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 this study, we present and evaluate the efficiency of a selection of methods for 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 calculations 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.
@article{arxiv.1901.05408,
title = {Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks},
author = {Joseph Karpie and Kostas Orginos and Alexander Rothkopf and Savvas Zafeiropoulos},
journal= {arXiv preprint arXiv:1901.05408},
year = {2019}
}