Ultrahigh energy neutrino interactions and weak-scale string theories

It has been suggested that ultrahigh energy neutrinos can acquire cross sections approaching hadronic size if the string scale is as low as 1–10 TeV. In this case, the vertical air showers observed with energies above the Greisen-Zatsepin-Kuzmin cutoff at $E\approx 6\times {10}^{19}\mathrm{eV}$ could be initiated by neutrinos which are the only known primaries able to travel long distances unimpeded. We have calculated the neutrino-nucleon cross section ${\sigma }_{N\nu }^{\mathrm{KK}}$ due to the exchange of Kaluza-Klein excitations of the graviton in a field theoretical framework. We have found that ${\sigma }_{N\nu }^{\mathrm{KK}}$ and the transferred energy per interaction are too small to explain vertical showers even in the most optimistic scenario.