Higgs phenomena in economical 3-3-1 models Phys. Rev. D. 73, (2006) 035004; 73, (2006),075005 & 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

- 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

- 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 3-3-1 model)

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

Proposal of Economical 3-3-1 Model Two Higgs triplets of the 3-3-1 model with RH neutrinos The 3-3-1 model with two Higgs triplets (Economical 3-3-1 model) P. V. Dong, et al, PRD 73, (2006) 035004

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

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

The above mixing leads to LFV interactions where +

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

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) 075005 No lepton number

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

where It follows The supersymmetric Higgs potential takes the form

We expand the fields around the VEVs as The constraint equations

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)

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.

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

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

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 3-3-1 model: the Higgs sector is quite constrained.Mass of only one Higgs boson is free.