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 $ρ$ parameter. Simultaneous fits to $σ_{tot}$ and $ρ$ are performed allowing very good statistical descriptions of the available data. Furthermore, predictions to $σ_{tot}$ and $ρ$ at energies not used in the fit procedures are presented. For $σ_{tot}$ we obtain predictions at RHIC, LHC and future HC energies.

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