Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model
description
Transcript of Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model
![Page 1: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/1.jpg)
1
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
![Page 2: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/2.jpg)
2
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
![Page 3: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/3.jpg)
3
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
![Page 4: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/4.jpg)
4
The two fields are at least introduced to span the scalar sector of the economical 3-3-1 model:
‘
with VEVs
, ,
![Page 5: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/5.jpg)
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.
![Page 6: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/6.jpg)
6
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®
![Page 7: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/7.jpg)
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,
![Page 8: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/8.jpg)
8
The constraint equations obtained from the minimum condition of the potential are given by
![Page 9: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/9.jpg)
9
We expand the neutral Higgs fields as
We get three massive physical particles from the Higgs sector.
where
![Page 10: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/10.jpg)
10
Charge Higgs
In the limit, ,v uw?
![Page 11: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/11.jpg)
11
Combining the equations obtained from the minimum potential and positive masses of Higgs we get
![Page 12: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/12.jpg)
12
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).
![Page 13: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/13.jpg)
13
Here the heavy Higgs decay rate is given by
with the coupling given by
This decay is accessible only if >2
![Page 14: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/14.jpg)
14
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
![Page 15: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/15.jpg)
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 --> 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
![Page 16: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/16.jpg)
16
Fig. vs , .~ ( 10-18 , 10-8 ) ; SM Higgs boson
2i
![Page 17: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/17.jpg)
17
Fig. Cos vs Higgs mass.cos ~ 1 => mixing angle of and is small ~S3~S2
![Page 18: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/18.jpg)
18
If are the same order (in the region (0.02, 1))< 300 GeV,
Fig. vs .can decay into
![Page 19: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/19.jpg)
19
• - 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 .
![Page 20: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/20.jpg)
20
• - 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
![Page 21: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/21.jpg)
21
• - 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.
![Page 22: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/22.jpg)
22
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.
![Page 23: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/23.jpg)
23
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 .
![Page 24: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/24.jpg)
24
3.The singlet as dark matter
WMAP (Wilkinson Microwave Anisotropy Probe) constraints on relic abundance arXiv: 1001.4538 [astro-ph]
![Page 25: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/25.jpg)
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
![Page 26: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/26.jpg)
26
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 , .
![Page 27: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/27.jpg)
27
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
![Page 28: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/28.jpg)
28
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).
![Page 29: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/29.jpg)
29
Fig. Total number of events/day/kg vs =120 GeV. The number of events/day/kg ~ 10-2 events.
![Page 30: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/30.jpg)
30
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 .
![Page 31: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/31.jpg)
31
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.
![Page 32: Can new Higgs boson be Dark Matter Candidate in the Economical 3-3-1 Model](https://reader036.fdocuments.net/reader036/viewer/2022062310/56816354550346895dd3fb97/html5/thumbnails/32.jpg)
32
Thanks for Your Attentions!