# 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:

- College of William and Mary, Williamsburg, VA (United States). Dept. of Physics; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Univ. of Stavanger (Norway). Faculty of Science and Technology
- 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 Laboratory-National Energy Research Scientific Computing Center (NERSC)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); USDOE Office of Science (SC), Workforce Development for Teachers and Scientists (WDTS) (SC-27); 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.
```

```
Karpie, Joseph, Orginos, Kostas, Rothkopf, Alexander, & Zafeiropoulos, Savvas. Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to neural networks. United States. doi:10.1007/JHEP04(2019)057.
```

```
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. doi:10.1007/JHEP04(2019)057. https://www.osti.gov/servlets/purl/1524153.
```

```
@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 = {2019},

month = {4}

}

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