An Overview of Lattice Results for Parton Distribution Functions

TL;DR

This paper reviews lattice QCD methods for determining parton distribution functions, discussing theoretical challenges and Bayesian approaches to inverse problems in hadron structure analysis.

Contribution

It provides an overview of lattice techniques for extracting parton densities and addresses the associated theoretical and computational difficulties.

Findings

Lattice QCD offers a promising avenue for probing hadron structure.

Inverse problems in extracting parton densities are complex and require advanced methods.

Bayesian frameworks can help mitigate uncertainties in lattice-based determinations.

Abstract

Following a ground-breaking proposal by Ji~\cite{PhysRevLett.110.262002}, numerical simulations of Quantum Chromo Dynamics (QCD) on a Euclidean lattice have provided new, valuable information on the structure of hadrons. In this talk, we briefly review the lattice approach to the reconstruction of parton densities, highlighting the connection between lattice observables and parton densities, with a focus on theoretical issues. Since parton distributions are extracted from lattice data by solving an inverse problem, we discuss some of the difficulties that affect these determinations and how they can be formulated in a Bayesian framework.