Proton root-mean-square radii and electron scattering

TL;DR

This paper highlights flaws in the standard method of extracting proton root-mean-square radii from electron scattering data, emphasizing the importance of physical density behavior for reliable measurements.

Contribution

It identifies the uncertainties in radius extraction due to model-dependent extrapolation and proposes criteria for physically meaningful density behavior.

Findings

Extrapolation uncertainties affect radius accuracy.

Physical density behavior is crucial for reliable radii.

Standard methods may underestimate uncertainties.

Abstract

The standard procedure of extracting the proton root-mean-square radii from models for the Sachs form factors $G_e (q)$ and $G_m (q)$ fitted to elastic electron-proton scattering data %has a serious flaw. is more uncertain than traditionally assumed. The extrapolation of $G(q)$, from the region $q_{min} < q < q_{max}$ covered by data to momentum transfer $q=0$ where the $rms$-radius is obtained, often depends on uncontrolled properties of the parameterization used. Only when ensuring that the corresponding densities have a physical behavior at large radii $r$ can reliable $rms$-radii be determined.