Phenomenological Analysis of \(pp\) and \(\bar{p}p\) Elastic Scattering Based on Theoretical Bounds in High-Energy Physics

Abstract

Considering the Froissart-Martin bound, Jin-Martin-Cornille bound and the optical theorem, we propose a novel parametrization for the total cross-section of proton-proton and antiproton-proton elastic scattering data. Using derivative dispersion relations we obtain the real part of the elastic scattering amplitude and thus the \(\rho\) parameter. Simultaneous fits to \(\sigma_{tot}\) and \(\rho\) are performed allowing very good statistical descriptions of the available data. Furthermore, predictions to \(\sigma_{tot}\) and \(\rho\) at energies not used in the fit procedures are presented. For \(\sigma_{tot}\) we obtain predictions at RHIC, LHC and future HC energies.