Gaussian processes for inferring parton distributions

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Abstract
A bstract: 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.
Funding Information
  • U.S. Department of Energy (DE-AC05-06OR23177)
  • Southeastern Universities Research Association (C2024-FEMT-011-03)
  • U.S. Department of Energy (DE-FG02-04ER41302)
  • Agence Nationale de la Recherche (ANR-23-CE31-0019)
  • U.S. Department of Energy (DE-SC0023646)
  • National Science Foundation (PHY-1626177)
  • U.S. Department of Energy (DE-AC02-05CH11231)
  • Institute for Development and Resources in Intensive Scientific Computing (A0080511504)

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