1. Split Two-Higgs Doublet and Neutrino Condensation Fei Wang Tsinghua University 2006.8.8

2. Based on our paper hep-ph/0601018 with Jinmin Yang and Wenyu Wang.

3. Split Two-Higgs Doublet and Neutrino Condensation Motivations: Coincidence between the very small neutrino mass scale and dark energy scale. Observed dark energy scale (10^{-3} eV)^4 Consequence: Two-Higgs doublet with vevs greatly split. Dynamical dark energy fields.

4. Main Points: Neutrino mass was given by the other set of higgs field from neutrino condensation without see-saw mechanism. Very tiny $tan\beta$ due to greatly split vevs. The dynamically generated light higgs field is responsible for dark energy field.

5. Two-Higgs Doublet model We introduce two-Higgs doublet with two very split vevs: Assume CP conservation and discrete symmetry:

6. Mass Eigenstate in Higgs Sector: So we get : Charged Goldstone and Higgs fields: Neutral CP-odd Goldstone and Higgs fields:

7. After EW symmetry broken, three degree of freedom was eaten. The remaining Higgs mass: CP-even mass matrix: At EW scale with o(1) \lambda.

8. CP even Higgs: Mass eigenvalue and eigenstate CP even Higgs: Mass eigenvalue and eigenstate with \alpha also small: m_H at EW scale m_h at neutrino mass scale.

9. Properties of the Scalars:

10. Possible Constraints:

11. Phenomenology at Collider

12. Neutrino Condensation To naturally get small mass and vevs for \Phi_2 through neutrino condensation. Similar process as top-condensation by Tanabashi, Hill etc. Here we assume neutrino of the third family \tau participate in certain four- fermion interactions:

13. whenTau neutrino condensate. We can induce auxiliary scalar field \Phi_2 to incorporate the condensation effects:

14. When energy scales run down, auxiliary fields get kinematic terms and quartic interactions:

15. Other neutrino mass was given by adding effective Yukawa coupling to \Phi_2 (Add symmetry to forbid couplings to \Phi_1)whose origin we do not care (Maybe ETC like.) To get the accurate mass of the composite particle and tau neutrino mass, one need to solve the renormalization equation. From the Pagels-Stokar formula we can estimate the scale \lambda at order Tev scale.

16. Cosmological Consequences We try to interpret the composite scalar from neutrino condensation as a phenomenological description of dark energy field. From the potential and the vev \sim 10^{- 3eV},we can get the dark energy value through the form:

17. Advantage Can naturally incorporate Froggatt-Nielsen mechanism to take account the mass hierarchy and bi-maximal mixing. An alternative to see-saw. However, stringent bounds from experiments.

18. Thank You!