https://doi.org/10.1140/epja/s10050-023-01227-w
Regular Article - Experimental Physics
Direct comparison of using a Z-transformation instead of the traditional 
for extraction of the proton radius from 
scattering data
1
North Carolina A &T State University, 27411, Greensboro, NC, USA
2
Lawrence Berkeley National Laboratory, 94720, Berkeley, CA, USA
3
Thomas Jefferson National Accelerator Facility, 23606, Newport News, VA, USA
4
The Governor’s School for Science and Technology, 23666, Hampton, VA, USA
Received:
20
September
2023
Accepted:
16
December
2023
Published online:
4
January
2024
A discrepancy in the determination of the proton’s charge radius, 
, between muonic hydrogen spectroscopy versus classic atomic spectroscopy and electron scattering data has become known as the proton radius puzzle. Extractions of from electron scattering data require determination of the slope of the proton’s charge form factor, 
, in the limit of 
through fitting and extrapolation. Some works have presented the Z-transformation fitting technique as the best choice for this type of extraction due to the true functional form of being mathematically guaranteed to exist within the parameter-space of the fit function. In this work, we test this claim by examining the mathematical bias and variances introduced by this technique as compared to the more traditional fits using statistically sampled parameterizations with known input radii. Our tests conclude that the quality of the Z-transformation technique depends on the range of data used. In the case of new experiments, the fit function and technique should be selected in advance by generating realistic pseudodata and assessing the power of different techniques.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epja/s10050-023-01227-w.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
