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

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.