Dark matter in the economical 3-3-1 model

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Transcript Dark matter in the economical 3-3-1 model 

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. 11-12, 2012
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Outline
1. A review of the economical 3-3-1 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
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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 Da are the
same as of the usual quarks.
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The two fields are at least introduced to span the scalar
sector of the economical 3-3-1 model:
β€˜
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 π‘†π‘ˆ 3
𝐿
βŠ—π‘ˆ 1
𝑋
is broken via two steps:
w
v ,u
SU (3)L Ä U (1)X ¾ ¾
® SU (2)L Ä U (1)Y ¾ ¾
¾® U (1)Q
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:
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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 π‘‘πœƒ =
𝑒
𝑀
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Charge Higgs
In the limit,
w ? v, u
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Combining the equations obtained from the minimum
potential and positive masses of Higgs we get
πœ†1 , πœ†2 , πœ†4 > 0
πœ†3 < 0
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Singlet mixing reduces the coupling strengths of the Higgs
states, 𝐻 0 , 𝐻10 to all SM fields by the factors
If 𝑀𝐻10 >2𝑀𝐻 0 , 𝐻10 can decay to pairs of 𝐻 0 , altering the 𝐻10
branching fractions to SM modes (XSM)
π›€β„Žπ‘†π‘€ 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 𝐻10 𝐻 0 𝐻 0 coupling given by
This decay is accessible only if 𝑀𝐻10 >2𝑀𝐻 0
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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
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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 πœ†1 , πœ†2 , πœ†3 , 𝑀.
--> We get the value of 𝑀𝐻 0 , 𝑀𝐻10 , the mixing angle and the
reduction factors.
Assume that πœ†1 , πœ†2 , |πœ†3 | are the same order, we vary
0.02<πœ†1,2 <1
- 1< πœ†3 < - 0.02
1 TeV < w < 50 TeV
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i2
Fig. πœ‰π‘–2
vs 𝑀𝐻 0 , 𝑀𝐻10 .
πœ‰12 ~1 and πœ‰22 ~ ( 10-18 , 10-8 ) ; 𝐻 0 ≑ SM Higgs boson
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Fig. Cos𝜁 vs Higgs mass.
cos𝜁 ~ 1 => mixing angle of
𝐻10
0
and 𝐻 is small
β‡’ 𝐻10 ~S3 and 𝐻 0 ~S2
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If πœ†1 , πœ†2 , πœ†3 are the same
order (in the region
(0.02, 1))
𝑀𝐻 0 < 300 GeV,
𝑀𝐻10 > 500 GeV
𝐻10 can decay into 𝐻 0 𝐻 0
Fig. 𝑀𝐻10 vs 𝑀𝐻 0 .
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β€’
𝐻10 - gauge boson interactions arise from
+ The coupling constants of 𝐻10 Higgs and SM gauge
bosons are proportional to
.
In the limit
,
-> 0.
+ In order to forbid the decay of 𝐻10 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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β€’ 𝐻10 - fermion interactions come from the Yukawa
interactions . 𝐻10 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 𝐻10
𝑀𝐻10 < π‘€π‘ˆ , 𝑀𝐻10 < 𝑀𝐷2,3 .
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β€’
𝐻10 - Higgs boson interactions arise from Higgs potential.
+To avoid decay 𝐻10 to 𝐻2± , we need the constraint
+There exits coupling 𝐻10 𝐻0 𝐻0 .
In order to forbid 𝐻10 β†’ 𝐻0 𝐻0 :
-New symmetry to remove the coupling 𝐻10 𝐻0 𝐻0 , which is in
πœ’πœ’ † πœ™πœ™ † β†’ πœ†3 =0.
-If 𝑀𝐻10 <2𝑀𝐻 0 , then 𝐻10 cannot decay in to 𝐻0 𝐻0 -> require
fine tuning parameters.
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Method 1:
For example, we extend the model based on extra dimension,
then not only πœ†3 =0 but also πœ†4 =0 -> the charged Higgs H2
becomes massless
-> the model is unrealistic.
Method 2:
We find out parameter space satisfying the mass condition
𝑀𝐻10 <2𝑀𝐻 0 .
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Fig. πœ†1 , πœ†2 , πœ†3 space (1 < w < 50 TeV).
Fig. 𝑀𝐻10 vs 𝑀𝐻 0 .
In the above πœ†1 , πœ†2 , πœ†3 space, 𝑀𝐻 0 < 𝑀𝐻10 < 2𝑀𝐻 0 .
→𝐻10 can be a candidate for dark matter if there is finetuning Higgs couplings πœ†1 , πœ†2 , πœ†3 .
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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 πœ†1 , πœ†2 , πœ†3 , πœ†4
+the VEV w
We study the behavior of π›Ίβ„Ž2 as a function of one
parameter each time.
Results:
+ The relic density almost does not depend on πœ†2 , πœ†3 , πœ†4 .
+ To study relic density as functons of πœ†1 , 𝑀 , we fix πœ†2 , πœ†3 ,
πœ†4 (πœ†2 ~0.12 β†’ 𝑀𝐻 0 = 120 GeV).
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Fig. 𝑀 vs πœ†1 .
β€’ Fix 𝑀𝐻 0 =120 GeV -> 120 GeV< 𝑀𝐻10 < 240 GeV
β€’ 𝑀 ~1/ πœ†1
β€’ Fix 𝑀= 10 TeV -> 0.00012< πœ†1 < 0.00028
β€’ Fix πœ†1 =2.5E-4 ->6.84 TeV 𝑀< 10.67 TeV
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3.2. Direct and indirect searches for the Dark Matter.
a. Direct search
Fig. 𝐻10 -nucleon cross section vs 𝑀𝐻10 for 𝑀𝐻 0 =120 GeV
(left) and experiment results (right).
Fig. 𝐻10 -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 𝑀𝐻10 for 𝑀𝐻 0 =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 𝑀𝐻10 .
+Dominate channel is 𝐻10 𝐻10 β†’ 𝑏𝑏 .
+The relativistic thermally averaged annihilation crosssection is < πœŽπ‘£ >∼ 10βˆ’26 𝑐 π‘š3 𝑠.
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4. Summary
β€’ 𝐻10 and 𝐻 0 are mixed by S3 and S2 . The mixing angle is
0
small, 𝐻 is identified as SM Higgs and 𝐻10 can be a
candidate for DM if the mass condition 𝑀𝐻10 < 2 𝑀𝐻 0 is
satisfied. However, there is fine-tuning Higgs couplings
πœ†1 , πœ†2 , πœ†3 .
β€’ 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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Thanks for Your Attentions!
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