Eikonal contributions to ultra high energy neutrino-nucleon cross sections in low scale gravity models

We calculate low scale gravity effects on the cross section for neutrino-nucleon scattering at center of mass energies up to the Greisen-Zatsepin-Kuzmin (GZK) scale, in the eikonal approximation. We compare the cases of an infinitely thin brane embedded in n=5 compactified extra-dimensions, and of a brane with a physical tension M_{S}=1 TeV and M_{S}=10 TeV. The extra dimensional Planck scale M_{D} is set at 10^{3} GeV and 2\times10^{3} GeV. We also compare our calculations with neutral current standard model calculations in the same energy range, and compare the thin brane eikonal cross section to its saddle point approximation. New physics effects enhance the cross section by orders of magnitude on average. They are quite sensitive to M_{S} and M_{D} choices, though much less sensitive to n.