Ab Initio Lattice Quantum Chromodynamics Calculations of Parton Physics in the Proton: Large-Momentum Effective Theory versus Short-Distance Expansion.

Although equivalent in the infinite-momentum limit, large-momentum effective theory (LaMET) and short-distance operator product expansion (SDE) are 2 very different approaches to obtain parton distribution functions (PDFs) from coordinate-space correlation functions computed in a large-momentum proton through lattice quantum chromodynamics (QCD). LaMET implements a momentum-space expansion in to directly calculate PDFs in a middle region of Bjorken . SDE applies perturbative QCD at small Euclidean distances to extract a range of leading-twist correlations, , corresponding to the Fourier transformation of PDFs. An incomplete leading-twist correlation from SDE cannot be readily converted to a momentum-space distribution, and solving its constraints on the PDFs (or the so-called "inverse problem") involves phenomenological modeling of the missing information beyond and has no systematic control of errors. I argue that the best use of short-distance correlations is to constrain the PDFs in the LaMET-complementary regions: and through expected end-point asymptotics, and use the results of the pion valence quark distribution from the ANL/BNL collaboration to demonstrate how this can be done.