Gaussian Processes for Inferring Parton Distributions
Abstract
The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a framework based on Gaussian Process Regression (GPR) to reconstruct PDFs from lattice QCD matrix elements. Within a Bayesian framework, Gaussian processes serve as flexible priors that encode uncertainties, correlations, and constraints without imposing rigid functional forms. We investigate a wide range of kernel choices, mean functions, and hyperparameter treatments. We quantify information gained from the data using the Kullback Leibler divergence. Synthetic data tests demonstrate the consistency and robustness of the method. Our study establishes GPR as a systematic and non-parametric approach to PDF reconstruction, offering controlled uncertainty estimates and reduced model bias in lattice QCD analyses.
Cite
@article{arxiv.2510.21041,
title = {Gaussian Processes for Inferring Parton Distributions},
author = {Yamil Cahuana Medrano and Hervé Dutrieux and Joseph Karpie and Kostas Orginos and Savvas Zafeiropoulos},
journal= {arXiv preprint arXiv:2510.21041},
year = {2026}
}