Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks
Peer reviewed, Journal article
Published version
Date
2019Metadata
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Original version
Karpie, J., Orginos, K., Rothkopf, A., & Zafeiropoulos, S. (2019). Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks. Journal of High Energy Physics, 2019(4), 1-43. 10.1007/JHEP04(2019)057Abstract
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.