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Energy dependence of cross sections in proton-proton and antiproton-proton collisions

V. A. Okorokov

Abstract

Energy dependence of global scattering parameters, mostly of total cross section, is studied for proton-proton and antiproton-proton collisions. Results are presented for physical analysis updated with taken into account the recent data from accelerator experiments as well as from cosmic ray measurements. The analytic parameterizations suggested within Axiomatic Quantum Field Theory (AQFT) provide the quantitative description of energy dependence of global scattering parameters for rather wide energy range. Detailed scan on low boundary of the fitting range for energy dependence of global scattering parameters allows the observation of the onsets for regions in which Pomeranchuk theorem and / or Froissart-Martin one is valid. It is obtained that global scattering parameters show the behavior corresponded to any formulations of Pomeranchuk theorem and closed to (modified) Froissart-Martin limit in functional sense in multi-TeV energy region. Bosonic condensation is considered as one of the possible dynamical mechanisms which would be provide the total cross section approaches to (modified) Froissart-Martin limit at quantitative level but not functionally only.

Energy dependence of cross sections in proton-proton and antiproton-proton collisions

Abstract

Energy dependence of global scattering parameters, mostly of total cross section, is studied for proton-proton and antiproton-proton collisions. Results are presented for physical analysis updated with taken into account the recent data from accelerator experiments as well as from cosmic ray measurements. The analytic parameterizations suggested within Axiomatic Quantum Field Theory (AQFT) provide the quantitative description of energy dependence of global scattering parameters for rather wide energy range. Detailed scan on low boundary of the fitting range for energy dependence of global scattering parameters allows the observation of the onsets for regions in which Pomeranchuk theorem and / or Froissart-Martin one is valid. It is obtained that global scattering parameters show the behavior corresponded to any formulations of Pomeranchuk theorem and closed to (modified) Froissart-Martin limit in functional sense in multi-TeV energy region. Bosonic condensation is considered as one of the possible dynamical mechanisms which would be provide the total cross section approaches to (modified) Froissart-Martin limit at quantitative level but not functionally only.
Paper Structure (5 sections, 5 equations, 2 figures, 4 tables)

This paper contains 5 sections, 5 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Asymptotic relations and AQFT model
  3. Experimental data and fit procedure
  4. Fit results and discussion
  5. Summary

Figures (2)

  • Figure 1: The energy dependence for $\sigma_{\scriptsize{\hbox{t}}}^{+}$ (a), $\sigma_{\scriptsize{\hbox{t}}}^{-}$ (b), $\rho^{+}$ (c), $\rho^{-}$ (d) and results of simultaneous fits of all four parameters by equations (\ref{['eq:2.4']}), (\ref{['eq:2.5']}). Solid points are from DB24 and these points are included in the fitted sample, open points are additional for DB24 and they are not included in the fitted data sample (detailed explanation -- see in text). The solid line corresponds to the fit at $\sqrt{s_{\scriptsize{\hbox{min}}}}=5$ GeV, the dashed line -- at $\sqrt{s_{\scriptsize{\hbox{min}}}}=30$ GeV and dotted line -- at $\sqrt{s_{\scriptsize{\hbox{min}}}}=1$ TeV.
  • Figure 2: Dependence on $\sqrt{s_{\scriptsize{\hbox{min}}}}$ for fit parameters $\alpha_{\pm}$ (a), $\beta_{\pm}$ (b) and $\gamma_{\pm}$ (c). Open points are for $pp$, solid ones -- for $\bar{p}p$. Dashed lines on (a, c) correspond to the asymptotic levels for $\alpha_{\pm}$ and $\gamma_{\pm}$. The points for $\bar{p}p$ are shifted on right for more comfortable and clear view.