On the origin of neutrino masses

We discuss the simplest mechanisms for generating neutrino masses at tree level and one loop level. We find a significant number of new possibilities where one can generate neutrino masses at the one-loop level by adding only two new types of representations. These models have renormalizable interactions that automatically conserve baryon number. Adding to the minimal standard model a scalar color octet with SU(3)⨂SU(2)⨂U(1) quantum numbers, $(8,2,1/2)$, and a fermionic color octet in the fundamental or adjoint representation of $SU(2)$, one can generate neutrino masses in agreement with experiment. Signals at the LHC and constraints from flavor violation are briefly discussed.