1. Higgs phenomena in economical 3-3-1 models
Phys. Rev. D. 73, (2006) ; 73, (2006), &
with M. C. Rodriguez, NPB. 772, (2007) 150, B795, (2008) 361
P. V. Dong, D. T. Huong, T. T. Huong, H. N. Long & D.V. Soa
ICFP 2009, Hanoi

2. - Mass of gauge boson  Higgs mechanism
Motivation
- Mass of gauge boson  Higgs mechanism
- Neutrino mass  beyond SM  3-3-1
models based on
gauge group
In non-SUSY models, Higgs mass is a
free parameter.
Current limit

3. - In SUSY models: Higgs masses are constrained: ~ gauge couplings g and VEV ,
for examples:
- In the previous 3-3-1, Higgs sector is complicated, but recently constructed
model, Higgs sector is very simple (we call it economical model)

4. -Lepton in triplet The model One quark family in triplet
Two other families are in anti-triplet

5. Proposal of Economical 3-3-1 Model
Two Higgs triplets of the model with RH neutrinos
The model with two Higgs triplets
(Economical model)
P. V. Dong, et al, PRD 73, (2006)

6. With only two Higgs triplets, gauge boson mass Lagrangian is given by

7. We have two kinds of mixing i). Mixing among charged gauge bosons:
ii) Mixing among neutral gauge bosons (among
components)

8. The above mixing leads to LFV interactions
where +

9. Note that there are LFV in the SM W boson!
For the neutral currents
where
There are LFV in the SM Z boson!

10. Higgs sector in E331 model Has lepton number 2 No lepton number
In the effective limit our Higgs can be represented as
Has lepton number 2
PV Dong, HNL, DV Soa,
PRD 73, (2006)
No lepton number

11. Higgs sector in SUSY economical 3-3-1 model
We use the notation
P.V.Dong, M. Rodriguez, et al
Nucl. Phys.B 772, (2007) 150
In the SUSY case, there are two extra Higgses
SBS thru two steps

12. where
It follows
The supersymmetric Higgs potential takes the form

13. We expand the fields around the VEVs as
The constraint equations

14. 1) Five pseudoscalar massless states:
Nucl. Phys. B 795, (2008) 361
Results
1) Five pseudoscalar massless states:
2) One pseudoscalar massive state with mass:
3) Three massless scalar fields
4) Three massive fields corresponding to the masses
This value is very closed to the lower limit of 89.8 GeV (95% CL)

15. Charged Higgs sector
1. Four charged massless scalar fields
2. Two massive charged bosons with masses
At the tree level, we cannot fix only one heavy
scalar Higgs boson with mass, while all remaining
fields gain masses of the gauge bosons in the model.

16. To Identify Higgs content, we need to calculate Higgs-gauge coupling

17. In the effective coupling limit, the triplet at second step of SBS, has a form

18. Summary
The Higgs triplet with two VEVs produces mixing of real part
of bilepton with neutral gauge bosons.This is a reason
for LNV interactions of the SM W and Z bosons .
2) The same situation happens in the Goldstone sector
3) In the SUSY E model: the Higgs sector is quite
constrained.Mass of only one Higgs boson is free.