Comparison of results for the electromagnetic form factors of the proton at low $Q^2$

TL;DR

This paper compares five parameterizations of the proton's electromagnetic form factors at low Q^2, demonstrating that a simple two-dipole model effectively supports phase-shift analyses by reducing dependence on extraneous sources.

Contribution

It introduces a simple two-dipole model for proton form factors that improves phase-shift analyses of low-energy pion-nucleon data by minimizing extraneous dependencies.

Findings

A simple two-dipole model suffices for low Q^2 form factor parameterization.

Replacing current form factors with this model reduces extraneous dependence in phase-shift analyses.

The model aligns well with existing data and simplifies the analysis process.

Abstract

The goal in this work is the comparison of five parameterisations of the Sachs form factors of the proton $G^p_E$ (electric) and $G^p_M$ (magnetic) at low $4$-momentum transfer $Q^2$. It will be shown that a simple model, based on two dipoles which admit as parameters the rms electric charge radius $r_{E;p}$ and the rms magnetic radius $r_{M;p}$ of the proton, suffices for the purposes of the phase-shift analyses (PSAs) of the low-energy pion-nucleon ($\pi N$) data. The replacement of the electromagnetic form factors, currently used in the ETH model of the $\pi N$ interaction, by the parameterisation of this work will enable the removal from the PSAs of this research programme of the largest part of the dependence on extraneous sources.