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

Journal of High Energy Physics volume 2019, Article number: 57 (2019) Cite this article

A preprint version of the article is available at arXiv.

Abstract

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.

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Authors and Affiliations

  1. Department of Physics, The College of William & Mary, Williamsburg, VA, 23187, U.S.A.

    Joseph Karpie & Kostas Orginos

  2. Thomas Jefferson National Accelerator Facility, Newport News, VA, 23606, U.S.A.

    Joseph Karpie & Kostas Orginos

  3. Faculty of Science and Technology, University of Stavanger, 4021, Stavanger, Norway

    Alexander Rothkopf

  4. Institute for Theoretical Physics, Heidelberg University, Philosophenweg 12, 69120, Heidelberg, Germany

    Savvas Zafeiropoulos

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  1. Joseph Karpie
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  2. Kostas Orginos
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  4. Savvas Zafeiropoulos
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Correspondence to Savvas Zafeiropoulos.

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ArXiv ePrint: 1901.05408

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Karpie, J., Orginos, K., Rothkopf, A. et al. Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks. J. High Energ. Phys. 2019, 57 (2019). https://doi.org/10.1007/JHEP04(2019)057

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  • DOI: https://doi.org/10.1007/JHEP04(2019)057

Keywords

  • Lattice QCD
  • Lattice Quantum Field Theory