Eikonal zeros in the momentum transfer space from proton-proton scattering: An empirical analysis

TL;DR

This paper empirically analyzes proton-proton scattering data to identify a zero in the imaginary part of the eikonal function in momentum space, revealing insights into scattering dynamics and model validity.

Contribution

It introduces a semi-analytical method to extract the eikonal from data, demonstrating the presence of a zero in the imaginary part and linking it to phenomenological models and form factor analyses.

Findings

Evidence of a zero in the imaginary eikonal at q^2 ≈ 7 GeV^2.

Models with one zero fit the data well across all momentum transfer ranges.

Discussion of the connection between eikonal features and proton form factors.

Abstract

By means of improved empirical fits to the differential cross section data on $pp$ elastic scattering at $19.4 \le\sqrt{s}\le 62.5$ GeV and making use of a semi-analytical method, we determine the eikonal in the momentum transfer space (the inverse scattering problem). This method allows the propagation of the uncertainties from the fit parameters up to the extracted eikonal, providing statistical evidence that the imaginary part of the eikonal (real part of the opacity function) presents a zero (change of signal) in the momentum space, at $q^2 \approx 7 \pm 1$ GeV$^2$. We discuss the implication of this change of signal in the phenomenological context, showing that eikonal models with one zero provide good descriptions of the differential cross sections in the full momentum transfer range, but that is not the case for models without zero. Empirical connections between the extracted eikonal and results from a recent global analysis on the proton electric form factor are also discussed, in special the Wu-Yang conjecture. In addition, we present a critical review on the $pp$ differential cross section data presently available at high energies.