清华大学：Split Two-Higgs Doublet and Neutrino Condensation

Split TWo-Higgs Doublet and Neutrino condensation Fei Wang TSinghua University 20068.8

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

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

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

Split Two-Higgs doublet and neutrino Condensation Motivations Consequence Coincidence TWO-Higgs doublet between the very small neutrino with vevs greatly split mass scale and dark energy scale Observed dark Dynamical dark energy scale energy fields (10^{-3}eV)44

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

Main points Neutrino mass was given by the other set of higgs field from neutrino condensation without see-saw mechanism Very tiny Stan\betas due to greatly split vevs The dynamically generated light higgs field is responsible for dark energy field

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 model We introduce two-Higgs eoi+on+ imo doublet with two very split veVs Reo2+2+ilmg U1~174GeV,2~10-eV Assume CP conservation and discrete symmetry:國;→-中 V中1,42)=A(41-2)2+2(42-2 +)(41-2)+(中2一 +入|(4①1)22)一(2(面1 +6m(2)

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

Mass eigenstate in Higgs Sector tan 22→0→ B So we get 1 Charged Goldstone and Higgs fields =中csB+士 8≈4 H1=-4sin+小cs月≈重, Neutral CP-odd Goldstone and Higgs fields C0=√2( Ingo cos+Im4sin≈v2m4 A 2(-Imd9 sin B+ Impg cos B)

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 freedom was eaten. The remaining Higgs mass At ew scale nH± 4(2+2)≈A with o(1) nAD A6(2+2)≈6 Lambda CP-even mass matrix 41+3)+2(413+)2 4A+)1n2422+)+k

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

CP even higgs Mass eigenvalue and eigenstate h≈Mn=4A1+入3) m≈M 4|(2+入3) +A3) H [(Re -v1)cos a+(Re U2)sInc 2(ReΦ 2[-(Re I- U1)sina+(R te 2 22)COS a √2(Re4-2 2M with lalpha also small: tan(2a) 12 U2/1 0 I11-122 m h at ew scale m h at neutrino mass scale

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

Properties of the Scalars () For A: All its couplings are the same as in the SM (i) For H=: They have Yukawa couplings only to LVR((=e p.T), but the coupling strength is at a natural order, say 0(1). Their gauge couplings ike H+H-y and H+H-Z are the same as in the usual 2HDM (ii) For A: It has Yukawa couplings only to neutrino pairs. It has gaug couplings like Zha as in the usual 2HDM (iv) For h: It has Yukawa couplings only to neutrino pairs. Its gauge couplings to W*W- and ZZ are very weak(proportional to u2)

Properties of the Scalars:

Possible constraints (1)For H: all direct and indirect experimental constraints are the same as for the SM higg 2s Doson (2)For H and Ao: the experimental constraints are similar as in the usual 2HDM except for the invalid constraints from various B-de ecavs (slich as b-78y. For example, from the unobservation of ete--H*H- at LEF II. H# should be heavier than about 100 GeV and thus A4 cannot be too sIna (3) For the ultra-light h: stringent constraints both from particle physics and from astrophysics are derived from its interactions with either photons electrons or nucleons. For example. stringent constraints may come from positronIum decays, Ineson decays, quarkonium decays or nuclear tran sitions. In our model. fortunately these constraints can be avoided or become quite weak since the coupling of h with photons, electrons or nul- eons are suppressed by 02/01 n 10-14 at tree-level. The most dangerous constraints may come from the invisible z decays. For example. from the three-body decay Z-h(A)*-hvv, some lower mass bound(say Tev) may be set on A

Possible Constraints: