We review recent theoretical developments concerning the definition and the renormalization of equal-time correlators that can be computed on the lattice and related to Parton Distribution Functions (PDFs) through a factorization formula. We show how these objects can be studied and analyzed within the framework of a nongauge theory, gaining insight through a one-loop computation. We use scalar field theory as a playground to revise, analyze and present the main features of these ideas, to explore their potential, and to understand their limitations for extracting PDFs. We then propose a framework that would allow to include the available lattice QCD data in a global analysis to extract PDFs.
@article{arxiv.2007.02131,
title = {Notes on lattice observables for parton distributions: nongauge theories},
author = {Luigi Del Debbio and Tommaso Giani and Christopher J. Monahan},
journal= {arXiv preprint arXiv:2007.02131},
year = {2020}
}