# Robust extraction of proton charge radius from electron-proton scattering data

## TL;DR

This paper develops a flexible framework to identify robust functional forms for extracting the proton charge radius from electron scattering data, minimizing bias and ensuring reliable results for upcoming experiments.

## Contribution

It introduces a general, expandable framework for testing various functional forms against pseudo-data to find those that reliably extract the proton radius across different input models.

## Key findings

- Two-parameter rational function reliably extracts the radius
- Second order polynomial in z effectively determines the radius
- Framework can be applied to optimize analysis of upcoming low Q^2 data

## Abstract

Extracting the proton charge radius from electron scattering data requires determining the slope of the charge form factor at $Q^2$ of zero. But as experimental data never reach that limit, numerous methods for making the extraction have been proposed, though often the functions are determined after seeing the data which can lead to confirmation bias. To find functional forms that will allow for a robust extraction of the input radius for a wide variety of functional forms in order to have confidence in the extraction from upcoming low $Q^2$ experimental data such as the Jefferson Lab PRad experiment, we create a general framework for inputting form-factor functions as well as various fitting functions. The input form factors are used to generate pseudo-data with fluctuations intended to mimic the binning and random uncertainty of a given set of real data. All combinations of input functions and fit functions can then be tested repeatedly against regenerated pseudo-data. Since the input radius is known, this allows us to find fit functions that are robust for radius extractions in an objective fashion. For the range and uncertainty of the PRad data, we find that a two-parameter rational function, a two-parameter continued fraction and the second order polynomial expansion of $z$ can extract the input radius regardless of the input charge form factor function that is used. We have created an easily expandable framework to search for functional forms that allow for a robust extraction of the radius from a given binning and uncertainty of pseudo-data generated from a wide variety of trial functions. This method has enabled a successful search for the best functional forms to extract the radius from the upcoming PRad data and can be used for other experiments.