Moments of parton distribution amplitudes and structure functions for the light mesons from lattice QCD

Abstract

This thesis presents the lattice calculation and the required renormalisation for the determination of two hadronic structure quantities. These are the parton distribution amplitudes (PDAs) which enter in the form-factor for exclusive scattering processes and the parton distribution functions (pdfs) that appear in inclusive processes. The PDA’s provide process independent partonic information about hadrons and are important quantities required for the calculation of weak physics parameters, such as CKM matrix elements and CP violating phases. We are able to calculate moments of the PDAs on the lattice using two point correlation functions of local operators. This calculation extracts the first two moments for the light mesons and is performed on three ensembles, with parameters, that enable a study of finite volume and discretisation effects. We use the Iwasaki gauge action and 2 + 1 flavours of domain wall fermions for all simulations. The calculation of the pdfs through the structure function moments uses three-point correlation functions of local operators. We extract the first odd moment for the pion on our finest lattice, using partially twisted boundary conditions. An important feature of both calculations is non-perturbative renormalisation, using the Rome-Southampton method. The effect of the projections used to isolate the desired renormalisation factors and the momentum choice, that sets the renormalisation scale, on the discretisation errors is detailed through the use of twisted boundary conditions. The results for all quantities are obtained to good precision