Correlations among elastic and inelastic cross-sections and slope parameter

TL;DR

This paper explores the relationships between elastic and inelastic cross-sections and the slope parameter in high-energy proton-proton interactions, highlighting how unitarity constraints explain observed energy-dependent behaviors.

Contribution

It reformulates the MacDowell-Martin unitarity bound to clarify the connection between elastic and inelastic quantities and links the growth of the elastic-to-total cross-section ratio to inelastic interaction dynamics.

Findings

Elastic to total cross-section ratio increases with energy.

Growth in inelastic interaction intensity explains slope parameter acceleration.

Elastic scattering acts as a shadow of particle production processes.

Abstract

We discuss the unitarity motivated relations among the elastic cross-section, slope parameter and inelastic cross-section of the high energy \textit{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 \textit{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.