Gaussian Processes for Inferring Parton Distributions

TL;DR

This paper introduces a Gaussian Process Regression framework for reconstructing parton distribution functions from lattice QCD data, providing a flexible, Bayesian, non-parametric approach with controlled uncertainties and reduced bias.

Contribution

It presents the first systematic application of Gaussian Process Regression to PDF extraction from lattice QCD, exploring kernel choices and uncertainty quantification.

Findings

GPR provides consistent and robust PDF reconstructions.

The method yields controlled uncertainty estimates.

GPR reduces model bias compared to traditional approaches.

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.