Split Two-Higgs Doublet and Split Two-Higgs Doublet and Neutrino CondensationNeutrino Condensation

Fei WangFei Wang

Tsinghua UniversityTsinghua University2006.8.82006.8.8

Based on our paper hep-ph/0601018

with Jinmin Yang and Wenyu Wang.

Split Two-Higgs Doublet and Neutrino Split Two-Higgs Doublet and Neutrino CondensationCondensation

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 en

ergy fields.

Main Points: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.

Two-Higgs Doublet modelTwo-Higgs Doublet modelWe introduce two-Higgs doublet with two very split vevs:

Assume CP conservation and discrete symmetry:

Mass Eigenstate in Higgs Sector:Mass Eigenstate in Higgs Sector:

So we get:

Charged Goldstone and Higgs fields:

Neutral CP-odd Goldstone and Higgs fields:

After EW symmetry broken , three degree of After EW symmetry broken , three degree of freedom was eaten. The remaining Higgs mass:freedom was eaten. The remaining Higgs mass:

CP-even mass matrix:

At EW scale with o(1) \lambda.

CP even Higgs: CP even Higgs: Mass eigenvalue and eigenstateMass eigenvalue and eigenstate

with \alpha also small:

m_H at EW scale m_h at neutrino mass scale.

Properties of the Scalars:Properties of the Scalars:

Possible Constraints:Possible Constraints:

Phenomenology at ColliderPhenomenology at Collider

Neutrino CondensationNeutrino 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:

when Tau neutrino condensate.

We can induce auxiliary scalar field \Phi_2 to incorporate the condensation effects:

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

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.

Cosmological ConsequencesCosmological 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:

AdvantageAdvantage

• 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.

Thank You!Thank You!