The approach of p [formula omitted] and pp elastic scattering to “asymptopia”

Abstract

We have previously made a model-free analysis of the t = 0 amplitude for p p and pp elastic scattering using data in the energy region 5<√ s<62 GeV. We use our high-energy values of σ tot and ϱ to fix the energy dependence of the Chou-Yang model of elastic scattering and compute the differential elastic scattering cross sections, d σ n /d t, at large − t. In this note, we show that this model, which is dominated at low energies by the matter distribution of the p p (pp) system, goes over at SSC energy, 40 TeV, essentially into a structureless black disk. The curvature parameter, C = ( 1 2 ) d 2[ log( dσ n/ dt]/ dt 2 at t=0 , is a sensitive indicator of this transition to “asymptopia”, being positive at ISR energies, going through zero near √ s=2 TeV (the tevatron collider), and becoming very negative at √ s=40 TezV (the SSC), where the predictions for the Chou-Yang model are hardly distinguishable from those for a sharp disk, after the diffraction minima have been filled in by the contribution of the real part.