Studies of Light Scalar Particles and Dressed Gauge Propagators in QCD

The equations of QCD are widely believed to describe the properties of mesons, baryons and their hadronisation after hard interactions at particle accelerators such as the LHC. However, the theoretical framework linking the fundamental Lagrangian of QCD to the mesons and baryons observed in experiment is still in development. The states observed by experiments can be investigated using a variety of other theoretical methods. We consider here two methods, Chiral Perturbation Theory and carefully considering the poles in a scattering amplitude. In chapters 2 and 3 we apply these methods to determine the composition of the sigma(600) and f0(980) scalar resonances observed in scattering. In chapter 4 we turn to make the connection between the fundamental Lagrangian and the observed physics. The first step here is to solve the Schwinger-Dyson equations for the gluons, ghosts and quarks which describe how a Green’s function behaves non-perturbatively. We primarily investigate the coupled gluon and ghost system without quarks. We find that non–trivial vertices are required to obtain self–consistent solutions in the simplest truncation and that a solution with a finite ghost dressing function appears to be preferred.