Speaker
Description
In recent years, methods such as large momentum effective theory (LaMET) and short distance factorization (SDF) have allowed us to extract the $x$-dependence of parton distribution functions (PDFs) utilizing non-local operators of a boosted hadron. Contained within the PDFs is information on fundamental hadronic properties, such as the fraction of the hadron momentum carried by quarks, which is stored in the Mellin moments. By utilizing SDF, we can extract these moments, which are then used as a benchmark of the validity of the PDF reconstructions. The pion is particularly interesting to study as it is the lightest hadron, and its SU(3) symmetry counterpart, the kaon, is also of interest. In studying both of these hadrons, we can compare the up and strange quark contributions individually, study SU(3) symmetry breaking, as well as PDF reconstruction. In this work, we extract the moments at NLO and NNLO accuracy, as well as utilize DGLAP evolution to study systematics associated with perturbative matching. We utilize an $N_f$ = 2+1+1 ensemble of twisted mass fermions with a clover improvement at a pion mass of 260 MeV.