H.Sung Cheon (천화성, 千和聖) - DESY Theory workshop 2008

Doubly Coexisting
Dark Matter Candidates
in an Extended Seesaw Model
H.Sung Cheon (천화성
Yonsei University, Seoul, S. Korea
Collaborate with Sin Kyu Kang and C.S.Kim (arXiv:0807.0981)
DESY THEORY WORKSHOP Sep. 29 - Oct. 2, 2008
Dark Matter at the Crossroads
DESY, Hamburg, Germany

http://antwrp.gsfc.nasa.gov/apod/ap060824.html
The Matter of the Bullet Cluster : Collisionless DM

http://antwrp.gsfc.nasa.gov/apod/ap070820.html
Dark Matter Core in the Abell 520 cluster :
Unknown interaction between DM particles
Credit: X-ray: NASA/CXC/UVic./A. Mahdavi et al. optical/lensing: CFHT/UVic./H. Hoekstra et al.

The only one kind of DM (ex : WIMP)
is NOT enough to explain these
all observations.

We consider two kinds of DM
candidates which can be coexisted
from an Extended Seesaw Model

Why is an Extended Seesaw Model?
(S.K.Kang, C.S.Kim, Phys. Lett. , (2007) 248 [arXiv:hep-ph/0607072])

Why is an Extended Seesaw Model?
(S.K.Kang, C.S.Kim, Phys. Lett. , (2007) 248 [arXiv:hep-ph/0607072])
We have an another problem
in our Universe.

Why there is more matter
than antimatter
in the present Universe?

JCAP 0805:004,2008 (hep-ph/0710.2416)
(H.Sung Cheon, Sin Kyu Kang, C.S.Kim)
L = L SM +Y D ν D HN + M N NN +YNφS + m S SS + 1 2 (∂ µφ) 2 − 1 2 m2 φφ 2 − λ s
4 φ4 − λH † Hφ 2 + h.c.
L SM : the Standard model Lagrangian, H : Higgs doublet
N : Heavy Majorana neutrino field, ϕ: Singlet Higgs field (SH)
S : Singlet intermediate Majorana neutrino field (SMN)
Our model is described by seven parameters : 1. dimensionless self coupling, λ s 2.the mass of ϕ,
M ɸ , 3. dimensionless coupling of ϕ to the Higgs field, λ, 4, the mass of Heavy Majorana neutrino,
M N, 5 the mass of S, M S, 6. Dirac Yukawa coupling, Y D, 7. Singlet Yukawa coupling, Y.

In order to guarantee the stability of the dark matter candidates,
1. Z 2 symmetry is conserved
2. Spontaneously symmetry break the EW gauge group
After the spontaneously EW symmetry breaking, the singlet scalar
dependent part of the scalar potential is given by
V = 1 2 (m2 0 + λv2 EW)φ 2 + λ s
4 φ4 + λv EW φ 2 h + h 2 φ2 h 2

Qing-Hong Cao, Ernst Ma, and Jose Wudka, C.P. Yuan,
Multipartite Dark Matter, hep-ph/0711.3881
They also introduce the two new fields, a new fermion, X, and a new scalar, S. and assume that
the Z 2 ☓Z’ 2 symmetry conservation.
Their Lagrangian is
where,
L = L S M + L D M
+ L S D M + L int
L χ DM = iχ ∂χ − m 1χ
L S DM = 1 2 ∂ µS∂ µ S + 1 2 m2 2S 2 + 1 4 λ 1S 4 ,
here, Λ is the new scale.
L int = 1 2 λ 2H † HSS + λ 3
Λ H† Hχχ + λ 4
2Λ χχSS,
They show that the lightest neutralino particle may relax the severe constraints on the
parameter space of the MSSM through the X,X->S,S annihilation process

So we introduce two new terms of Qing-Hong Cao, Ernst Ma, and
Jose Wudka, C.P. Yuan, hep-ph/0711.3881
L = L 1DM + g 1
Λ H† HS T S + g 2
2Λ ST SΦΦ
After breaking the EW gauge symmetry (In order to have acceptable particle
masses), the Φ-dependent part of the scalar potential is given by
V = 1 2 (m2 Φ 0 + λν 2 EW)Φ 2 + λ s
4 Φ4 + λ 2 h2 Φ 2 + λν EW hΦ 2
In addition we have the new effective interaction terms,
L Int = −(m S
0 − λ 2v EW
2
)S 2 + λ 2
2v EW
h 2 S 2 + λ 2 hS 2 + λ 3
v EW
S 2 Φ 2

We demand that
In order to guarantee the stability of two dark matter candidates,
✽ Z 2 ☓Z’ 2 Symmetry should be conserved
Z 2 ☓Z’ 2 Symmetry
ϕ
Z 2 ☓Z’ 2 Symmetry is conserved.

Of course,
this is NOT renormalizable.

Historically
ν µ
µ
G F
ν µ¯ν e
e
µ
W −
¯ν e
e
So, the electroweak theory is Renormalizable !!!

Effective terms of our model
L = L 1DM + g 1
Λ H† HS T S + g 2
2Λ ST SΦΦ
S
h
S
Φ
h
S
h
S
h
S
φ
S
Φ
φ
S
φ
S
φ
We introduce a New Heavy Scalar particle Φ

Before Spontaneously Symmetry Breaking
L = L SM + K.E. +(Y D ¯νHN + Y s ¯NφS + h.c.)+MR N T N − m S S T S − 1 2 m2 φ φ2 − λ s
4! φ4
−
λH † Hφ 2 + 1 2 m2 Φ Φ2 − λ e
4! Φ4 − λ Φ H † HΦ 2 − λ a S T SΦ − λ b φφΦΦ
φ
: Singlet Scalar field (SH)
Φ
: New Heavy SM like {(+,+) parity} singlet scalar particle

Relic abundance in
doubly coexisting DM model

Λ
Λ ⩵
Λ ⩵
Λ ⩵
⩵ Ε ⩵ Ε ⩵
⩵
⩵
Λ
Λ ⩵
⩵ Ε ⩵ Ε ⩵
⩵
⩵
Λ ⩵
Λ ⩵
The relation
between λ 2 and
mass of S
which is chosen to
be Ω CDM h 2 = 0.110
Λ
Λ ⩵
Λ ⩵
Λ ⩵
⩵ Ε ⩵ Ε ⩵
⩵
⩵
Λ ⩵
Λ ⩵
Λ
Λ ⩵
Λ ⩵
Λ ⩵
⩵ Ε ⩵ Ε ⩵
⩵
⩵
Λ ⩵
Ω S h 2 + Ω Φ h 2
= Ω CDM h 2
= 0.110 ± 0.006
ɛ i = Ω ih 2
Ω CDM h 2
Λ
Λ ⩵
Λ
Λ ⩵
⩵ Ε ⩵ Ε ∼
⩵
⩵
Λ ⩵
⩵ Ε ⩵ Ε ∼
⩵
⩵

First, we can relax the parameter space when S is one
of dark matter candidates through the conserved
Z2 ×Z ′ 2 symmetry and the enough
S,S→ Φ, Φ annihilation cross section

The nucleon recoil experiment
(Direct Dark Matter Search)

Feynman diagrams relevant to
(a) S-nucleon elastic scattering
(b) Φ-nucleon elastic scattering
σ S ≈ λ2 2 |A n| 2
π
( m
2
∗
m 4 h
)
,
σ Φ = λ2 ν 2 EW |A n| 2
4π
( m
2
∗
m 2 Φ m4 h
)
m ∗ = m S m n /(m S + m n )
where
. So far most experiments of direct detection
assume that there exist the only one kind of dark matter, whereas we
assume that two kinds of dark matter can be coexist. So in order to compare
our results with experimental data we use a following relation,
σ el
(Cao, Ma, Wudka, Yuan)
where is the σ el is the cross section of DM-nucleon elastic scattering and
m 0
is the mass of WIMP.
= ɛ S
σ S + ɛ Φ
σ Φ
m 0 m S m Φ

Σ
⩵ Ε ⩵ Ε ⩵
⩵
⩵
Λ ⩵
Λ ⩵
Σ
⩵ Ε ⩵ Ε ⩵
⩵
⩵
Λ ⩵
Λ ⩵
Σ
⩵ Ε ⩵ Ε ⩵
⩵
⩵
Λ ⩵
Λ ⩵
Σ
Λ ⩵
Λ ⩵
⩵ Ε ⩵ Ε ⩵
⩵
⩵
Plots of the
elastic cross
section σ el as
a function of m S
Σ
Λ ⩵
⩵
Λ ⩵
⩵ Ε ⩵ Ε ∼
⩵
Σ
Λ ⩵
Λ ⩵
⩵ Ε ⩵ Ε ∼
⩵
⩵

Let us implicate for Higgs searches
in LHC

Here we will search for only the case
for 2m s < m h or 2m Φ < m h
because LHC is unlikely place
for the case of both 2m Φ > m h and 2m s > m h.

The invisible Higgs decay width is given at three level by
√
Γ H→φφ = λ2 v 2 EW
1 − 4m2 S
32πm h m 2 h
Γ H→S,S = λ2 2m h
8π
(
1 − 4m2 S
m 2 h
) 3/2

1.0
a
m ⩵120 GeV
1.0
b
m ⩵90 GeV
0.9
0.8
0.8
m ⩵58 GeV
R
0.7
m ⩵90 GeV
R
0.6
0.6
Λ 3 ⩵0.6
0.5
⩵0.110, Ε S ⩵1, Ε ∼ 0
m h ⩵200 GeV
0.4
70 75 80 85 90 95 100
m S
0.4
0.2
0.0
Λ 3 ⩵0.1
⩵0.110, Ε S ⩵0.9, Ε ⩵ 0.1
m h ⩵130 GeV
54 56 58 60 62 64
m S
Plots of the ratio R as a function of m S . Here the shadowed region represents the
forbidden due to XENON10 Dark Matter Experiment.
(a) R = Br H→W + W − ,Z,Z,¯bb,¯ττ,¯cc(SM + S)
Br H→W + W − ,Z,Z,¯bb,¯ττ,¯cc(SM)
=
Γ H,total (SM)
Γ H→S,S +Γ H,total (SM) .
(b)
R =
=
Γ H,total (SM)
Γ H→S,S +Γ H→Φ,Φ +Γ H,total (SM) . (2m S

If we assume 2m Φ < m h , we can observe the invisible
Higgs signal in anywhere of the possible m S into dark
matter candidate, even in 2m S ≥ m h , at LHC

DAMA experiment

DAMA experiment
(R. Bernabei et al. [DAMA Collaboration], arXiv:0804.2741 [astro-ph])
Recently, the DAMA collaboration announced the model independent annual
modulation signature for dark matter particles in recoil scattering off NaI(Tl) detectors at
the Gran Sasso Najtional Laboratory.
Actually the DAMA had already found an annual modulation
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(P. Gondolo & G. Gelmini) and (F.J.Petriello & K.M. Zurek) found that
there is a region of WIMP parameter space
which can simultaneously accommodate DAMA experiment
and the null results of the other direct dark matter detection experiments

P. Gondolo & G. Gelmini
Phys. Rev. D 71, 123520 (2005) [arXiv:hep-ph/0504010]
Range of WIMP masses m for which there is a compatible region between the DAMA
modulation and the other experimental results at various stream heliocentric speeds vstr

F.J.Petriello & K.M. Zurek arXiv:0806.3989 [hep-ph],
Christopher Savage, Graciela Gelmini, Paolo Gondolo, Katherine Freese,
arXiv:0808.3607 [astro-ph]
3GeV m DM 8GeV
3 × 10 −41 cm 2 σ SI
p 5 × 10 −39 cm 2
F.J.Petriello & K.M. Zurek, 2008

Our Model & DAMA experiment
38
a
38
b
Log Σelnucleoncm 2
39
40
41
42
43
Dotted : m h ⩵150 GeV
Solid : m h ⩵120 GeV
m S
⩵80 GeV
⩵0.11, Ε ⩵1, Ε S ∼0
Λ 3 ⩵0.6
Log Σelnucleoncm 2
39
40
41
42
43
Red : Singlet DM model
Dotted : Ε ⩵1, Ε S ∼0
Blue : Ε ⩵0.5, Ε S ⩵0.5
m h ⩵150 GeV, m S
⩵80 GeV
⩵0.11, Λ 3 ⩵0.6
44
2 4 6 8 10
44
2 4 6 8 10
m GeV
m GeV
Here the shadowed region can accommodate DAMA and
the other direct dark matter detection experiments.
Fig-(a) : Same relic density -> same annihilation cross section -> same
λ 2
ratio
M 4 h
S. Andreas, T. Hambye and M. H. G. Tytgat, arXiv:0808.0255 [hep-ph].
Fig-(b) :
σ el
m 0
= ɛ S
m S
σ S + ɛ Φ
m Φ
σ Φ
⇒ σ el ≈ ɛ φ σ φ

Conclusion

We consider coexisting two kinds of DM, Singlet fermion and Singlet
scalar, from an Extended Seesaw Model.
We expect to explain several problems of the observations into our
model.
Large scale (>>1 Mpc) : Standard CDM (WIMP)
-> Singlet Fermion
Small scale (< few Mpc) : The density problem of the center of
galaxy & DAMA experiment
-> Singlet Scalar (self-interacting DM : David N. Spergel and Paul J.
Steinhardt )
Abell 520 Cluster :
1) Self-interacting
2) Interaction between Singlet scalar and Singlet
fermion (I notice that this case)

We consider coexisting two kinds of DM, Singlet fermion and Singlet
scalar, from an Extended Seesaw Model.
We expect to explain several problems of the observations into our
model.
Large scale (>>1 Mpc) : Standard CDM (WIMP)
-> Singlet Fermion
Small scale (< few Mpc) : The density problem of the center of
galaxy I don’t & DAMA know whether experiment this suggestion is right or not because I
-> didn’t Singlet check Scalar constraints (self-interacting (except DM DM density : David parameter N. Spergel and constraint) Paul J.
Steinhardt and I ) don’t know what constraints we must consider. Here we
considered just dark matter density parameter. So if you know
what constraints we must Abell consider 520 Cluster here, : tell me them anytime,
1) Self-interacting anywhere, I’m very welcome to that.
2) Interaction complement@yonsei.ac.kr between Singlet scalar : My and e-mail Singletaddress
fermion (I notice that this case)

I have an
another problem

Brain Hierarchy Problem
(H.S.Cheon, DESY workshop, 2008)
Language ability Brain
(not brane)
Other abilities Brain
(not brane)
in English, even in Korean
too low scale
(DE or Axion or
neutrino scale)
Normal scale
(EW scale)
e −2Ht
(H.S.Cheon, http://charm.phys.nthu.edu.tw/~cheung/summer2004/HSCheon.ppt, 2004)
When you ask or teach me something, please can you speak slowly?