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.
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 consider the production at the LHC of exotic composite leptons of charge Q=+2e. Such states are allowed in composite models which contain extended isospin multiplets (Iw=1 and Iw=3/2). These doubly charged leptons couple with Standard Model [SM] f
ermions via gauge interactions, thereby delineating and restricting their possible decay channels. We discuss the production cross section at the LHC of L++ (p p --> L++, l-) and concentrate on the leptonic signature deriving from the cascade decays L++ --> W+, l+ --> l+, l+, u_l i.e. p p --> l-, l+, l+, u_l showing that the invariant mass distribution of the like-sign dilepton has a sharp end point corresponding to excited lepton mass m*. We find that the sqrt{s}=7 TeV run is sensitive at the 3-sigma (5-sigma) level to a mass of the order of 600 GeV if L=10 fb^-1 (L=20 fb^-1). The sqrt{s}=14 TeV run can reach a sensitivity at 3-sigma (5-sigma) level up to m*=1 TeV for L=20 fb^-1 (L=60 fb^-1).
