1. Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model
N. T. Thuy
Yonsei Univ.
Theoretical Particle Physics Group
Report at Yonsei Univ., Jun , 2012

2. Outline
1. A review of the economical model 2. Singlet mixed Higgs boson 3. The singlet as dark matter 3.1. Implication for parameter space from WMAP constraint 3.2. Direct and indirect searches for the Dark Matter 4. Summary

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

4. The two fields are at least introduced to span the scalar sector of the economical 3-3-1 model:‘
with VEVs
, ,

5. 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.

6. The gauge group 𝑆𝑈 3 𝐿 ⊗𝑈 1 𝑋 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:

7. 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,

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

9. We expand the neutral Higgs fields as
We get three massive physical particles from the Higgs
sector.
where 𝑡 𝜃 = 𝑢 𝑤

10. Charge Higgs In the limit,

11. Combining the equations obtained from the minimum potential and positive masses of Higgs we get 𝜆 1 , 𝜆 2 , 𝜆 4 >0 𝜆 3 <0

12. Singlet mixing reduces the coupling strengths of the Higgs states, 𝐻 0 , 𝐻 1 0 to all SM fields by the factors If 𝑀 𝐻 1 0 >2 𝑀 𝐻 0 , 𝐻 1 0 can decay to pairs of 𝐻 0 , altering the 𝐻 1 0 branching fractions to SM modes (XSM) 𝛤 ℎ 𝑆𝑀 is total decay rate of SM Higgs boson to SM modes given in PDG (Particle Data Group).

13. Here the heavy Higgs decay rate is given by with the 𝐻 1 0 𝐻 0 𝐻 0 coupling given by This decay is accessible only if 𝑀 𝐻 1 0 >2 𝑀 𝐻 0

14. A reduction in the branching fractions and coupling can result in a decrease in the SM statistical significance of Higgs discovery at the LHC. This reduction factor can be written as

15. 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 𝜆 1 , 𝜆 2 , 𝜆 3 , 𝑤. --> We get the value of 𝑀 𝐻 0 , 𝑀 𝐻 1 0 , the mixing angle and the reduction factors. Assume that 𝜆 1 , 𝜆 2 , |𝜆 3 | are the same order, we vary 0.02< 𝜆 1,2 <1 - 1< 𝜆 3 < TeV < w < 50 TeV

16. Fig. 𝜉 𝑖 2 vs 𝑀 𝐻 0 , 𝑀 𝐻 1 0 . 𝜉 1 2 ~1 and 𝜉 2 2 ~ ( 10-18 , 10-8 ) ; 𝐻 0 ≡ SM Higgs boson

17. Fig. Cos𝜁 vs Higgs mass. cos𝜁 ~ 1 => mixing angle of 𝐻 1 0 and 𝐻 0 is small ⇒ 𝐻 1 0 ~S3 and 𝐻 0 ~S2

18. If 𝜆 1 , 𝜆 2 , 𝜆 3 are the same order (in the region (0
If 𝜆 1 , 𝜆 2 , 𝜆 3 are the same order (in the region (0.02, 1)) 𝑀 𝐻 0 < 300 GeV, 𝑀 𝐻 1 0 >500 GeV Fig. 𝑀 𝐻 1 0 vs 𝑀 𝐻 0 . 𝐻 1 0 can decay into 𝐻 0 𝐻 0

19. 𝐻 1 0 - gauge boson interactions arise from
+ The coupling constants of 𝐻 Higgs and SM gauge
bosons are proportional to
In the limit , > 0.
+ In order to forbid the decay of 𝐻 1 0 to new gauge bosons,
we need the constraint
+ The interaction can be gauged away by a
unitary transformation because of Goldstone boson

20. 𝐻 1 0 - fermion interactions come from the Yukawa interactions
𝐻 fermion interactions come from the Yukawa interactions . 𝐻 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 𝐻 1 0
𝑀 𝐻 1 0 < 𝑀 𝑈 , 𝑀 𝐻 1 0 < 𝑀 𝐷 2,3 .

21. 𝐻 1 0 - Higgs boson interactions arise from Higgs potential.
+To avoid decay 𝐻 to 𝐻 2 ± , we need the constraint
+There exits coupling 𝐻 1 0 𝐻 0 𝐻 0 .
In order to forbid 𝐻 1 0 → 𝐻 0 𝐻 0 :
-New symmetry to remove the coupling 𝐻 1 0 𝐻 0 𝐻 0 , which is in
𝜒 𝜒 † 𝜙 𝜙 † → 𝜆 3 =0.
-If 𝑀 𝐻 1 0 <2 𝑀 𝐻 0 , then 𝐻 cannot decay in to 𝐻 0 𝐻 0 -> require fine tuning parameters.

22. Method 1: For example, we extend the model based on extra dimension, then not only 𝜆 3 =0 but also 𝜆 4 =0 -> the charged Higgs H2 becomes massless -> the model is unrealistic. Method 2: We find out parameter space satisfying the mass condition 𝑀 𝐻 1 0 <2 𝑀 𝐻 0 .

23. Fig. 𝜆 1 , 𝜆 2 , 𝜆 3 space (1 < w < 50 TeV). Fig
Fig. 𝜆 1 , 𝜆 2 , 𝜆 3 space (1 < w < 50 TeV). Fig. 𝑀 𝐻 1 0 vs 𝑀 𝐻 0 . In the above 𝜆 1 , 𝜆 2 , 𝜆 3 space, 𝑀 𝐻 0 < 𝑀 𝐻 1 0 <2𝑀 𝐻 0 . → 𝐻 1 0 can be a candidate for dark matter if there is fine-tuning Higgs couplings 𝜆 1 , 𝜆 2 , 𝜆 3 .

24. 3.The singlet as dark matter
WMAP (Wilkinson Microwave Anisotropy Probe) constraints
on relic abundance
arXiv: [astro-ph]

25. 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

26. 3.1. Implication for parameter space from WMAP constraint.
The parameters of our model are
+the self-Higgs couplings 𝜆 1 , 𝜆 2 , 𝜆 3 , 𝜆 4
+the VEV w
We study the behavior of 𝛺 ℎ 2 as a function of one
parameter each time.
Results:
+ The relic density almost does not depend on 𝜆 2 , 𝜆 3 , 𝜆 4 .
+ To study relic density as functons of 𝜆 1 ,𝑤 , we fix 𝜆 2 , 𝜆 3 , 𝜆 4 ( 𝜆 2 ~0.12→ 𝑀 𝐻 0 =120 GeV).

27. Fig. 𝑤 vs 𝜆 1 .
Fix 𝑀 𝐻 0 =120 GeV -> 120 GeV< 𝑀 𝐻 < 240 GeV
𝑤 ~1/ 𝜆 1
Fix 𝑤= 10 TeV -> < 𝜆 1 <
Fix 𝜆 1 =2.5E-4 ->6.84 TeV 𝑤< TeV

28. 3.2. Direct and indirect searches for the Dark Matter.
a. Direct search
Fig. 𝐻 nucleon cross section vs 𝑀 𝐻 for 𝑀 𝐻 0 =120 GeV
(left) and experiment results (right).
Fig. 𝐻 nucleon cross section is in order of
10-8 (pb)= (cm2).

29. Fig. Total number of events/day/kg vs 𝑀 𝐻 1 0 for 𝑀 𝐻 0 =120 GeV
Fig. Total number of events/day/kg vs 𝑀 𝐻 1 0 for 𝑀 𝐻 0 =120 GeV. The number of events/day/kg ~ 10-2 events.

30. b. Indirect search Fig. The annihilation cross section times the relative velocity of incoming DM particles vs 𝑀 𝐻 Dominate channel is 𝐻 1 0 𝐻 1 0 →𝑏 𝑏 . +The relativistic thermally averaged annihilation cross- section is <𝜎𝑣>∼ 10 −26 𝑐 𝑚 3 𝑠 .

31. 4. Summary
𝐻 and 𝐻 0 are mixed by S3 and S2 . The mixing angle is small, 𝐻 is identified as SM Higgs and 𝐻 can be a candidate for DM if the mass condition 𝑀 𝐻 < 2 𝑀 𝐻 is satisfied. However, there is fine-tuning Higgs couplings 𝜆 1 , 𝜆 2 , 𝜆 3 .
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.

32. Thanks for Your Attentions!