Scaling laws for the elastic scattering amplitude

TL;DR

This paper derives and solves a PDE for the imaginary part of the elastic scattering amplitude, demonstrating its asymptotic scaling behavior and exploring modifications in preasymptotic regions, contributing to understanding scattering at high energies.

Contribution

It introduces a PDE approach to analyze the elastic scattering amplitude and proves its geometrical scaling in the asymptotic limit, extending the understanding of scattering behavior.

Findings

Asymptotic scaling behavior matches geometrical scaling.

Derived PDE for the imaginary part of the amplitude.

Explored modifications of scaling laws in preasymptotic regions.

Abstract

The partial differential equation for the imaginary part of the elastic scattering amplitude is derived. It is solved in the black disk limit. The asymptotical scaling behavior of the amplitude coinciding with the geometrical scaling is proved. Its extension to preasymptotical region and modifications of scaling laws for the differential cross section are considered.