Small neutrino masses and gauge coupling unification

The physics responsible for gauge coupling unification may also induce small neutrino masses. We propose a novel gauge mediated radiative seesaw mechanism for calculable neutrino masses. These arise from quantum corrections mediated by new $SU(3)_c \times SU(2)_L \times U(1)_X$ (3-3-1) gauge bosons and the physics driving gauge coupling unification. Gauge couplings unify for a 3-3-1 scale in the TeV range, making the model directly testable at the LHC.