Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks

  • Joseph Karpie
  • Kostas Orginos
  • Alexander Rothkopf
  • Savvas ZafeiropoulosEmail author
Open Access
Regular Article - Theoretical Physics


The computation of the parton distribution functions (PDF) or distribution amplitudes (DA) of hadrons from first principles lattice QCD constitutes a central open problem in high energy nuclear physics. In this study, we present and evaluate the efficiency of several numerical methods, well established in the study of inverse problems, to reconstruct the full x-dependence of PDFs. Our starting point are the so called Ioffe time PDFs, which are accessible from Euclidean time simulations in conjunction with a matching procedure. Using realistic mock data tests, we find that the ill-posed incomplete Fourier transform underlying the reconstruction requires careful regularization, for which both the Bayesian approach as well as neural networks are efficient and flexible choices.


Lattice QCD Lattice Quantum Field Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Joseph Karpie
    • 1
    • 2
  • Kostas Orginos
    • 1
    • 2
  • Alexander Rothkopf
    • 3
  • Savvas Zafeiropoulos
    • 4
    Email author
  1. 1.Department of PhysicsThe College of William & MaryWilliamsburgU.S.A.
  2. 2.Thomas Jefferson National Accelerator FacilityNewport NewsU.S.A.
  3. 3.Faculty of Science and TechnologyUniversity of StavangerStavangerNorway
  4. 4.Institute for Theoretical PhysicsHeidelberg UniversityHeidelbergGermany

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