Abstract
We discuss the unitarity motivated relations among the elastic cross-section, slope parameter and inelastic cross-section of the high energy pp interaction. In particular, the MacDowell-Martin unitarity bound is written down in another form to make a relation between the elastic and inelastic quantities more transparent. On the basis of an unitarity motivated relation we argue that the growth with energy of the elastic to total cross-section ratio is a consequence of the increasing with energy of the inelastic interaction intensity. The latter circumstance is an underlying reason for the acceleration of the slope parameter growth, for the slowing of the growth of the elastic to total cross-section ratio and for other interesting phenomena, which are observed in the TeV energy range. All of this confirms the old idea that the elastic scattering is a shadow of the particle production processes.
Highlights
A growth with energy of the pp total cross-section σtot(s) = σel(s)+σinel(s) is due to that of the elastic σel(s) and the inelastic σinel(s) cross-sections [1,2,3,4,5,6,7]
The unitarity condition relates the properties of the elastic scattering amplitude with the contribution from the inelastic channels and the elastic scattering can be considered as a shadow of the particle production processes [9]
It is well known that due to the unitarity condition the properties of the elastic scattering amplitude are related with that of a sum of the inelastic channels and the elastic scattering can be considered as a shadow of the particle production processes
Summary
As can be seen from the experimental data [1,2,3,4,5,6,7], the ratio σinel(s)/B(s) is an increasing function of energy It means that the inelastic cross-section grows due to the growth of the radius of the interaction region and due to the increasing of the inelastic interaction intensity in the expanding with energy central part of the interaction region [18,19,20,21,22,23,24]. The unitarity motivated Eq (4) enables to consider all these phenomena, as well as the σel/σtot growth itself, as a consequence of the increasing of the intensity of the inelastic interaction (σinel/B).
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