# Hadron structure in high-energy collisions

## TL;DR

This paper reviews the concept of parton distribution functions (PDFs) in hadrons, focusing on their definitions, how they are fitted to data, and methods to test the validity of the assumptions involved.

## Contribution

It provides a comprehensive overview of PDFs in protons and nuclei, detailing the statistical fitting process and validation tests, with insights into handling assumption failures.

## Key findings

- Detailed explanation of PDF definitions and their relation to cross sections
- Discussion of the Hessian method for fitting PDFs to data
- Proposals for testing and addressing invalid assumptions in PDF analysis

## Abstract

Parton distribution functions (PDFs) describe the structure of hadrons as composed of quarks and gluons. They are needed to make predictions for short-distance processes in high-energy collisions and are determined by fitting to cross section data. We review definitions of the PDFs and their relations to high-energy cross sections. We focus on the PDFs in protons, but also discuss PDFs in nuclei. We review in some detail the standard statistical treatment needed to fit the PDFs to data using the Hessian method. We discuss tests that can be used to critically examine whether the assumptions are indeed valid. We also present some ideas of what one can do in the case that the tests indicate that the assumptions fail.