Comment on "More on Heisenberg's model for high energy nucleon-nucleon scattering"

TL;DR

This paper critiques a recent Heisenberg model extension, showing that its predicted ratio of elastic to total cross sections at high energies is inconsistent with experimental data, emphasizing the correct black-disk limit of 1/2.

Contribution

It clarifies the discrepancy between the model's predicted cross section ratios and experimental results, correcting the interpretation of asymptotic scattering behavior.

Findings

The model's total cross section does not match experimental measurements.

The predicted ratio of elastic to total cross sections is too small by a factor of 2.

Experimental data supports the black-disk limit ratio of 1/2.

Abstract

We comment on the treatment of asymptotic black-disk scattering in a recent paper of Nastase and Sonnenschein, Phys.\ Rev.\ D\ {\bf 92}, 015028 (2015), on scattering in an updated version of the Heisenberg model which gives $pp$ and $\bar{p}p$ cross sections which increase at very high energies as $\ln^2s$. We show that the total cross section they define does not correspond to that measured in experiments, with the result that their limit for the ratio $\sigma_{\rm elas}/\sigma_{\rm tot}$ is too small by a factor 2. The correct ratio for black-disk scattering, $\sigma_{\rm elas}/\sigma_{\rm tot} \rightarrow 1/2$ for $s\rightarrow\infty$, is strongly supported by experiment.