We consider right-handed neutrinos propagating in $δ$ (large) extra dimensions, whose only coupling to Standard Model fields is the Yukawa coupling to the left-handed neutrino and the Higgs boson. These theories are attractive as they can explain the smallness of the neutrino mass, as has already been shown. We show that if $δ$ is bigger than two, there are strong constraints on the radius of the extra dimensions, resulting from the experimental limit on the probability of an active state to mix into the large number of sterile Kaluza-Klein states of the bulk neutrino. We also calculate the bounds on the radius resulting from requiring that perturbative unitarity be valid in the theory, in an imagined Higgs-Higgs scattering channel.

24 pages, 4 figures, revtex4. v2: Minor typos corrected, references added