Weak-scale string theories and ultrahigh energy neutrino interactions

We discuss if ultrahigh energy (UHE) neutrinos can be responsible for the observed vertical extensive air showers with energy ∼ 1020 eV. After briefly reviewing the proposal that the decay products from UHE neutrinos annihilations on relic neutrinos are the observed UHE primaries, we concentrate on the suggestion that UHE neutrinos can acquire cross-sections approaching hadronic size if the string scale is as low as ∼ 10 TeV. In this case, the vertical air showers observed with energies above the Greisen-Zatsepin-Kuzmin cutoff at E ∼ 6 · 1019 eV could be initiated directly by neutrinos which are the only known primaries able to travel long distances unimpeded. We review the calculation of the neutrino-nucleon cross-section σKKNν due to the exchange of Kaluza-Klein excitations of the graviton in a field theoretical framework and discuss the issue of unitarity. We find that σKKNν and the transferred energy per interaction are too small to explain vertical showers even in the most optimistic scenario