TeV gravity at neutrino telescopes

Cosmogenic neutrinos reach the Earth with energies around 10^9 GeV, and their interactions with matter will be measured in upcoming experiments (Auger, IceCube). Models with extra dimensions and the fundamental scale at the TeV could imply signals in these experiments. In particular, the production of microscopic black holes by cosmogenic neutrinos has been extensively studied in the literature. Here we make a complete analysis of gravity-mediated interactions at larger distances, where they can be calculated in the eikonal approximation. In these processes a neutrino of energy E_\nu interacts elastically with a parton inside a nucleon, loses a small fraction y of its energy, and starts a hadronic shower of energy y E_\nu << E_\nu. We analyze the ultraviolet dependence and the relevance of graviton emission in these processes, and show that they are negligible. We also study the energy distribution of cosmogenic events in AMANDA and IceCube and the possibility of multiple-bang events. For any neutrino flux, the observation of an enhanced rate of neutral current events above 100 TeV in neutrino telescopes could be explained by TeV-gravity interactions. The values of the fundamental scale of gravity that IceCube could reach are comparable to those to be explored at the LHC.