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 ~10/sup 20/ e V. 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 approximately=10 TeV. In this case, the vertical air showers observed with energies above the Greisen-Zatsepin-Kuzmin cutoff at E approximately=6.10/sup 19/ 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 sigma /sub N nu //sup KK/ 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 sigma /sub N nu //sup KK/ and the transferred energy per interaction are too small to explain vertical showers even in the most optimistic scenario. (15 refs).