Implications of a massless neutralino for neutrino physics

We consider the phenomenological implications of a soft supersymmetry (SUSY) breaking term $\tilde{B}N$ at the TeV scale [here $\tilde{B}$ is the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_Y$ gaugino and N is the right-handed neutrino field]. In models with a massless (or nearly massless) neutralino, such a term will give rise through the seesaw mechanism to new contributions to the mass matrix of the light neutrinos. We treat the massless neutralino as an (almost) sterile neutrino and find that its mass depends on the square of the soft SUSY breaking scale, with interesting consequences for neutrino physics. We also show that, although it requires finetuning, a massless neutralino in the minimal supersymmetric standard model or next-to-minimal supersymmetric standard model is not experimentally excluded. The implications of this scenario for neutrino physics are discussed.