Soft edge of hadron scattering and mini-jet models for the total and inelastic pp cross-sections at LHC and beyond

TL;DR

This paper presents a mini-jet model with soft gluon resummation to explain the soft edge in proton-proton collisions, providing predictions for LHC and cosmic ray energies and analyzing the breakdown of total cross-sections.

Contribution

It introduces a mini-jet model with soft gluon resummation that naturally explains the soft edge phenomenon in pp collisions and offers detailed predictions for high-energy regimes.

Findings

Soft edge arises from mini-jet dynamics and soft gluon effects.

Model successfully fits existing LHC data at 7 and 8 TeV.

Predictions extend to higher LHC and cosmic ray energies.

Abstract

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.