On the calculation of parton distributions from Lattice QCD

A new method for calculating parton distribution functions from lattice QCD is implemented and studied. Lattice QCD calculable matrix elements with space-like separated fields have an analogous operator product expansion to experimental scattering cross sections and thus these matrix elements are known as “Good Lattice Cross Sections”. Using the colinear factorization approach, a Good Lattice Cross Section can be factorized to the short distance matching kernels that are computed in perturbation theory and the non-perturbative parton distribution functions. As a result, using the perturbative matching kernels and the non-perturbatively computed matrix elements, one can obtain the parton distribution functions. The nucleon and pion matrix elements are determined on a set of 2+1 flavors of clover improved quarks with heavier than physical pion mass. The determination of the parton distributions from Good Lattice Cross Sections constitutes an ill-posed inverse problem. Methods for accurate determination of parton distributions from the Good Lattice Cross Sections are studied. With the calculation of several Good Lattice Cross Sections, the determination of the parton distributions can be improved with a simultaneous analysis, similar to the global parton distribution fits to experimental cross sections.