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. 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

arXiv comment11 pages, 9 figures, 4 tables

References in corpus (27)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• To Explain or to Predict?
• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• High-precision determination of the electric and magnetic form factors of the proton
• Muonic hydrogen and the proton radius puzzle
• The electric and magnetic form factors of the proton
• The Proton Radius Puzzle
• On the rms-radius of the proton
• Model independent extraction of the proton charge radius from electron scattering
• The form factors of the nucleon at small momentum transfer
• Extraction of the proton radius from electron-proton scattering data
• The size of the proton - closing in on the radius puzzle
• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Defining the Proton Radius: a Unified Treatment
• Are Electron Scattering Data Consistent with a Small Proton Radius?
• The Proton Radius from Electron Scattering Data
• Reduction of the proton radius discrepancy by 3 sigma
• Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory
• First measurement of proton's charge form factor at very low $Q^2$ with initial state radiation
• Evaluation of the strength of electron-proton scattering data for determining the proton charge radius
• Proton radius from electron-proton scattering and chiral perturbation theory
• Revisiting the proton-radius problem using constrained Gaussian processes
• Robust extraction of proton charge radius from electron-proton scattering data
• The Proton Radius from Bayesian Inference
• Accurate nucleon electromagnetic form factors from dispersively improved chiral effective field theory
• Reinterpretation of classic proton charge form factor measurements
• Lower bound on the proton charge radius from electron scattering data

Cited by in corpus (14)

• Parameterization and applications of the low-$Q^2$ nucleon vector form factors
• Precise determination of proton magnetic radius from electron scattering data
• An experimental program with high duty-cycle polarized and unpolarized positron beams at Jefferson Lab
• Fresh extraction of the proton charge radius from electron scattering
• Pion charge radius from pion+electron elastic scattering data
• Hadron and light nucleus radii from electron scattering
• PRad-II: A New Upgraded High Precision Measurement of the Proton Charge Radius
• Advanced extraction of the deuteron charge radius from electron-deuteron scattering data
• Understanding the systematic differences in extractions of the proton electric form factors at low-$Q^2$
• Pauli radius of the proton
• Elastic Positron-Proton Scattering at Low Q${}^2$
• The neutron and proton mass radii from the vector meson photoproduction data on the deuterium target
• Note on the electromagnetic radius of proton
• Connecting spatial moments and momentum densities