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

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.

Authors:
 [1];  [1];  [2];  [3]
+ Show Author Affiliations
  1. College of William and Mary, Williamsburg, VA (United States). Dept. of Physics; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. Univ. of Stavanger (Norway). Faculty of Science and Technology
  3. Heidelberg Univ. (Germany). Inst. for Theoretical Physics
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States); Heidelberg Univ. (Germany); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Workforce Development for Teachers and Scientists (WDTS); National Science Foundation (NSF); German Research Foundation (DFG); Science and Technology Facilities Council (STFC) (United Kingdom)
OSTI Identifier:
1524153
Alternate Identifier(s):
OSTI ID: 1542915
Report Number(s):
JLAB-THY-19-2898; DOE/OR/23177-4647; arXiv:1901.05408
Journal ID: ISSN 1029-8479
Grant/Contract Number:  
AC05-06OR23177; FG02-04ER41302; SC0014664; AC02-05CH11231; PHY-1626177; SFB 1225; ST/P000681/1
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 4; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; lattice QCD; lattice quantum field theory

Citation Formats

Karpie, Joseph, Orginos, Kostas, Rothkopf, Alexander, and Zafeiropoulos, Savvas. Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks. United States: N. p., 2019. Web. doi:10.1007/JHEP04(2019)057.
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Karpie, Joseph, Orginos, Kostas, Rothkopf, Alexander, & Zafeiropoulos, Savvas. Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks. United States. https://doi.org/10.1007/JHEP04(2019)057
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Karpie, Joseph, Orginos, Kostas, Rothkopf, Alexander, and Zafeiropoulos, Savvas. Fri . "Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks". United States. https://doi.org/10.1007/JHEP04(2019)057. https://www.osti.gov/servlets/purl/1524153.
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@article{osti_1524153,
title = {Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks},
author = {Karpie, Joseph and Orginos, Kostas and Rothkopf, Alexander and Zafeiropoulos, Savvas},
abstractNote = {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.},
doi = {10.1007/JHEP04(2019)057},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2019,
place = {United States},
year = {Fri Apr 05 00:00:00 EDT 2019},
month = {Fri Apr 05 00:00:00 EDT 2019}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1007/JHEP04(2019)057
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Citation Metrics:
Cited by: 64 works
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Figures / Tables:

Figure 1 Figure 1: Eigenvalues $λ$$k$ of the Kernel matrix for the direct inversion method on the left and the derivative inversion method on the right calculated with different discretization intervals of $ν$. Note that only for the case corresponding to a genuine discrete Fourier transform, $ν$ = [0, 40$π$], do allmore » the eigenvalues remain of the same order. All other ranges show exponentially suppressed eigenvalues. The realistic case of $ν$ = [0, 20] already shows a significant degradation of the eigenvalue spectrum.« less
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text, January 2010

Reweighting NNPDFs: the W lepton asymmetry
text, January 2010

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text, January 2013

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text, January 2016

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text, January 2017

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text, January 2017

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text, January 2017

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text, January 2017

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    Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
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