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

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.