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.

22 pages, 7 figures and 11 tables. We corrected some formulas and results of the fitting procedure. This work present intermediate steps and results that are not shown in the published version

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Cited by in corpus (8)

• Elastic scattering of hadrons
• Energy dependence of slope parameter in elastic nucleon-nucleon scattering
• Analysis of $pp$ and $\bar{p}p$ Elastic Scattering Based on Theoretical Bounds in High-Energy Physics: an Update
• Odderon and Pomeron as Fractal Dimension in $pp$ and $\bar{p}p$ Total Cross Sections
• Interplay of total cross sections and ratios of real to imaginary parts of hadron amplitudes
• The energy dependence of the ratio of elastic to total cross section in $pp$ and $\bar{p}p$ collisions
• Optical Theorem, Crossing Property and Derivative Dispersion Relations: Implications on the Asymptotic Behavior of ${\sigma }_{tot}(s)$ and $\rho (s)$
• Soft Pomeron in light of the LHC correlated data