Euclidean versus Minkowski short distance

TL;DR

This paper critically examines methods for extracting parton distribution functions from lattice QCD simulations, highlighting the renormalization challenges that hinder direct Euclidean calculations.

Contribution

It analyzes various approaches, including quasi-PDFs and Ioffe-time distributions, and demonstrates the renormalization obstacles in direct Euclidean computations.

Findings

Renormalization issues impede direct Euclidean PDF calculations

Lattice momentum limitations pose significant challenges

Direct computation of PDFs from Euclidean space remains problematic

Abstract

In this note we reexamine the possibility of extracting parton distribution functions from lattice simulations. We discuss the case of quasi-parton distribution functions, the possibility of using the reduced Ioffe-time distributions and the more recent proposal of directly making reference to the computation of the current-current $T$-product. We show that in all cases the process of renormalization hindered by lattice momenta limitation represents an obstruction to a direct Euclidean calculation of the parton distribution function.