How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data
Abstract
Scientists often try to incorporate prior knowledge into their regression algorithms, such as a particular analytic behavior or a known value at a kinematic endpoint. Unfortunately, there is often no unique way to make use of this prior knowledge, and thus, different analytic choices can lead to very different regression results from the same set of data. In this paper, to illustrate this point in the context of the proton electromagnetic form factors, we use the Mainz elastic data with its 1422 cross section points and 31 normalization parameters. Starting with a complex unbound non-linear regression, we will show how the addition of a single theory-motivated constraint removes an oscillation from the magnetic form factor and shifts the extracted proton charge radius. We then repeat both regressions using the same algorithm, but with a rebinned version of the Mainz dataset. These examples illustrate how analytic choices, such as the function that is being used or even the binning of the data, can dramatically affect the results of a complex regression. These results also demonstrate why it is critical when using regression algorithms to have either a physical model in mind or a firm mathematical basis
- Authors:
-
[1];
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Publication Date:
- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1638180
- Report Number(s):
- JLAB-PHY-19-2887; DOE/OR-23177-5000; arXiv:1902.08185
Journal ID: ISSN 2469-9985;2469-9993; TRN: US2201745
- Grant/Contract Number:
- AC05-06OR23177
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. C
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 1; Journal ID: ISSN 2469-9985
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Photonuclear reactions; protons; form factors; nuclear data analysis & compilation; statistical methods; proton radius; confirmation bias; regression; robust methods
Citation Formats
Barcus, Scott K., Higinbotham, Douglas W., and McClellan, Randall Evan. How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data. United States: N. p., 2020.
Web. doi:10.1103/physrevc.102.015205.
Barcus, Scott K., Higinbotham, Douglas W., & McClellan, Randall Evan. How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data. United States. https://doi.org/10.1103/physrevc.102.015205
Barcus, Scott K., Higinbotham, Douglas W., and McClellan, Randall Evan. Fri .
"How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data". United States. https://doi.org/10.1103/physrevc.102.015205. https://www.osti.gov/servlets/purl/1638180.
@article{osti_1638180,
title = {How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data},
author = {Barcus, Scott K. and Higinbotham, Douglas W. and McClellan, Randall Evan},
abstractNote = {Scientists often try to incorporate prior knowledge into their regression algorithms, such as a particular analytic behavior or a known value at a kinematic endpoint. Unfortunately, there is often no unique way to make use of this prior knowledge, and thus, different analytic choices can lead to very different regression results from the same set of data. In this paper, to illustrate this point in the context of the proton electromagnetic form factors, we use the Mainz elastic data with its 1422 cross section points and 31 normalization parameters. Starting with a complex unbound non-linear regression, we will show how the addition of a single theory-motivated constraint removes an oscillation from the magnetic form factor and shifts the extracted proton charge radius. We then repeat both regressions using the same algorithm, but with a rebinned version of the Mainz dataset. These examples illustrate how analytic choices, such as the function that is being used or even the binning of the data, can dramatically affect the results of a complex regression. These results also demonstrate why it is critical when using regression algorithms to have either a physical model in mind or a firm mathematical basis},
doi = {10.1103/physrevc.102.015205},
journal = {Physical Review. C},
number = 1,
volume = 102,
place = {United States},
year = {Fri Jul 10 00:00:00 EDT 2020},
month = {Fri Jul 10 00:00:00 EDT 2020}
}
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