Testing scaling laws for the elastic scattering of protons

TL;DR

This paper tests various proposed scaling laws for proton elastic scattering cross sections against experimental data, identifying conditions under which scaling holds or breaks down across different energy ranges.

Contribution

It evaluates multiple scaling variables for differential cross sections and explains deviations due to proton blackness increase with energy.

Findings

Scaling holds in the diffraction cone for certain variables.

Violations of scaling linked to increased proton blackness.

High-t region scaling violations discussed.

Abstract

Theoretical proposals of scaling laws for the differential elastic scattering cross sections of protons are confronted with experimental data over a wide energy range. Different combinations of the transferred momentum and energy resulting from the solution of the definite partial differential equation are attempted as scaling variables. Reasonable scaling of the differential cross sections in the diffraction cone has been shown for one of these variables. The violation of the geometrical scaling is ascribed to the increase of the proton blackness with energy. The origin of high-t region violations of scaling laws is discussed.