QCD Interactions in Hadrons

Abstract

In this work, we use functional methods, namely the formalism of Dyson-Schwinger and Bethe-Salpeter equations (DSEs and BSEs) and the n-particle irreducible effective action formalism, to describe properties of quarks and mesons as bound states of quarks and antiquarks. We explore how truncations of these equations relate to the phenomenon of dynamical chiral symmetry breaking in quantum chromodynamics (QCD). Within the rainbow-ladder truncation, we explore, how different effective running couplings give rise to interaction potentials and how they relate to Regge behaviour in the resulting meson spectra. In particular, we explore spectra of light mesons, kaons, ss-states, charmonia and bottomonia with total angular momenta up to J ≤ 5 within this truncation. Furthermore, we use a universal kernel-first truncation to construct a quark self-energy from a quark-antiquark scattering kernel, such that the axialvector Ward-Takahashi identity and thus the effects of dynamical chiral symmetry breaking are conserved. In this truncation we solve the equations of motion for the quark propagator and quark-photon vertex to investigate, whether the vector Ward- Takahashi identity is fulfilled. Starting from a three particle irreducible effective action, we use this method to extract exploratory spectra of light mesons, kaons and ss-states with total angular momentum up to J ≤ 4 and sketch a way to expand this framework to heavier quarkonia and heavy-light mesons.