Neutrino masses from SUSY breaking in radiative seesaw models

Radiatively generated neutrino masses (mν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\nu $$\end{document}) 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 ([inline-graphic not available: see fulltext]). In addition to contributions from sources of [inline-graphic not available: see fulltext] that are involved in electroweak symmetry breaking ([inline-graphic not available: see fulltext] contributions), and which are manifest from ⟨FH†⟩=μ⟨H¯⟩≠0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle F^\dagger _H \rangle = \mu \langle \bar{H} \rangle \ne 0$$\end{document} and ⟨D⟩=g∑H⟨H†⊗HH⟩≠0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle D \rangle = g \sum _H \langle H^\dagger \otimes _H H \rangle \ne 0$$\end{document}, radiatively generated mν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\nu $$\end{document} can also receive contributions from [inline-graphic not available: see fulltext] sources that are unrelated to EWSB ([inline-graphic not available: see fulltext] contributions). We point out that recent literature overlooks pure-[inline-graphic not available: see fulltext] contributions (∝μ/M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\propto \mu / M$$\end{document}) that can arise at the same order of perturbation theory as the leading order contribution from [inline-graphic not available: see fulltext]. We show that there exist realistic radiative seesaw models in which the leading order contribution to mν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\nu $$\end{document} is proportional to [inline-graphic not available: see fulltext]. 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 [inline-graphic not available: see fulltext]. We show that in one-loop realisations LLHH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L L H H$$\end{document} operators are suppressed by at least μmsoft/M3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \, {m_\text {soft}}/ M^3$$\end{document} or msoft2/M3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{\mathrm{soft}}^2/M^3$$\end{document}. 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-[inline-graphic not available: see fulltext] effects generating the leading order mν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\nu $$\end{document} can be quite small without conflicting with lower limits on the mass of new particles.