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

TL;DR

This paper critiques a recent claim that certain ultrahigh-energy neutrino-nucleon cross sections violate the Froissart bound, clarifying that the original authors misinterpreted the bounds and our results are consistent with it.

Contribution

The authors correct misconceptions in a recent paper regarding the Froissart bound and ultrahigh-energy neutrino cross sections, reaffirming their compliance with theoretical limits.

Findings

Clarification that the Froissart bound is not violated by the reported cross sections

Correction of the misinterpretation of previous work's compliance with the Froissart bound

Reaffirmation of the theoretical consistency of the cross section models

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.