Structure of the Pion from First Principles Calculation in Lattice QCD

A long-standing challenge in lattice QCD is the direct computation of key measures of hadron structure, including parton distribution functions, quark distribution amplitudes, and three-dimensional measures such as the transverse-momentum-dependent distributions, and generalized parton dis- tributions. Recently, new approaches have been proposed that enable their direct computation, and these are characterized by a requirement that the hadron of interest be increasingly relativis- tic. This Class A Continuation proposal aims to capitalize on recent developments, and our previous USQCD allocation, to compute the structure functions of the pion and nucleon using the pseudo-PDF and current-current matrix element formulation using the distillation framework, and to extend the calculation to that of the gluon contribution to hadron structure, and to embark on calculations of three-dimensional imaging through the calculation of GPDs in the pseudo-PDF approach. This project is relevant to the hadron structure experimental programs at JLab, and at RHIC-spin. With the recent CD0 and site selection of the EIC, the extension to the gluon distri- butions is particularly timely. We request an allocation of 63.6 KNL-core-hours, 0.88M GeForge GPU-Hours, 6.5M SKX-core-hours, together with an addition 100 TByte tape storage, and 60 Tbyte of disk storage. So…. …Use Operator-Product-Expansion to formulate in terms of Mellin Moments with respect to Bjorken x.