Neutrino masses from SUSY breaking in radiative seesaw models

Abstract

Radiatively generated neutrino masses ($m_{\nu }$) are proportional to supersymmetry (SUSY) breaking, as a result of the SUSY non-renormalisation theorem. In this work, we investigate the space of SUSY radiative seesaw models with regard to their dependence on SUSY breaking ($\require{cancel}\cancel{\text{SUSY}}$). In addition to contributions from sources of $\cancel{\text{SUSY}}$ that are involved in electroweak symmetry breaking (${\cancel{\text{SUSY}}}_{\text{EWSB}}$ contributions), and which are manifest from $⟨F_H^{†}⟩=\mu ⟨\bar{H}⟩\ne 0$ and $⟨D⟩=g{\sum }_H⟨H^{†}{\otimes }_{H}H⟩\ne 0$, radiatively generated $m_{\nu }$ can also receive contributions from $\cancel{\text{SUSY}}$ sources that are unrelated to EWSB (${\cancel{\text{SUSY}}}_{\text{EWS}}$ contributions). We point out that recent literature overlooks pure-${\cancel{\text{SUSY}}}_{\text{EWSB}}$ contributions ($\propto \mu /M$) that can arise at the same order of perturbation theory as the leading order contribution from ${\cancel{\text{SUSY}}}_{\text{EWS}}$. We show that there exist realistic radiative seesaw models in which the leading order contribution to $m_{\nu }$ is proportional to ${\cancel{\text{SUSY}}}_{\text{EWS}}$. To our knowledge no model with such a feature exists in the literature. We give a complete description of the simplest model-topologies and their leading dependence on $\cancel{\text{SUSY}}$. We show that in one-loop realisations $LLHH$ operators are suppressed by at least $\mu m_{\text{soft}}/M^3$ or $m_{\text{soft}}^2/M^3$. We construct a model example based on a one-loop type-II seesaw. An interesting aspect of these models lies in the fact that the scale of soft-$\cancel{\text{SUSY}}$ effects generating the leading order $m_{\nu }$ can be quite small without conflicting with lower limits on the mass of new particles.

arXiv commentAccepted for publication in European Physical Journal C; 23 pages + appendices; references updated; minor revisions; extended conclusions

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