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Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model

N. T. ThuyYonsei Univ.

Theoretical Particle Physics Group Report at Yonsei Univ., Jun. 11-12, 2012

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Outline

1. A review of the economical 3-3-1 model2. Singlet mixed Higgs boson3. The singlet as dark matter3.1. Implication for parameter space from WMAP constraint3.2. Direct and indirect searches for the Dark Matter4. Summary

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a. Particle content The particle content in this model is given as follow:

Electric charges of the exotic quarks U and are the same as of the usual quarks.

1. A review of the economical 3-3-1 model

Da

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The two fields are at least introduced to span the scalar sector of the economical 3-3-1 model:

‘

with VEVs

, ,

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The Yukawa interactions can be written in the most general form as follows

where the subscripts LNC and LNV, respectively indicate to the lepton number conserving and lepton number violating ones.

where a, b, and c stand for SU(3) L indices.

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The gauge group is broken via two steps:

The VEV w is responsible for the first step of symmetry breaking giving mass for the exotic quarks, while the second step is due to u and v giving mass for the usual quarks and all ordinary leptons. Therefore, they have to satisfy the constraints:

,(3) (1) (2) (1) (1)w vuL X L Y QSU U SU U UÄ ¾¾® Ä ¾¾¾®

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2. Singlet mixed Higgs boson

In this model, the most general Higgs potential has very simple form

Let us shift the Higgs fields into physical ones,

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The constraint equations obtained from the minimum condition of the potential are given by

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We expand the neutral Higgs fields as

We get three massive physical particles from the Higgs sector.

where

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Charge Higgs

In the limit, ,v uw?

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Combining the equations obtained from the minimum potential and positive masses of Higgs we get

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Singlet mixing reduces the coupling strengths of the Higgs states, to all SM fields by the factors

If >2, can decay to pairs of , altering the branching fractions to SM modes (XSM)

is total decay rate of SM Higgs boson to SM modes given in PDG (Particle Data Group).

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Here the heavy Higgs decay rate is given by

with the coupling given by

This decay is accessible only if >2

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A reduction in the branching fractions and coupling can resultin a decrease in the SM statistical significance of Higgsdiscovery at the LHC. This reduction factor can be writtenas

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We fix u=2 GeV, v=246 GeV.We perform a numerical scan over the parameter space in the model by taking random value of --> We get the value of , , the mixing angle and the reduction factors.

Assume that are the same order, we vary 0.02< <1- 1< < - 0.02

1 TeV < w < 50 TeV

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Fig. vs , .~ ( 10-18 , 10-8 ) ; SM Higgs boson

2i

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Fig. Cos vs Higgs mass.cos ~ 1 => mixing angle of and is small ~S3~S2

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If are the same order (in the region (0.02, 1))< 300 GeV,

Fig. vs .can decay into

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• - gauge boson interactions arise from

+ The coupling constants of Higgs and SM gauge bosons are proportional to . In the limit , -> 0. + In order to forbid the decay of to new gauge bosons, we need the constraint

+ The interaction can be gauged away by a unitary transformation because of Goldstone boson .

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• - fermion interactions come from the Yukawa interactions . does not interact with SM leptons but interacts with exotic quarks, which are heavy ones. We assume that their masses are heavier than that of

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• - Higgs boson interactions arise from Higgs potential.

+To avoid decay to , we need the constraint

+There exits coupling . In order to forbid :-New symmetry to remove the coupling , which is in=0.-If 2, then -> require fine tuning parameters.

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Method 1: For example, we extend the model based on extra dimension, then not only =0 but also =0 -> the charged Higgs H2 becomes massless -> the model is unrealistic.

Method 2: We find out parameter space satisfying the mass condition 2.

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Fig. space (1 < w < 50 TeV). Fig. vs .In the above space, . → can be a candidate for dark matter if there is fine-tuning Higgs couplings .

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3.The singlet as dark matter

WMAP (Wilkinson Microwave Anisotropy Probe) constraints on relic abundance arXiv: 1001.4538 [astro-ph]

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In order to calculate the DM relic abundance we use micrOMEGAs 2.4, which is a code to calculate the properties of a stable massive particle in a generic model.

Construct calcHEP model files +prtcls1.mdl contains all particles in this model and their properties, such as spin, mass, width, color … +lgrng1.mdl shows factors as well as Lorentz part of all vertices. +vars1.mdl lists the independent parameters +func1.mdl contains the constrained parameters Modify the code

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3.1. Implication for parameter space from WMAP constraint. The parameters of our model are +the self-Higgs couplings , +the VEV w We study the behavior of as a function of one parameter each time.

Results: + The relic density almost does not depend on , . + To study relic density , we fix , .

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Fig. vs .• Fix =120 GeV -> 120 GeV< < 240 GeV • ~1/ • Fix = 10 TeV -> 0.00012< < 0.00028• Fix =2.5E-4 ->6.84 TeV < 10.67 TeV

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3.2. Direct and indirect searches for the Dark Matter.

a. Direct search

-nucleon cross section vs for =120 GeV (left) and experiment results (right). -nucleon cross section is in order of 10-8 (pb)= 10-44 (cm2).

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Fig. Total number of events/day/kg vs =120 GeV. The number of events/day/kg ~ 10-2 events.

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b. Indirect search

Fig. The annihilation cross section times the relative velocity of incoming DM particles vs . +Dominate channel is . +The relativistic thermally averaged annihilation cross- section is .

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4. Summary• and are mixed by S3 and S2 . The mixing angle is small, is

identified as SM Higgs and can be a candidate for DM if the mass condition < 2 is satisfied. However, there is fine-tuning Higgs couplings .

• We can find parameter space of the Higgs couplings and the value of w satisfying WMAP allowed region. The direct and indirect searches are fit to the experiment results.

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