On the structure of nucleon excited states in lattice QCD

Abstract

The structure of the nucleon and its excited states is governed by Quantum Chromodynamics (QCD), the theory of the strong force that binds constituent particles known as quarks into hadrons. The vacuum of QCD is non-trivial, and contains complicated, topologically non-trivial structures such as centre clusters. As a result, QCD cannot be solved by standard perturbative methods. Instead we formulate the theory on a discrete space-time lattice and evaluate expectation values computationally. Centre clusters are localised spatial regions which play an important role in the confinement of quarks into hadrons. By visualising these centre clusters, we investigate their structure and observe the way they evolve under the algorithms used to solve QCD on the lattice. This gives insight into the role they play in confinement and hence how they underpin hadronic structure. Moving on to the hadrons themselves, we develop the novel PEVA technique, which allows for the isolation of the nucleon, its excitations, and other baryons at finite momentum on the lattice. We then extend this technique to the calculation of form factors of baryons. Utilising this technique, we extract the Sachs electric and magnetic form factors for the ground stat nucleon, and demonstrate the necessity of PEVA for precision calculations of such form factors. Finally, we turn our attention to the excitations of the nucleon. We present world first calculations of the Sachs electric and magnetic form factors of three localised excitations of the nucleon on the lattice. These results give fascinating insight into the structure of these states and pave the way for future effective field theory studies of the N*(1535) and N*(1650) resonances. These results would not have been possible without first developing the PEVA technique. Now that it has been developed, it will become a staple for investigations of baryon excited states.