Absorptive Corrections to the Electromagnetic Form Factor in High-Energy Elastic Proton-Proton Scattering

Recently, it was noted that absorptive corrections to the electromagnetic form factor in high-energy proton-proton scattering are important for the theoretical interpretation of the p^↑p and p^↑A analyzing power AN(t) measurements with the Hydrogen Jet Target polarimeter (HJET) at RHIC. Here, a concise expression for the absorptive correction was derived within the eikonal approach. The resulting analysis reveals a systematic bias, nearly independent of the beam energy, in the experimental determination of the real-to-imaginary ratio ρ when absorption effects are overlooked in the data analysis. Quantification of this bias, as ρᵐeas=ρ + (0.036±0.016)bias, was achieved using a Regge fit applied to available proton-proton measurements of ρᵐeas(s) and σᵐeasₜot(s). Considering the potential impact of such an effect on the experimentally determined AN(t), one may enhance consistency between the HJET and STAR measurements of the hadronic spin-flip amplitude. While the sign of the bias in the value of ρ aligns with the anticipated effective increase in the proton charge radius in $pp$ scattering due to absorption, it amplifies the observed discrepancy between σᵐeasₜot and ρᵐeas values at √s=13\,TeV as measured in the TOTEM experiment. Evaluation (using published TOTEM data) of the measured proton-proton dσ/dt dependence on the absorptive corrections indicated that possible soft photon corrections to the hadronic amplitude slope may be essential for such data analysis.