Split Two-Higgs-Doublet Model and Neutrino Condensation

We split the two-Higgs-doublet model by assuming very different vevs for the two doublets: the vev is at weak scale (174 GeV) for the doublet \Phi_1 and at neutrino-mass scale (10^{-2} \sim 10^{-3} eV) for the doublet \Phi_2. \Phi_1 is responsible for giving masses to all fermions except neutrinos; while \Phi_2 is responsible for giving neutrino masses through its tiny vev without introducing see-saw mechanism. Among the predicted five physical scalars H, h, A^0 and H^{\pm}, the CP-even scalar h is as light as 10^{-2} \sim 10^{-3}eV while others are at weak scale. We identify h as the cosmic dark energy field and the other CP-even scalar H as the Standard Model Higgs boson; while the CP-odd A^0 and the charged H^{\pm} are the exotic scalars to be discovered at future colliders. Also we demonstrate a possible dynamical origin for the doublet \Phi_2 from neutrino condensation caused by some unknown dynamics.