# Sensitivity of the elastic electron-proton cross section to the proton radius

## TL;DR

This paper examines how sensitive the elastic electron-proton scattering cross section is to the proton radius, highlighting the extreme precision needed in measurements and the significant systematic errors involved.

## Contribution

It provides a detailed analysis of the precision requirements and systematic uncertainties in extracting the proton radius from scattering data, emphasizing the challenges in achieving accurate measurements.

## Key findings

- Required precision on cross section is two orders of magnitude higher than current measurements.
- Systematic errors in radius determination are much larger than previously assumed.
- Different data fits and extrapolations significantly affect the proton radius estimate.

## Abstract

The precise determination of the proton radius from recent elastic scattering electron-proton data is discussed. The necessary precision on the elastic cross section to discriminate among the values coming from atomic spectroscopy is scrutinized in terms of the relevant quantity, i.e., the derivative of the form factor. It is shown that such precision is two orders of magnitude higher than the precision on the cross section, that is the measured observable. Different fits on the available data and of their discrete derivative, with analytical constraints are shown. The systematic error associated to the radius is evaluated taking into account the uncertainties from different sources, as the extrapolation to the static point, the choice of the class of fitting functions and the range of the data sample. This error is shown to be even orders of magnitude larger than commonly assumed.