# Quasi-PDFs, momentum distributions and pseudo-PDFs

## TL;DR

This paper explores the relationship between quasi-PDFs, pseudo-PDFs, and Ioffe-time distributions, proposing pseudo-PDFs as a more effective alternative for extracting parton distributions from lattice QCD data.

## Contribution

It introduces pseudo-PDFs as a generalization of light-front PDFs that are related to Ioffe-time distributions, offering a practical approach to mitigate lattice renormalization issues.

## Key findings

- Pseudo-PDFs exhibit a convolution structure similar to quasi-PDFs.
- Pseudo-PDFs allow division of $z_3^2$ dependence, simplifying analysis.
- Ioffe-time distributions retain shape information of PDFs.

## Abstract

We show that quasi-PDFs may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large $p_3 \sim 3$ GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose to use pseudo-PDFs $P(x, z_3^2)$ that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions $M (\nu, z_3^2)$, the functions of the Ioffe time $\nu = p_3 z_3$ and the distance parameter $z_3^2$ with respect to which it displays perturbative evolution for small $z_3$. In this form, one may divide out the $z_3^2$ dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The $\nu$-dependence remains intact and determines the shape of PDFs.