"Seesawing" away the hierarchy problem

We describe a model for the scalar sector where all interactions occur either at an ultra-high scale L_U ~ 10^16 - 10^19 GeV or at an intermediate scale L_I=10^9 - 10^11 GeV. The interaction of physics on these two scales results in an SU(2) Higgs condensate at the electroweak (EW) scale, L_EW, through a seesaw-like Higgs mechanism, L_EW ~ (L_I)^2/L_U, while the breaking of the SM SU(2)XU(1) gauge symmetry occurs at the intermediate scale L_I. 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 our seesaw-Higgs'' model predicts 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: m_nu ~ (L_I)^4/(L_U)^3 ~ (L_EW)^2/L_U. We also show that our seesaw Higgs model can be naturally embedded in theories with tiny extra dimensions of size R ~ 1/L_U ~ 10^{-16} fm, where the seesaw induced EW scale arises from a violation of a symmetry at a distant brane if there are 7 tiny extra dimensions.