Lower Energy Consequences of an Anomalous High-Energy Neutrino Cross-Section

A new strong-interaction has been postulated for neutrinos above ~10^{19} eV to explain the production of highest-energy cosmic ray events. We derive a dispersion relation relating the hypothesized high-energy cross-section to the lower-energy neutrino-nucleon elastic amplitude. Remarkably, we find that the real forward amplitude becomes anomalous seven orders of magnitude lower in energy than does the total cross-section. We discuss possible measurable consequences of this early onset of new neutrino physics, and conclude that a significantly enhanced elastic \nu-N scattering rate may occur for the neutrino beams available at Fermilab and CERN.