Counting extra dimensions: magnetic Cherenkov radiation from high energy neutrinos

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 three-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.