  Recent theoretical developments have shown that extra spacetime dimensions
can lower the fundamental GUT, Planck, and string scales. However, recent
evidence for neutrino oscillations suggests the existence of light non-zero
neutrino masses, which in turn suggests the need for a heavy mass scale via the
seesaw mechanism. In this paper, we make several observations in this regard.
First, we point out that allowing the right-handed neutrino to experience extra
spacetime dimensions naturally permits the left-handed neutrino mass to be
power-law suppressed relative to the masses of the other fermions. This occurs
due to the power-law running of the neutrino Yukawa couplings, and therefore
does not require a heavy scale for the right-handed neutrino. Second, we show
that a higher-dimensional analogue of the seesaw mechanism may also be capable
of generating naturally light neutrino masses without the introduction of a
heavy mass scale. Third, we show that such a higher-dimensional seesaw
mechanism may even be able to explain neutrino oscillations without neutrino
masses, with oscillations induced indirectly via the masses of the Kaluza-Klein
states. Fourth, we point out that even when higher-dimensional right-handed
neutrinos are given a bare Majorana mass, the higher-dimensional seesaw
mechanism surprisingly replaces this mass scale with the radius scale of the
extra dimensions. Finally, we also discuss a possible new mechanism for
inducing lepton-number violation by shifting the positions of D-branes in Type
I string theory.
