  In theories which require a space of dimension d>4, there is a natural
mechanism of suppressing neutrino masses: while Standard Model fields are
confined to a 3-brane, right handed neutrinos live in the bulk. Due to
Kaluza-Klein excitations, the effective magnetic moments of neutrinos are
enhanced. The effective magnetic moment is a monotonically growing function of
the energy of the neutrino: consequently, high energy neutrinos can emit
observable amounts of magnetic Cherenkov radiation. By observing the energy
dependence of the magnetic Cherenkov radiation, one may be able to determine
the number of compactified dimensions.
