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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 re-summation. Here the model is optimized for LHC at √ s = 7, 8 T eV 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.

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In this note, we summarize and compare various model predictions for pp total cross-section σ pp tot , giving an estimate of the range of predictions for the total crosssection, σ pp tot expected at the LHC. We concentrate on the results for σ pp tot obtained in a particular QCD based model of the energy dependence of the total cross-section, including the effect of soft gluon radiation. We obtain the range of predictions in this model by exploring the allowed range of model parameters. We further give a handy parametrisation of these results which incidentally spans the range of various other available predictions at the LHC as well.