Optical theorem, crossing property, and derivative dispersion relations: implications on the asymptotic behavior of and

Abstract

In this paper, we present some results on the behavior of the total cross section and ρ-parameter at asymptotic energies in proton–proton ( ) and antiproton–proton ( ) collisions. Hence, we consider three of the main theoretical results in high energy physics: the crossing property, derivative dispersion relation, and optical theorem. The use of such machinery facilitates the derivation of analytic formulas for a wide set of the measured global scattering parameters and some important relations between them. The suggested parameterizations approximate the energy dependence for the total cross section and ρ-parameter for and with a statistically acceptable quality in the multi-TeV region. Additionally, the qualitative description is obtained for important interrelations, namely difference, sum, and ratio of the antiparticle–particle and particle–particle total cross sections. Despite the reduced number of experimental data for the total cross section and ρ-parameter at the TeV-scale, which complicates any prediction for the beginning of the asymptotic domain, the fitting procedures indicates that asymptotia occur in the energy range 25.5–130 TeV. Moreover, in the asymptotic regime, we obtain . A detailed quantitative study of the energy behavior of the measured scattering parameters and their combinations in the ultra–high energy domain indicates that the scenario with the generalized formulation of the Pomeranchuk theorem is more favorable with respect to the original formulation of this theorem.