Hadron structure and the Feynman-Hellmann theorem in lattice quantum chromodynamics

Abstract

The vast majority of visible matter in the universe is made up of protons and neutrons, the fundamental building blocks of atomic nuclei. Protons and neutrons are examples of hadrons, composite states formed from point-like quarks and gluons. Understanding the dynamics of quarks and gluons inside hadrons has far-reaching implications, from the properties of heavy nuclei to the dynamics of neutron stars. Quantum Chromodynamics (QCD) is the gauge field theory (GFT) describing the interactions of colour-charged quarks and gluons. At the low energy scales relevant to hadron structure calculations, QCD is non-perturbative, and the techniques applied to other GFTs cannot be used. At the forefront of the non-perturbative methods is Lattice QCD, a first-principles approach in which physical observables are calculated numerically through a discretisation of the Feynman path integral. Hadron structure calculations in lattice QCD have made significant advances in recent years, however many challenges still remain. Most notably amongst these are precise calculations of ‘disconnected’ contributions to hadronic quantities, the control of excited-state contamination, and the calculation of matrix elements at large boosts. In this thesis we develop and show how a method based on the Feynman-Hellmann (FH) theorem deals with many of these issues. The method allows matrix elements to be determined indirectly, through the introduction of artificial couplings to the QCD Lagrangian, and the calculation of the resulting shifts in the hadron spectrum. We have calculated disconnected contributions to the axial charge of the nucleon, and see excellent agreement with existing stochastic results, as well as good excited-state control. Our results for the electromagnetic form factors of the proton are the first in lattice to show agreement with the linear decrease of GE,p/GM,p [E,p and M,p subscript] observed in experiment. Additionally, exploratory simulations have shown that an extension of the FH theorem to second order allows direct access to the structure functions of the nucleon, another first in lattice QCD. These calculations demonstrate an expanded scope for lattice studies of hadronic observables, particular for processes involving high momentum transfer. Extensions of this work will have important implications for future experimental investigations at the upgraded Continuous Electron Beam Accelerator Facility.