Black disk radius constrained by unitarity

Abstract

We argue that if the elastic proton-proton cross section increases with energy, the Froissart-like high energy behaviour of the elastic amplitude (which corresponds to a `black disk' of radius $R(s)=c\ln s-\beta \ln (\ln s)$) is the only possibility to satisfy the unitarity equation at each value of the impact parameter, $b$. Otherwise the cross section of events with Large Rapidity Gaps grows faster than the total cross section at the same $b$. That is, these `gap' events require {\it maximal} growth of the high-energy (asymptotic) cross section and of the interaction radius $R(s)$ in order to be consistent with unitarity.

9 pages, 3 figures. text added, arXiv admin note: substantial text overlap with arXiv:1801.07065

References in corpus (4)

• Black disk, maximal Odderon and unitarity
• Evidence for a Constant `Edge' in Proton-Proton Scattering at Very High Energies
• Correlations among elastic and inelastic cross-sections and slope parameter
• The Energy-Dependent Black-Disk Fraction in Proton-Proton Scattering

Cited by in corpus (3)

• Gravitational Regge bounds
• Multigap diffraction cross sections. Problems in eikonal methods for the pomeron unitarization
• Soft Pomeron in light of the LHC correlated data