Proton–proton cross-sections: The interplay between density and radius

We argue that there are two mechanisms responsible for the growth of high energy cross-sections – σtotσtot and σelσel, say – in pp collisions. One is by the increase of matter density, resulting in the black disk saturation. The other is exclusively by radial expansion affecting the periphery of the overlap area. Within this simple model we can reproduce all available data in pp from ISR to LHC. In order to achieve a fast growth in the very high energy cosmic ray energies, we propose a fast black disk saturation followed by the dominance of geometric scaling (GS).

► Available data on proton–proton cross-sections are fitted with a grey disk model. ► The cross-sections are interpreted in terms of a density and an effective radius. ► σel/σtotσel/σtot data shows a change of behavior at s∼160 GeV. ► This model can explain the Auger data in terms of a rapid cross-section increase. ► The transition into a black disk (100 TeV) does not violates the Froissart bound.