Generalised Parton Distributions from Lattice Feynman-Hellmann Techniques

Abstract

Generalised parton distributions (GPDs) are observables that contain an abundance of previously inaccessible information about hadron structure. However, GPDs have proven di cult to measure from experiment, and rst principles calculations in lattice Quantum Chromodynamics (QCD) have largely been limited to their lowest Mellin moments. In this thesis, we outline a completely novel approach to determine GPD-related information using Feynman-Hellmann techniques in lattice QCD. We present both the formalisms that make this numerical computation possible, and an exploratory calculation using this method. The results appear very promising. First, we show how lattice Feynman-Hellmann techniques can be applied to calculate the o -forward Compton tensor (OFCT). The result is a relation between the OFCT and the energy shifts of a two-point function for a carefully chosen perturbed Lagrangian. Moreover, since the OFCT is both o -forward and second order, the Lagrangian mixes momentum eigenstates in a non-trivial way. Therefore, we also show how to control this mixing by a careful choice of the parameters in our perturbed Lagrangian. Second, we need a form of the OFCT with kinematics that are suitable for the Euclidean lattice. We use an operator product expansion to derive an expression for the leading order (twist-two) contribution to the OFCT in terms of the Mellin moments of GPDs. This result can be compared to a lattice calculation of the OFCT for large momentum transfer, and hence allows us to extract the moments of GPDs. Finally, we present our calculation of the Euclidean OFCT using lattice Feynman- Hellmann techniques. Our results exhibit behaviour that is consistent with the theoretical expressions derived in the previous chapters. We nd that the magnitude of our results is signi cantly larger than what is expected from a simple phenomenological model, but that the t dependence of our results is consistent with this model. As such, this study paves the way for a rst principles calculation of higher GPD moments. Moreover, it allows us to investigate the behaviour of the OFCT in the Euclidean region as it pertains to scaling, factorisation, and other properties of interest.