Manifestations of Extra Dimensions in a Neutrino Telescope

Theories with large extra dimensions provide the possibility that a flavor neutrino, localized in a 3+1 brane, can mix with a singlet neutrino living in the bulk. This mixing leads to unconventional patterns of neutrino matter oscillations and we examine in details how these oscillations depend upon two parameters: the brane-bulk coupling $\xi$ and the effective mass $\mu$ of the flavor neutrino inside matter. We find that high energy $(E \ge 50$ GeV) $\nu_\mu$ neutrinos, to be detected by neutrino telescopes, can give signals of extra dimensions. With a 1 k$m^{3}$ neutrino telescope extra dimensions with radius down to $1\mu m$ can be tested directly, while for smaller radius an indirect evidence can be established.