# Charting the coming synergy between lattice QCD and high-energy phenomenology

## TL;DR

This paper explores how future high-energy experiments and lattice QCD calculations can work together to better understand the internal structure of nucleons, emphasizing the importance of upcoming collider data.

## Contribution

It provides a comprehensive sensitivity analysis linking lattice QCD observables with high-energy experimental data, highlighting the potential for synergy between the two fields.

## Key findings

- Future lepton-hadron colliders can significantly constrain lattice QCD calculations.
- High-energy data can improve the determination of nucleon parton distribution functions.
- Lattice and phenomenological approaches can collaboratively enhance understanding of nucleon structure.

## Abstract

Building upon the PDFSense framework developed in Ref. [1], we perform a comprehensive analysis of the sensitivity of present and future high-energy data to a number of quantities commonly evaluated in lattice gauge theory, with a particular focus on the integrated Mellin moments of nucleon parton distribution functions (PDFs), such as $\langle x \rangle_{u^+ - d^+}$ and $\langle x \rangle_{g}$, as well as $x$-dependent quark quasi-distributions -- in particular, that of the isovector combination. Our results demonstrate the potential for lattice calculations and phenomenological quark distributions informed by high-energy experimental data to cooperatively improve the picture of the nucleon's collinear structure. This will increasingly be the case as computational resources for lattice calculations further expand, and QCD global analyses continue to grow in sophistication. Our sensitivity analysis suggests that a future lepton-hadron collider would be especially instrumental in providing phenomenological constraints to lattice observables.