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

TL;DR

The paper tackles the problem of reliably extracting proton electric and magnetic form factors $G_E(Q^2)$ and $G_M(Q^2)$ from elastic $ep$ scattering, highlighting limitations of the traditional Rosenbluth separation. It introduces Hofstadter–Herman visualization in Sachs space to plot bands of $G_E^2$ versus $G_M^2$ and demonstrates its diagnostic power by reanalyzing the 1994 SLAC data, uncovering normalization-related tensions that are not obvious in standard plots. The study shows that a small normalization shift (about 4% at $1.6$ GeV) can move measurements away from the region favored by modern global fits, whereas the unnormalized data may align better with those fits, illustrating the method's utility for data vetting before global analyses. The findings advocate adopting geometry-based, band-intersection visualizations at future facilities such as the Electron–Ion Collider to improve cross-checks, flag biases early, and enhance the reliability of form-factor extractions.

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.

Figures (8)

• Figure 1: An example of a standard Rosenbluth separation method plot, here at $Q^2=1.75$ GeV.
• Figure 2: An example of the Hofstadter-Herman visualization method, here at $Q^2=1.75$ GeV.
• Figure 3: Conventional plot of normalized SLAC data reflecting a 4% normalization applied to the 1.6 GeV spectrometer subset, as in the original analysis; see text for discussion.
• Figure 4: Conventional plot of SLAC data without the normalization adjustment, illustrating the original measurements without the applied 4% normalization to the 1.6 GeV spectrometer subset.
• Figure 5: Hofstadter-Herman plot of normalization-adjusted SLAC data.