Seesaw induced electroweak scale, the hierarchy problemand sub-eV neutrino masses

We describe a model for the scalar sector where all interactions occur either at an ultra-high scale, ΛU~1016-1019 GeV, or at an intermediate scale, ΛI = 109-1011 GeV. The interaction of physics on these two scales results in an SU(2) Higgs condensate at the electroweak (EW) scale, ΛEW, through a seesaw-like Higgs mechanism, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Lambda_{\mathrm{{EW}}} \sim \Lambda_{\mathrm{I}}^2/\Lambda_{\mathrm{U}}$\end{document}, while the breaking of the SM SU(2) x U(1) gauge symmetry occurs at the intermediate scale ΛI . The EW scale is, therefore, not fundamental but is naturally generated in terms of ultra-high energy phenomena and so the hierarchy problem is alleviated. We show that the class of such "seesaw Higgs" models predict the existence of sub-eV neutrino masses which are generated through a "two-step" seesaw mechanism in terms of the same two ultra-high scales: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$m_\nu \sim \Lambda_{\mathrm{I}}^4/\Lambda_{\mathrm{U}}^3 \sim \Lambda_{\mathrm{{EW}}}^2/\Lambda_{\mathrm{U}} $\end{document}. The neutrinos can be either Dirac or Majorana, depending on the structure of the scalar potential. We also show that our seesaw Higgs model can be naturally embedded in theories with tiny extra dimensions of size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R \sim \Lambda_{\mathrm{U}}^{-1} \sim 10^{-16}$\end{document} fm, where the seesaw induced EW scale arises from a violation of a symmetry at a distant brane; in particular, in the scenario presented there are seven tiny extra dimensions.