Hofstadter-Herman visualization as a diagnostic tool for systematic effects in electromagnetic form factor extractions

The internal charge and magnetization distributions of the proton are characterized by the electromagnetic form factors G E and G M . They are extracted from elastic electron-proton cross sections measured at fixed momentum transfer over a range of beam energies and scattering angles via Rosenbluth separation. Conventionally, form factor values are obtained by plotting reduced cross sections against the virtual photon polarization parameter ϵ and then extracting the slope and intercept of the best-fit lines. An alternative visualization method, proposed by Hofstadter and Herman in 1960, plots form factors directly instead. The values of G E 2 and G M 2 are immediately visible from the intersection region of the curves and their uncertainty bands. In this work, we apply Hofstadter-Herman visualization to classic 1994 SLAC elastic scattering data. The 1994 data include a ∼ 4% downward normalization adjustment applied to the 1.6 GeV/ c spectrometer measurements. Overlaying modern global fit extractions on Hofstadter-Herman plots, we show that intersection regions obtained without including this adjustment sit closer to the global fit values. Such tensions are not readily visible in conventional plots. 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.