Hofstadter-Herman Visualization as a Diagnostic Tool for Systematic Effects in Electromagnetic Form Factor Extractions

TL;DR

This paper demonstrates that Hofstadter-Herman visualization effectively reveals systematic effects and discrepancies in electromagnetic form factor data, serving as a diagnostic tool for more accurate proton structure analysis.

Contribution

It introduces the Hofstadter-Herman visualization as a routine diagnostic method for identifying systematic effects in form factor extractions.

Findings

Reveals previously obscured regions of parameter space

Highlights subtle experimental discrepancies

Motivates routine use at Electron-Ion Collider

Abstract

The internal charge and magnetization distributions of the proton are characterized by electromagnetic form factors GE and GM. They are experimentally extracted via Rosenbluth separation, which measures the elastic scattering of electrons and protons at multiple beam energies and angles at fixed momentum transfer Q2. Conventionally, form factor values are obtained by plotting reduced cross sections against the virtual photon polarization parameter epsilon and then extracting the slope and intercept of the best fit lines. An alternative visualization method, proposed by Hofstadter and Herman in 1960, plots GM2 vs. GE2 curves instead. The best fit values of GE2 and GM2 are immediately visible from the intersection region of the curves and their uncertainty bands. In this work, we apply both conventional and Hofstadter-Herman visualizations to classic 1994 SLAC elastic scattering data. We demonstrate that the Hofstadter-Herman method reveals previously obscured regions of form factor parameter space and highlights subtle experimental discrepancies among data sets. Our results motivate adopting this visualization method as a routine diagnostic cross-check at the Electron-Ion Collider and elsewhere to flag normalization shifts and related adjustments before they enter global fits.