Understanding the systematic differences in extractions of the proton electric form factors at low-$Q^2$

TL;DR

This paper investigates the discrepancies in proton electric form factor measurements at low Q^2 by using a simple analytic function to re-analyze data and theoretical calculations, revealing that normalization shifts can explain the differences.

Contribution

It introduces a simple rational function approach to reconcile systematic differences in proton form factor extractions and demonstrates its effectiveness through data re-analysis and theoretical comparison.

Findings

Normalization shifts significantly affect form factor extraction.

The rational function accurately describes complex theoretical calculations.

Discrepancies can be resolved with simple analytic modeling.

Abstract

Systematic differences exist between values of the proton's electric form factors in the low-$Q^2$ region extracted by different experimental and theoretical groups, though they are all making use of basically the same electron-proton scattering data. To try understand the source of these differences, we make use of the analytically well-behaved rational (N=1, M=1) function, a predictive function that can be reasonably used for extrapolations at $Q^{2} \rightarrow 0$. First, we test how well this deceptively simple two-parameter function describes the extremely complex and state-of-the-art dispersively improved chiral effective field theory calculations. Second, we carry out a complete re-analysis of the 34 sets of eletron-proton elastic scattering cross-section data of the Mainz A1 Collaboration with its unconstrained 31 normalization parameters up to $Q^{2} = 0.5~{\rm (GeV/c)^{2}}$. We find that subtle shifts in the normalization parameters can result in relatively large changes in the extracted physical qualities. In conclusion, we show that by simply using a well-behaved analytic function, the apparent discrepancy between recent form-factor extractions can be resolved.