No-go limitations on UV completions of the neutrino option

We discuss the possible origin of the Majorana mass scale(s) required for the “neutrino option” where the electroweak scale is generated simultaneously with light neutrino masses in a type-I seesaw model by common dimension four interactions. We establish no-go constraints on the perturbative generation of the Majorana masses required due to global symmetries of the seesaw Lagrangian.

Figure 1

One-loop threshold corrections generating the EW scale in the neutrino option. The one loop diagram is linked to neutrino mass generation by connecting the lepton line.

Figure 2

$\mathrm{\Delta }L=2$ two-loop diagram that allows a perturbative generation of a Majorana mass term $M_{pr}$.

Figure 3

A sample one-loop diagram that can radiatively generate a new nonzero Majorana neutrino mass, starting from a unique nonvanishing eigenvalue $M_{33}$. The state $\chi$ is an unspecified boson whose properties can be partially derived, see the main text.