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

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.