What do experimental data "say" about growth of hadronic total cross-section?

Abstract

We reanalyse $\bar p p$ and $pp$ high energy data of the elastic scattering above $\sqrt{s}=5$ GeV on the total cross-section $σ_{tot}$ and on the forward $ρ$-ratio for various models of Pomeron, utilizing two methods. The first one is based on analytic amplitudes, the other one relies on assumptions for $σ_{tot}$ and on dispersion relation for $ρ$. We argue that it is not possible, from fitting only existing data for forward scattering, to select a definite asymptotic growth with the energy of $σ_{tot}$. We find equivalent fits to the data together with a logarithmic Pomeron giving a behavior $σ_{tot} \propto \ln ^γs$, $γ\in [0.5,2.20]$ and with a supercritical Pomeron giving a behavior $σ_{tot} \propto s^ε$, $ε\in [0.01,0.10]$.