCD). In the main part the coupled system of Dyson-Schwinger equations for gluons, ghosts and quarks in Landau gauge QCD is investigated. The solutions are discussed for various numbers of fermion flavours and for different current quark masses. The pattern and strength of chiral symmetry breaking is discussed and the positivity properties of the gluon- and quark propagators are examined. The last part focusses on phenomenological constraints on the quark propagator. It will be shown that meson production processes like kaon photoproduction are especially well suited to give constraints on the quark propagator in the timelike region. This complements the Dyson-Schwinger studies which are set up for spacelike momenta.