Neutrino masses from large extra dimensions

Recently it was proposed that the standard model (SM) degrees of freedom reside on a (3+1)-dimensional wall or “3-brane” embedded in a higher-dimensional spacetime. Furthermore, in this picture it is possible for the fundamental Planck mass $M_{*}$ to be as small as the weak scale $M_{*}\simeq O\left(\mathrm{TeV}\right)$ and the observed weakness of gravity at long distances is due the existence of new submillimeter spatial dimensions. We show that in this picture it is natural to expect neutrino masses to occur in the ${10}^{-1}–{10}^{-4}\hspace{0.5em}\mathrm{eV}$ range, despite the lack of any fundamental scale higher than $M_{*}.$ Such suppressed neutrino masses are not the result of a seesaw, but have intrinsically higher-dimensional explanations. We explore two possibilities. The first mechanism identifies any massless bulk fermions as right-handed neutrinos. These give naturally small Dirac masses for the same reason that gravity is weak at long distances in this framework. The second mechanism takes advantage of the large infrared desert: the space in the extra dimensions. Here, small Majorana neutrino masses are generated by a breaking lepton number on distant branes.