Testing momentum dependence of the nonperturbative hadron structure in a global QCD analysis

TL;DR

This paper explores how to effectively compare nonperturbative QCD predictions for parton distribution functions with experimental data, emphasizing the importance of using power-law behaviors rather than direct functional forms due to mathematical ambiguities.

Contribution

It introduces a framework for comparing nonperturbative QCD predictions with experiments by focusing on effective power-law behaviors of PDFs, addressing issues with direct functional form comparisons.

Findings

Demonstrates the mathematical mimicry problem in PDF parametrizations.

Proposes using effective power laws of (1-x) for comparison.

Compares quark counting rule expectations with CT18 PDFs.

Abstract

We discuss strategies for comparisons of nonperturbative QCD predictions for parton distribution functions (PDFs) with high-energy experiments in the region of large partonic momentum fractions $x$. Analytic functional forms for PDFs cannot be uniquely determined solely based on discrete experimental measurements because of a mathematical property of mimicry of PDF parametrizations that we prove using a representation based on B\'ezier curves. Predictions of nonperturbative QCD approaches for the $x$ dependence of PDFs instead should be cast in a form that enables decisive comparisons against experimental measurements. Predictions for effective power laws of $(1-x)$ dependence of PDFs may play this role. Expectations for PDFs in a proton based on quark counting rules are compared against the effective power laws of $(1-x)$ dependence satisfied by CT18 next-to-next-to-leading order parton distributions. We comment on implications for studies of PDFs in a pion, in particular on the comparison of nonperturbative approaches with phenomenological PDFs.