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

A bstract 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, wel...

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Bibliographic Details
Published in:The journal of high energy physics 2019-04, Vol.2019 (4), p.1-43, Article 57
Main Authors: Karpie, Joseph, Orginos, Kostas, Rothkopf, Alexander, Zafeiropoulos, Savvas
Format: Article
Language:English
Subjects:
Bayesian analysis
Classical and Quantum Gravitation
Computer simulation
Dependence
Distribution functions
Elementary Particles
First principles
Fourier transforms
Hadrons
High energy physics
Ill posed problems
Inverse problems
Lattice QCD
Lattice Quantum Field Theory
Neural networks
Nuclear physics
NUCLEAR PHYSICS AND RADIATION PHYSICS
Numerical methods
Physics
Physics and Astronomy
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Quantum chromodynamics
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Regularization
Relativity Theory
String Theory
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Summary:A bstract 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP04(2019)057