Multi-scale chiral dynamics

Abstract

In this work, we examine two possible extensions of the low-energy effective field theory of quantum chromodynamics (QCD), called chiral perturbation theory (ChPT). Both those extensions are related to the presence of resonances in the effective field theory. The additional mass scales (the masses of the resonances) generally lead to complications concerning the structure of the effective field theory. In particular, the power counting scheme, which determines the ordering of the perturbation series, can only be maintained using specific renormalization prescriptions for loop graph contributions. Such renormalization schemes will be worked out in chapters 2 and 3. In chapters 4 and 5, the resonance fields will not be included explicitly in the theory. Instead, we will employ a nonperturbative method (the Bethe-Salpeter integral equation) to describe the meson-baryon scattering process in a resonance-dominated process (kaon electroproduction). It is the aim of chapter 4 to devise a method which implements the principle of gauge invariance in this extension of ChPT. In chapter 5, we will apply our method to the description of kaon electroproduction on the proton.