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

TL;DR

This paper introduces a new parametrization for proton-proton and antiproton-proton elastic scattering cross-sections based on theoretical bounds, providing accurate fits and predictions for high-energy collider experiments.

Contribution

It develops a novel parametrization respecting theoretical bounds and uses dispersion relations to accurately fit and predict scattering data at high energies.

Findings

Good statistical fit to existing data

Predictions for RHIC, LHC, and future colliders

Accurate estimation of the $ ho$ parameter

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.