Three Loop Neutrino Model with Isolated $k^{\pm\pm}$

Abstract

We propose a three loop radiative neutrino mass scenario with an isolated doubly charged singlet scalar $k^{\pm\pm}$ without couplings to the charged leptons, while two other singly charged scalars $h_1^\pm$ and $h_2^\pm$ attach to them. In this setup, the lepton flavor violation originating from $k^{\pm\pm}$ exchanges is suppressed and the model is less constrained, where some couplings can take sizable values. As reported in our previous work, the loop suppression factor at the three loop level would be too strong and realized neutrino masses in a three loop scenario could be smaller than the observed minuscule values. The sizable couplings can help us to enhance neutrino masses without drastically large scalar trilinear couplings appearing in a neutrino mass matrix, which tends to drive the vacuum stability to become jeopardized at the one loop level. Now the doubly charged scalar $k^{\pm\pm}$ has less constraint via lepton flavor violation and the vacuum can be quite stable, and thus a few hundred GeV mass in $k^{\pm\pm}$ is possible, which is within the LHC reach and this model can be tested in the near future. Note that the other $h_1^\pm$ and $h_2^\pm$ should be heavy at least around a few TeV. We suitably arrange the charges of an additional global $U(1)$ symmetry, where the decay constant of the associated Nambu-Goldstone boson can be around a TeV scale consistently. Also, this model is indirectly limited through a global analysis on results of the LHC Higgs search and issues on a dark matter candidate, the lightest Majorana neutrino. After $h_1^\pm$ and $h_2^\pm$ are decoupled, this particle couples to the standard model particles only through two charge parity even scalars in theory and thus information on this scalar sector is important. Consistent solutions are found, but a part of them is now on the edge.