Baryon Structure Using the Feynman-Hellmann Theorem in Lattice Quantum Chromodynamics

Abstract

Baryons such as the proton and neutron make up the large majority of all visible matter in the universe. According to the standard model, the structure of these baryons is defined by the interactions of their constituent parts, the quarks and gluons. The gauge field theory which governs these interactions is called Quantum Chromodynamics (QCD), which has a property that prevents the application of perturbative methods at low energies. Currently, the best first-principles approach to studying the effects of QCD at low energies is Lattice QCD, which relies on a discretisation of spacetime. In this thesis we go through the derivation of the Feynman-Hellmann theorem and its application to lattice QCD, specifically for the calculation of baryon matrix elements. This Feynman-Hellmann method provides us with an alternative approach to conventional lattice QCD techniques. To study the internal structure of baryons we use the Feynman- Hellmann method to calculate the electromagnetic form factors of the octet baryons at high momentum transfers. In this calculation we take advantage of the improved control of excited states provided by the Feynman-Hellmann method as well as a weighted-averaging approach to provide a robust analysis over a wide range of momenta. The form factor results are then extrapolated to physical quark masses through the use of a flavour breaking expansion. Our results for the electric form factor GE show good agreement with experimental results, however the results for the magnetic form factor GM do not agree well, indicating that there could be more systematic effects presently unaccounted for. The use of an expanded version of the Feynman-Hellmann method which allows for the consideration of quasi-degenerate energy states, allows for the investigation of the transition form factors of hyperons These are valuable as they can provide insight into the oscillations between quark flavour permitted by the standard model. We present results for the matrix element of the Σ− to neutron transition which agree well with a similar calculation using the conventional three-point function method. This is promising as this novel method could provide an independent approach to the determination of the CKM matrix elements.