  In a previous work a novel parametrization was proposed for the $pp$ and
$\bar{p}p$ total cross section. Here, results are presented for 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 observables with robust
values of fit parameters. Based on the fit results the estimations are derived
for the total cross section and the $\rho$ parameter in elastic $pp$ scattering
at various $\sqrt{s}$ up to energy frontier $\sqrt{s}=10$ PeV which can be
useful for present and future hadron colliders as well as for cosmic ray
measurements at ultra-high energies.
