We show that the onset and rise of QCD mini-jets provide the dynamical mechanism behind the appearance of a soft edge in pp collisions around ISR energies and thus such a soft edge is built in our mini-jet model with soft gluon resummation. Here the
model is optimized for LHC at $sqrt{s} = 7, 8 TeV$ and predictions made for higher LHC and cosmic ray energies. Further, we provide a phenomenological picture to discuss the breakup of the total cross-section into its elastic, uncorrelated and correlated inelastic pieces in the framework of a one-channel eikonal function.
We present a model-independent analysis of the experimental data on the ratio $X$ between the elastic and total cross-sections from $pp$ and $bar{p}p$ scattering in the c.m. energy interval 5 GeV - 8 TeV. Using a novel empirical parametrization for t
hat ratio as a function of the energy and based on theoretical and empirical arguments, we investigate three distinct asymptotic scenarios: either the black-disk (BD) limit or scenarios above and below that limit. Our analysis favors a scenario below the BD, with asymptotic ratio $X = 0.36 pm 0.08$.
For the p-air production cross-section, we use a Glauber formalism which inputs the pp inelastic cross-section from a mini-jet model embedded in a single-channel eikonal expression, which provides the needed contribution of uncorrelated processes. It
is then shown that current LO parton density functions for the pp mini-jet cross-sections, with a rise tempered by collinearity induced by soft gluon re-summation, are well suited to reproduce recent cosmic ray results. By comparing results for GRV, MRST72 and MSTW parametrizations, we estimate the uncertainty related to the low-x behavior of these densities.
We present the result of an empirical model for elastic $pp$ scattering at LHC which indicates that the asymptotic black disk limit ${cal R}=sigel/sigtotrightarrow1/2$ is not yet reached and discuss the implications on classical geometrical scaling b
ehavior. We propose a geometrical scaling law for the position of the dip in elastic $pp$ scattering which allows to make predictions valid both for intermediate and asymptotic energies.
We discuss whether the behaviour of some hadronic quantities, such as the total cross-section, the ratio of the elastic to the total cross-section, are presently exhibiting the asymptotic behaviour expected at very large energies. We find phenomenolo
gical evidence that at LHC7 there is still space for further evolution.
Using a novel representation for the Martins real-part formula without the full scaling property, an almost model-independent description of the proton-proton differential cross section data at high energies (19.4 GeV - 62.5 GeV) is obtained. In the
impact parameter and eikonal frameworks, the extracted inelastic overlap function presents a peripheral effect (tail) above 2 fm and the extracted opacity function is characterized by a zero (change of sign) in the momentum transfer space, confirming results from previous model-independent analyses. Analytical parametrization for these empirical results are introduced and discussed. The importance of investigations on the inverse problems in high-energy elastic hadron scattering is stressed and the relevance of the proposed representation is commented. A short critical review on the use of Martins formula is also presented.
