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.
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.
An empirical model for the $pp$ elastic differential cross section is proposed. Inspired by early work by Barger and Phillips, we parametrize the scattering amplitude in building blocks, comprising of two exponentials with a relative phase, supplemen
ting the dominant term at small $-t$ with the proton form factor. This model suitably applies to LHC7 and ISR data, enabling to make simple predictions for higher LHC energies and to check whether asymptotia might be achieved.
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.
We discuss the infrared limit for soft gluon kt-resummation and relate it to physical observables such as the intrinsic transverse momentum and the high energy limit of total cross-sections.
We study soft gluon kt-resummation and the relevance of zero momentum gluons for the energy dependence of total hadronic cross-sections. We discuss a model in which consistency of the energy dependence of the cross-section with the limitation of the
Froissart bound, is directly related to the behaviour of the strong coupling constant in the infrared region. Our predictions for the asymptotic behaviour are shown to be related to the ansatz that the infrared behaviour of the QCD strong coupling constant follows an inverse power law.
We present the predictions of a model for proton-proton total cross-section at LHC. It takes into account both hard partonic processes and soft gluon emission effects to describe the proper high energy behavior and to respect the Froissart bound.
In this paper we apply to photoproduction total cross-section a model we have proposed for purely hadronic processes and which is based on QCD mini-jets and soft gluon re-summation. We compare the predictions of our model with the HERA data as well a
s with other models. For cosmic rays, our model predicts substantially higher cross-sections at TeV energies than models based on factorization but lower than models based on mini-jets alone, without soft gluons. We discuss the origin of this difference.
