Notes on lattice observables for parton distributions: nongauge theories

TL;DR

This paper reviews recent theoretical advances in defining and renormalizing lattice correlators related to parton distribution functions, using scalar field theory as a simplified model to understand their properties and limitations.

Contribution

It introduces a framework for incorporating lattice QCD data into global PDF analyses, based on insights gained from nongauge scalar field theory models.

Findings

One-loop analysis clarifies correlator properties in nongauge theories.

Scalar field theory serves as a useful testbed for lattice PDF methods.

Proposed framework aims to integrate lattice data into global PDF extractions.

Abstract

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.