Comment on "Ultrahigh-Energy Neutrino-Nucleon Deep-Inelastic Scattering and the Froissart Bound": Phys. Rev. Lett. 106, 231802 (2011)

Abstract

The authors of a recent paper, "Ultrahigh-Energy Neutrino-Nucleon Deep-Inelastic Scattering and the Froissart Bound", A. Illarianov, B. Kniehl and A. Kotikov, Phys. Rev. Lett. 106, 231802 (2011), derive an approximate formula for the UHE limit of $\sigma_{\nu N}(s)$ in a class of models that includes our own and assert that they are led "to the important observation that $\sigma_{BBT}^{\nu N} \propto ln^3s$, which manifestly violates the Froissart bound [2] in contrast to what is stated in Refs. [6-8]", the latter reference being to our work and the $\sigma_{BBT}^{\nu N}$ to the cross sections we reported there. We here correct their erroneous implication that $\sigma_{\nu N}(s) should satisfy the Froissart bound and their mistaken assertion that we state that $\sigma_{BBT}^{\nu N}$ satisfies it.