The black disk and the dip in the differential elastic cross section at asymptotic energy

TL;DR

This paper investigates the approach to the black disk limit in elastic scattering by analyzing the evolution of the dip in the differential cross section at asymptotic energies, focusing on the scaling variable involving total cross section and dip position.

Contribution

It introduces a method to test the black disk limit by studying the evolution of the dip in the differential elastic cross section using a specific scaling variable.

Findings

The scaling variable $ au$ approaches the black disk value at high energies.

The study supports the validity of the black disk limit in elastic scattering.

The evolution of the dip provides insights into asymptotic scattering behavior.

Abstract

We test the validity of the black disk limit in elastic scattering by studying the evolution of the dip in the scaling variable $\tau=-t_{D}\sigma^{tot}$, where $t_{D}$ is the transverse momentum squared at the dip and $\sigma_{tot}$ the total cross section. As $s\rightarrow \infty $ and $-t_{D} \rightarrow 0 $, $\tau$ may consistently be approaching the black disc value, $\tau \xrightarrow[ \sqrt{s}\rightarrow \infty ]{} \tau_{BD}=35.92$ GeV$^{2}$ mb.