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 $SU(3{)}_C\otimes SU(3{)}_L\otimes U(1{)}_X$ (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.

Figure 1

Running of the gauge couplings in the SM (dashed lines) and in the model in Ref. [16] (solid lines). Here the $M_{331}$ scale is set to 1 TeV.

Figure 2

Gauge coupling unification in the $SU(3{)}_C\otimes SU(3{)}_L\otimes U(1{)}_X$ model with three fermion octets with a 3 TeV mass.

Figure 3

Values of the gauge coupling constants near unification, assuming that the 3-3-1 scale is 1 TeV. The thickness of the ${\alpha }_C$ line reflects the $1\sigma$ uncertainty in the measurement of the strong coupling constant at the $m_Z$ scale [3], while the octet mass affects the running of ${\alpha }_L$. One sees how unification prefers $M_8/M_{331}$ to lie roughly between 1 and 6.

Figure 4

Diagrams contributing to light neutrino mass.