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

Joseph Karpie, Kostas Orginos, Alexander Rothkopf, Savvas Zafeiropoulos
2019 Journal of High Energy 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 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
more » ... stic 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.
doi:10.1007/jhep04(2019)057 fatcat:fybp53emezdytktm65luukbjye