Radiative Neutrino Mass and Dark Sector

Radiative Neutrino Mass and Dark Sector

Radiative Seesaw Model and Dark Sector
Mayumi Aoki
Mayumi Aoki
(Kanazawa U. )
Exploring the dark sector
March. 17, 2015
1
Contents
I.
Introduction
II.
Neutrino Mass
III.
Radiative Seesaw Model
IV.
Multicomponent DM
V.
Radiative Seesaw Model
with Multicomponent DM
VI. Summary
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2
Neutrino
Neutrino oscillation data indicate that neutrinos have masses and
mix with each other.
2-flavor:
P⌫↵ !⌫ = sin2 2✓ sin2
m2ij L
4E
- Neutrino Flavor States ⇔ Mass States
νe, ν!, ντ ν1, ν2, ν3
- The neutrino mixings are given by Pontecorvo-Maki-Nakagawa-Sakata (PMNS)
matrix.
µ
Jcc
= (ē, µ̄, ⌧¯)
⌫↵ =
UPMNS
2
3
X
µ
(1
UP M N S ⌫i
(↵ = e, µ, ⌧ )
i=1
c12 c13
= 4 s12 c23 c12 s23 s13 ei
s12 s23 c12 c23 s13 ei
Mayumi Aoki
T
)U
(⌫
,
⌫
,
⌫
)
5
1 2 3
P MNS
s12 c13
c12 c23 s12 s23 s13 ei
c12 s23 s12 c23 s13 ei
Exploring the dark sector
i
3
s13 e
s23 c13 5 ⇥ diag(1, ei'1 , ei'2 )
c23 c13
cij=cosθij , sij=sinθij
March. 17, 2015
3
Neutrino
Neutrino parameters
- Masses and Mixings
∆m212 ~8×10-5 eV2 , |∆m322|~ 3×10-3 eV2
θ12~30°, θ23~45°, θ13~10°
Σmν ＜0.23 eV
∆mij2=mi2 - mj2
Neutrino oscillation experiments
Cosmological data
- Mass Hierarchy (Sign of ∆m322 ) : unknown
Normal hierarchy : ∆m322 > 0
Inverted hierarchy : ∆m322 < 0
normal
Normal
inverted
Inverted
- CP phases (Dirac δ, Majorana 𝜑1, 𝜑2 ) : unknown
NH : -115° < δ < -60° ,
IH: +50° < δ < +130° for θ23=45°
T2K, arXiv:1409.7469[hep-ex]
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Beyond the Standard Model
Physics beyond the SM
Neutrino Mass and Mixings
mν~0.1eV
How we can naturally explain the small masses with less fine tuning?
Dark Matter
- The dark matter is inferred to exist.
- The DM contributes 27% to the energy
density of the Universe.
Galaxy rotation curves Gravitational lens
Dark Energy
68%
Bullet Cluster
Dark Matter
Matter ５%
2７%
These two problems are related ?
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5
Neutrino Masses
Effective dimension 5 operator
φ
φ
νL
fij
0 0
Li Lj ⇥
⇥
m =
ij
νL
fij
fij
0 2
⇥⇥ ⇤ ~0.1eV
O(10
14
) GeV
1
Seesaw mechanism
Minkowshi 77; Yanagida 79; Gell-Man et al. 79; Glashow 80; Mohapatra, Senjanovic 80
Type I
Right-handed neutrino NR
L=
=
1
˜ = i⌧2
(NR )c M NR + h.c.
2
p ◆✓ c ◆
✓
0 p vy/ 2
⌫L
c
NR
NR
vy T / 2
M
yL ˜ NR
⌫L
Φ0
⇤
νL
ν
- The lighter neutrino masses are
v2 y2
m⌫ '
2M
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Φ0
×
νL
NR
N
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6
Type-I Seesaw
v2 y2
m⌫ '
2M
- If y ~O(1), M~1014 GeV
mν = 0.1 eV
0
10
y
10
10
Low scale seesaw
→ Within LHC reach
M
-6
10
10
10
-4
-8
- If y ~ ye, M~100 GeV
Mayumi Aoki
-2
D=
10
m
Leptogenesis
Far from experimental reach
-10
-12
-9
10
-6
10
Exploring the dark sector
-3
10
0
10
3
6
10 10
M [GeV]
9
10
March. 17, 2015
10
12
15
10
7
Type-I Seesaw
LHC signal
- The NR production can happen only through ν-NR mixing.
T. Han and B. Zhang , PRL97 (2006); F. del Aguila, J. A. Aguilar-Saavedra and R. Pittau,
JHEP 0710 (2007); A. Atre, T. Han, S. Pascoli and B. Zhang, JHEP 0905 (2009).
- Both opposite-sign and same-sign lepton pairs are produced.
- The cross section can be observable only if ν-NR mixing > 0.01.
del Aguila et al. JHEP 0710 (2007) 047
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Type-I Seesaw
v2 y2
m⌫ '
2M
- If y ~O(1), M~1014 GeV
mν = 0.1 eV
0
10
y
10
10
Low scale seesaw
10
- If y ~10-7, M2,3~1 GeV
y ~10-12, M1~keV → Warm DM
M
-6
10
→ Within LHC reach
Mayumi Aoki
-4
-8
- If y ~ ye, M~100 GeV
νMSM
-2
D=
10
m
Leptogenesis
Far from experimental reach
10
-10
-12
-9
10
-6
10
-3
10
0
10
3
6
10 10
M [GeV]
9
10
10
12
15
10
Asaka, Shaposhnikov, PLB620 (2005) etc
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Type-II, Type-III
Type II
Type III
Konetschny, Kummer 77; Cheng, Li 80;
Gelmini, Roncadelli 81
SU(2)L triplet
scalar ∆
(Y=2)
⇥
⇥
=
+
/ 2
SU(2)L triplet fermion Σ (Y=0)
++
⇥
+
/ 2
0
Φ0
He et al. 89
0
=
Φ0
●
∆0
⇥
/ 2
Φ0
×
νL
νL
νL
+
0
Φ0
*
⇥
/ 2
⇥
νL
Σ0
m⌫ ' 2hh
LHC
0
hµv 2
i= p
2M 2
m⌫ '
qq’→∆++∆− −, ∆±±∆∓
v2 T 1
Y⌃
Y⌃
2
M
qq’→ Σ+Σ-, Σ±Σ0
leptonic mode
∆++→ll,
∆-→lν
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m∆++ ≳ 400 GeV
Σ+ → Wν, Σ0 → Wl
Exploring the dark sector
mΣ ≳ 250 GeV
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10
Radiative seesaw model
An alternative way to obtain the small mass is the radiative
seesaw mechanism.
0
10
-2
φ
φ
10
2loop
-4
10
N-loop :
y
νL
f
νL
m =
ij
1
16
2
⇥N
1loop
fij
-6
10
-8
10
⇥0 ⇥2
-10
10
-12
10
-9
10
-6
10
-3
10
0
10
3
6
10 10
M [GeV]
9
10
12
10
10
- Neutrino masses are generated via the radiative effect.
- Due to the loop suppression factor, Λ can be lower.
- Neutrino masses would be explained by the TeV-scale physics
(for the unsuppressed couplings).
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15
Zee model, Zee-Babu model
Zee model
Zee-Babu model
Zee, PLB93,389 (1980), PLB161,141 (1985)
Zee, NPB264,99 (1986)
Babu, PLB203,132 (1988)
1-loop
●
lL
k−−
ω−
●
S+
νL
2-loop
<Hj>
Hi
νL
νL
lR
lL
lR
v
<Hi>
ω−
lR
lL
νL
v
SM + ω± + K±±
SM + H2 + S±
H2 : doublet scalar
S± : charged singlet scalar (#L=∓2)
ω± : singly charged singlet scalar (#L=∓2)
K±± : doubly charged singlet scalar (#L=∓2)
No DM candidates
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Models with N
Krauss-Nasri-Trodden model
Ma model
Ma, PRD73, 077301 (2006)
Krauss, Nasri, Trodden PRD67,085002 (2003)
v
v
1-loop
3-loop
S1
νL
+
S2 +
i
lL lR
S1
S2 +
c α lR lL
+
νL
νLi
NR
v
η0
η0
j
v
SM+N R + S 1 ± + S 2 ±
S1± , S2± : singly charged singlet scalars (#L=∓2)
cα
NR
SM+N R + η
η :Inert doublet
✓
⌘=
νLj
+
⌘
p
0
0
(⌘R + i⌘I )/ 2
◆
h⌘i = 0
,
DM: NR, η0R or η0I
DM: NR
- Majorana mass term of NR is the source of the lepton number violation.
Z2 symmetry :
even: SM even even
odd: NR
- forbids the Dirac ν mass term.
- guarantees the stability of DM.
×
Φ0
νL
even
Φ0
×
NR
odd
νL
even
⇒ The framework would explain the neutrino mass and the DM.
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13
Models with N
Krauss-Nasri-Trodden model
Krauss, Nasri, Trodden PRD67,085002 (2003)
Ma, PRD73, 077301 (2006)
v
v
1-loop
3-loop
νL
Ma model
S1
+
S2 +
i
lL lR
S1
S2 +
+
νL
c α lR lL
νLi
NR
v
η0
η0
j
cα
NR
v
- Because of large loop suppression factor of 3-loop
and the charged lepton masses, the model can
naturally have order 1 coupling.
νLj
Yν Yν λ5 ~ 10-10
New masses ~O(100) GeV ⇒ λffgg ~ O(1)
LFV Constraints :
*→eγ :
DM relic density :
NR DM :
*
e
YνYν ≲ 10-4
0h2 = 0.12 ⇒ YνYν ~ O(1)
N
l+
N
l-
- Flavor structure should be considered.
less fine-tuning
KNT Cheung, Seto, PRD69 (2004)
Ma Suematsu, Toma, Yoshida, PRD79 (2009)
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Models with N
Models with Z2 odd NR
S1 +
νLi
v
S2 +
lL lR
S2 +
NR
v
Aoki-Kanemura-Seto model
cα
v
S1 +
νL j
lR lL
η0
η0
νL i
v
cα
NR
νL j
M.A., Kanemura, Seto PRL102 (2009)
v
SM+H 2 +N R + S ± + η
v
η0
#
S± : singly charged singlet scalars
η : real singlet scalar
!Li
H"
H"
!Lj
S" S"
e!R i
- Electroweak Baryogenesis
- DM: NR or η
- O(1) coupling he~O(1)
e"R j
NR
A typical mass scale :
mH ± = 100 GeV, mS ± = 400 GeV, m⌘ = 50 GeV, M = 5 TeV
Common Feature
1. Extend scalar sector
Mayumi Aoki
2. NR (Majorana nature)
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Electron-positron collisions
ILC
- The pair production of Z2 odd charged scalar bosons at the e+e- collision.
Z2 odd charged scalar
10
2
↓ ↓
t-channel
e+
>
γ/Z*
e­
φ­
e­
>
φ＋
10
1
+ -
>
φ＋
>
e+
+
-
e+ e− → φ+ φ−
σ(e e ->H H ) [fb]
s-channel
α
NR
φ­
0
10 0
1000
2000
3000
√s [GeV]
- s-channel + t-channel exchange of NR.
- The t-channel effects show specific dependences on the √s in the production
Atwood, Bar- Shalom, Soni, PRD76 (2007)
cross section.
- The contribution of t-channel diagrams is one of the discriminative features
of radiative seesaw models.
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Electron-positron collisions
v
Aoki-Kanemura-Seto model
v
η
#0
mH ± = 100 GeV, mS ± = 400 GeV, m⌘ = 50 GeV, M = 5 TeV
H"
!Li
H"
e!R i
e+ e- → S+ S- →H+ H- η0η0 →ττννη0η0
signal : τ+τ- + /E
!Lj
S" S"
e"R j
NR
S±
κ
H±
η0
τ
ν
Br~100%
- Since the signal dominantly comes from the t-channel diagram, it becomes larger for larger √s.
- √s=1 TeV with Lum=500 fb-1, S/√B= 12.8
- √s scan helps to confirm that the signal rate comes from the t-channel diagrams.
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Electron-electron collisions
- The ILC has a further advantage to test radiative seesaw models via
the experiment at the e-e- collision option.
e−e− collision option
v
e− e− → φ− φ−
e­
H"
yi
!Li
α
NR
e­
⇥(e e ⇥ S S ) =
＞
⇧
dt
tmin
S" S"
e"R i
1
128 s
2
⌅
=1
(|he |2 mNR )
⇥
t
κ
H"
yj
!Lj
e"R j
hi !
φ­
tmax
η
#0
κ
φ­
＞
v
!
c ! hj
NR
1
+
2
mN
u
R
1
m2N
R
⇤
2
- D=5 operator, e-e-φ+φ+, is the sub-diagram of the loop diagrams for ν mass.
Direct test of the radiative seesaw models.
- Due to the Majorana nature of the t-channel diagram, we obtain much
larger cross section in the e-e- collision than in the e+e- collision.
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Electron-electron collisions
"
●
e− e− → φ− φ−
ILC
Zee-Babu model:
mκ++=1200GeV
mω+=300GeV
ω-ω- (→*-*-νν)
5
10
Cross section [fb]
4
10
10
AKS e e
!l
e!L k e!R k eR eL! l
i
fik
500
1000
s [GeV]
v
gee~0.2
SS
WW
κ­­
e­
e e
1500
v
Exploring the dark sector
●
η0
#
κ
!Li
H"
yi
κ
S" S"
e"R i
H"
yj
e"R j
hi !
March. 17, 2015
ω­
v
!
c ! hj
NR
- The signal in the AKS model and the Zee-Babu model can be observed.
- The e-e- collision experiment is useful to test the Majorana nature of
radiative seesaw models.
Mayumi Aoki
ω­
~800GeV
AKS model:
2
SM e e
fjl
g’kl
v
mNR=5TeV
ms+=400GeV
S-S- (→τ-τ-ννηη)
1
!!
k!!
e­
10
10
"L
Zee-Babu e e
3
!!
!Lj
"
Various Variations
New Symmetry
- Z2, SUSY, Z3, Z4, ……
- Accidental (Residual) symmetry of local/global U(1) symmetry, flavor symmetry, …
ex)
The Z2 symmetry is the residual symmetry of a spontaneous broken U(1) symmetry.
U(1)0
Z2
Q↵
2q
+1
Ū↵
2q
+1
D̄↵
2q
+1
L↵
0
+1
Ē↵
0
+1
N̄1
0
+1
N̄2
q
1
H
0
+1
⌘
q
1
Kubo, Suematsu, PLB643 (2006)
2q
+1
- φ : singlet scalar
- non-renormalizable term φ(η†H)2+h.c.
Residual symmetry of local U(1)’
- The neutrino mass is generated by both the Type-I seesaw with N1 and the one-loop radiative
seesaw of Ma model with N2.
Topology
E.Ma, PLB662(2008) etc
Gustafsson, No, Rivera, PRL110(2013) etc
Baek, Okada, Toma, PLB732 (2014) etc
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Kajiyama, Okada, Yagyu, JHEP10 (2013) etc
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Multicomponent DM
If the DM stabilizing symmetry is larger than Z2 , a multicomponent
DM system can be realized.
e.g.) ● Model with Z2 × Z2’
Z2
Z2’
χ1
−
+
2 stable particles
χ2
+
−
3 stable particles
χ3
−
−
m3 > m2 > m1
- m3 > m1 +m2
χ3 →χ1 χ2
- m3 < m1 +m2
● Model with Z4 symmetry
- m2 > m1 +m1
χ2 →χ1 χ1
X2 (Z4=2)
1 stable particle
- m2 < m1 +m1
2 stable particles
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X1 (Z4=1)
X1* (Z4=−1)
SM (Z4=0)
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21
Multicomponent DM
- In the single-component WIMP case, the DM remains by pair annihilation into SM particles.
- The DM relic abundance is roughly related to the pair annihilation cross section at freezeout.
Standard annihilation
χ χ →XSM XSM
WIMP DM:
XSM
χ
XSM
2
|v|i(n
!XSM XSM
h
ṅ + 3Hn =
χ
n̄2 )
<σWIMPv> ~ 10-9 GeV-2
0h2 ~ 0.12
Multicomponent DM
Boehm, Fayet and Silk, PRD69 (2004); D’Eramo and Thaler, JHEP 1006 (2010); Belanger et al,
JCAP 1204 (2012), arXiv:1403.4960 [hep-ph]; Ivanov and Keus, Phys. Rev. D 86, (2012), etc.
DM conversion
Semi-annihilation
χiχi →χjχj
χiχj →χkXSM
χi
χj
χi
χk
χi
χj
χj
XSM
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Multicomponent DM
Example:
Z2
● χ1
● χ2
● χ3
m1=200 GeV, m2=160 GeV, m3=140 GeV
<σv> ( ×10-9 GeV-2)
●●→XSMXSM 0.1
●●→X
2
SMXSM
Standard
10
●●→XSMXSM 6
●●→●XSM
Semi●●→●XSM
annihilation
●●→●XSM
0
0
0
2
0
0
0
−
−
−
Standard only
χ1
1
0hh2
●●→●●
●●→●●
●●→●●
+
Evolution of 0h2
10
DM
Conversion
−
Z2’
+
11
χ2
2
0.10.1
0.01
0.01
0
3
χ3
10
20
30
40
50
50
x
60
70
x=*/T
80
90
100
100
1/*=Σimi-1
0h2 =0χ1h2+0χ2h2+0χ3h2 > 0h2obs~0.12
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Multicomponent DM
Example:
Z2
● χ1
● χ2
● χ3
m1=200 GeV, m2=160 GeV, m3=140 GeV
<σv> ( ×10-9 GeV-2)
●●→XSMXSM 0.1
●●→X
2
SMXSM
Standard
10
●●→XSMXSM 6
−
Z2’
+
+
−
−
−
Evolution of 0h2
●●→●XSM
Semi●●→●XSM
annihilation
●●→●XSM
5.2
5.2
5.2
0
0
0
2
●●→●●
●●→●●
●●→●●
h
DM
Conversion
0h2
10
Standard + Conversion
11
0.10.1
0.01
0.01
0
10
20
30
40
50
50
x
60
70
80
x=*/T
90
100
100
0h2tot ~ 0.12
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Multicomponent DM
Example:
Z2
● χ1
● χ2
● χ3
m1=200 GeV, m2=160 GeV, m3=140 GeV
<σv> ( ×10-9 GeV-2)
●●→XSMXSM 0.1
●●→X
2
SMXSM
Standard
●●→XSMXSM 6
10
●●→●XSM
Semi●●→●XSM
annihilation
●●→●XSM
5.1
5.1
5.1
2
−
−
−
Standard
+ Semi-annihilation
1
0hh2
DM
Conversion
0
0
0
+
Evolution of 0h2
10
●●→●●
●●→●●
●●→●●
−
Z2’
+
1
0.1
0.1
0.01
0.01
0.001
0
0
10
20
30
40
50
50
x
60
70
x=*/T
80
90
100
100
0h2tot ~ 0.12
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Multicomponent DM
Standard annihilation
χ χ →XSM XSM
χ
XSM
χ
XSM
Model with Z3 symmetry
Multicomponent DM
Semi-annihilation
DM conversion
χiχi →χjχj
Semi-annihilation
χiχj →χkXSM
χi
χj
χi
χk
χ
χ
χj
χj
XSM
χ
XSM
χi
χ χ →χ† XSM
D’Eramo, Thaler, JHEP06 (2010), Belanger et al,
JCAP04(2012), Belanger et al, JCAP01(2013), Ko, Tang,
JCAP05 (2014), JCAP01 (2015), M.A., Toma, JCAP09
(2014), Guo et al, arXiv:1502.00508 [hep-ph]. etc.
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Radiative Seesaw Model with Z3
E.Ma, PLB662 (2008)
｛
SM+
V = µ2
+
†
+ µ2⌘ ⌘ † ⌘ + µ2
†
3
✓
+ µ
0
⌘† ⌘ +
†
⌘
†
4
00
µ
+
3!
†
+
⌘
2
1/2
1
2/3
i
Dirac fermions
ψi
Inert doublet scalar η
Inert singlet scalar χ
SU (2)
U (1)Y
Z3
L number
1
†
4
†
⌘ ⌘† +
◆
3
+ h.c.
2
+
2
1
0
1
1/3
⌘† ⌘
4
†
2
+
†
4
+
1
0
1
2/3
2
†
⌘† ⌘
⌘
†
- At least two ψ are required.
- <η>=<χ>=0
- L is softly broken in the scalar potential.
- Dark Matter
Dirac fermion
'L
1 or Complex scalar ✓
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0
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◆
=
✓
cos ↵
sin ↵
sin ↵
cos ↵
◆✓
'H
'L
March. 17, 2015
◆
,
27
Radiative Seesaw Model with Z3
Standard annihilation
M.A,, Toma JCAP1409 (2014)
Semi-annihilation
! ``, ⌫⌫
! ⌫ , h'† , Z'†
Yν
Yν
Yν
mL = 400 GeV, mH = 500 GeV
106
10
sin α = 0.1
sin α = 0.5
sin α = 0.9
Ωh2 = 0.12
5
104
BM-F1
Ωh2
103
10
2
10
1
Yν =0.01
2
=
=
⌘
=
= 0.1,
3
=
4
= 0.5, m2 = 1 TeV.
µ00 sin2 ↵ = 100 MeV
100
- Damps at mψ=mL/2 and mH/2.
- Semi-annihilations are important.
10−1
10
−2
10−3
10−4
100
150
Mayumi Aoki
200
250
mψ [GeV]
300
350
400
Exploring the dark sector
March. 17, 2015
28
Radiative seesaw model with
Multicomponent DM
M.A., Kubo, Takano, PRD90 (2014)
We study the multicomponent DM system in the extended Ma model.
Mayumi Aoki
Exploring the dark sector
March. 17, 2015
29
Ma model
v
SM+N R + η
field
(⌫Li , li )
lic
Nic
H = (H + , H 0 )
⌘ = (⌘ + , ⌘ 0 )
SU (2)L
2
1
1
2
2
U (1)Y
1/2
1
0
1/2
1/2
- Inert doublet scalar
- Relevant Lagrangian
L=
Yik⌫ Li ✏⌘Nkc
- Single component DM
Mayumi Aoki
Z2
+
+
η0
νL i
⌘=

v
η0
+
✓
Ma, PRD73, 077301 (2006)
νL j
cα
NR
+
⌘
p
0
0
(⌘R + i⌘I )/ 2
1
1
c
c
Mk NRk NRk +
2
2
◆
,
h⌘i = 0
† 2
(H
⌘) + h.c.
5
NR, η0R or η0I
Exploring the dark sector
March. 17, 2015
30
Ma model
● Neutrino masses
(M⌫ )ij =
X
k
⌫
Yik⌫ Yjk
Mk
16⇡ 2
"
m2⌘0
R
m2⌘0
R
Mk2
ln
✓
m⌘R0
Mk
◆2
2
2
5 v =m⌘R
m20 =
m2⌘I
Mk2
m2⌘0
I
ln
✓
m⌘I0
Mk
v
◆2 #
0
- small λ5 case (λ5v << m0)
2
m2⌘0
I
m2⌘0 + m2⌘0
8
<
Yik Yjk 5 v 2
Mk
1
(M⌫ )ij '
8⇡ 2
m20 Mk2 :
R
L
I
2
Mk2
m20
Mk2
ln
m20
Mk2
v
λ5
0
i
L
c
NR
9
=
;
Mν = 0.1 eV, New masses ~O(100) GeV → |Yν Yν λ5 |~ 10-10
● Lepton Flavor Violation :
- *→eγ constraint :
B(%→eγ)exp ≲ 5.7×10-13
+
η
#+
MEG(2013)
YνYν ≲ 10-4
Mayumi Aoki
Exploring the dark sector
#
!
NR
"γ
ee
NR
March. 17, 2015
31
j
Ma model
● Dark Matter (single component)
NR, η0R or η0I
η DM :
η0R
XSM
η0R
XSM
η0R
h
η0R
h
χ
XSM
χ
XSM
η0R
h
h
•••
η0R
h
Two mass regions of DM consistent with the data.
- low-mass region ( 50 GeV < mη < 70 GeV)
- high-mass region ( > 600 GeV)
Lopez Honorez et al., JCAP0702(2007);
Gustafsson et al. PRD86 (2012) , Arhrib et al
JCAP1406(2014), Abe et al, arXiv:1411.1335
NR DM :
L
N
0h2 ~ 0.12 → Yν Yν 1
η
Kubo et al. PLB642 (2006)
LFV constraints → Yν Yν ≲ 10-4 → 0h2 >> 0.12
N
-L
In our model, this tension is relaxed by multicomponent DM system.
Mayumi Aoki
Exploring the dark sector
March. 17, 2015
32
Model
Two-loop radiative seesaw model
field
(⌫L , lL )
c
lR
NRc
H = (H + , H 0 )
⌘ = (⌘ + , ⌘ 0 )
SU (2)L
2
1
1
2
2
1
1
U (1)Y
1/2
1
0
1/2
1/2
0
0
Z2
+
+
+
+
Z20
+
+
+
+
+
L
1
1
0
0
1
0
1
M.A., Kubo, Takano, PRD90 (2014)
v
κ
η0
νLi
χ : singlet real scalar
φ: singlet complex
scalar
p
=(
R
+i
I )/
φ
v
κ
χ
η0
cα
NR
νLj
2.
• The λ5 term , λ5 (H†η)2+h.c., in Ma model is forbidden by #L.
• The λ5eff is generated at the 1-loop level.
•New relevant terms for neutrino mass :
⇤ 1 2
⇥ †
V
(H ⌘) + h.c. + m5 [
2
2
• #L is softly violated at m52 term.
2
+(
⇤ 2
) ]
• mηR = mηI at the tree level. The degeneracy is lifted by λ5eff.
• DM candidates are
N, η0R/I, χ, φR/I
(Z2, Z2’) = (−,+), (+,−), (−,−)
Mayumi Aoki
Exploring the dark sector
Multicomponent DM system
→ N, χ , φR
March. 17, 2015
33
Neutrino mass
● Neutrino mass
(M⌫ )ij '
e↵ 2
5 vh
8⇡ 2
X
k
v
⌫
Yik⌫ Yjk
Mk
m2⌘0 Mk2
"
Mk2
1
m2⌘0
Mk2
ln
m2⌘0
Mk2
#
.
m⌘0 = m⌘R0 ' m⌘I0
v
φ
χ
η0
νLi
η0
νLj
cα
NR
λ5eff term (for m52 = mφR2 - mφI2 << mφR2 )
e↵ '
5
2
m25

64⇡ 2 m2 R
m2
"
2
1
m
m2 R
2
m R
ln 2
m2
m
#
v
v
λ5eff
0
0
L
i
c
N
- The neutrino mass is proportional to |Yν κ|2 m52.
- Mν = 0.1 eV, New physical masses ~O(100) GeV → κYν m5 ~ 10-2 GeV
L
j
R
- κ~0.1, Yν~0.01 → m5 ~ 10 GeV,
Mayumi Aoki
λ5eff ~10-5
Exploring the dark sector
March. 17, 2015
34
Dark matter
We assume NR, χ and φR are the DM.
Three-component DM system.
DM annihilation processes:
We assume mφ > mχ .
Standard annihilation : N N ! XX 0 ,
DM conversion :
R R
Semiannihilation : N
R
!
R R
,
! ⌫,
N!
- Annihilation processes of φI
Standard annihilation :
I
I
DM conversion :
I
I
Semiannihilation : N
I
! XX 0 ,
R ⌫,
! N ⌫,
- Conversion between φI⇄φR
! XX 0 ,
!
R
! XX 0 ,
,
! ⌫,
χ
φR
φI
ηR0
N!
I ⌫,
I
! N ⌫.
SM
ηI0
Z
SM
- We sum up the number densities of φI and φR, nφ = nφI + nφR , and solve the
Boltzmann equation of nN , nφ and nχ .
Mayumi Aoki
Exploring the dark sector
March. 17, 2015
35
Dark matter
Standard
l+/ν
Yν
N
0
η +/ηR,I
N
Wh−, Z φR,I , χ
hf
χ
Wh+, Z φR,I , χ
,χ
φφR,I
,χ
R,I
φR,I
χ
γ7
χ
φR,I
χ
φR,I
Semi-annihilation:
0
ηR,I
N
κ
ν
χ
N
0
ηR,I
χ
Exploring the dark sector
χ
φR,I
Yν
ν
χ
φR,I
χ
0
ηR,I
N
- In the Ma model, the 0Nh2 tends to be larger than 0.12.
However, in this model, the contribution from the semiannihilation can enhance the annihilation rate for NR .
- The tension between the constraints of LFV and 0Nh2
becomes mild.
Mayumi Aoki
h
0
ηR,I
φR,I
φR,I
...
φR,I , χ
h
φR,I
h
hh
φR,I
, χ, χ
φR,I
φR,I
DM Conversion:
,χ
R,I
,χ
φφR,I
h
γ5,γ2
l−/ν
Yν
hf¯
φR,I
, χ, χ
φR,I
ν
N1 N1 Semi-ann.
φφ
χχ
SM
March. 17, 2015
36
Relic abundance
Benchmark Point
M1
m⌘R0
m I
m R
⌘ 2,5,7

Y⌫
50 GeV
300 GeV
m + m R 10 GeV
m + 60 GeV
m + 50 GeV
0.1
0.4
0.01
χ
h2
||
ηR,ηI
- Semi-annihilation tends to decrease 0Nh2.
- 0h2~0.12
→ γ=0.1,
0
0totaltotal
h2h2
-1
0φhh
22
0χ h
22
0 Nh
Nh
140
160
180
Mayumi Aoki
200 220 240
m [GeV]
260
mχ~200 GeV
Scalar DM
φ
mφ~250GeV, 260 GeV
mN=300GeV
h2 2
10-2
10-3
φI
1 TeV
|
N2, N3
•Neutrino mass scale
•Vacuum stability
•Perturbativity | i |, | i |, || < 1
101
10
φR
300 GeV
|
N1
- The mχ, mφR, mφI are varied with a fixed mass deference.
102
10
10 GeV
280
300
→ γ ≳ 0.2, mχ~220 GeV
Exploring the dark sector
η0R
N DM
mφ~250GeV, 260 GeV
mN=300GeV
March. 17, 2015
N
37
Direct detection
- The current upper bound for the DM-nucleon cross section is estimated assuming
the single component DM scenario.
Constraint on the detection rate in the multicomponent DM scenario.
effective cross section :
Our model
e↵
i
=
i
✓
2
⌦i h
⌦total h2
◆
χ, φR
h
- χ and φR have interactions to the quarks.
e↵
=
✓
The γ is changed so as to realize the
2
⌦ h
⌦tot h2
◆
0totalh2~0.12
) [cm2]
R
⌦ Rh
⌦tot h2
◆
0h2=0.12.
- At mχ=220 (380) GeV for M1=300 (500)GeV
→ large γ , small 0χ,φ
10
- The obtained cross section is accessible to
XENON1ton.
XENON100
LUX
10
Mayumi Aoki
-44
eff(
R
=
2
q
)+
e↵
✓
q
eff(
- The effective cross sections :
γ2, γ5/2 χ, φ
R
Exploring the dark sector
-45
100
M1 = 300 GeV
150
200
M1 = 500 GeV
250
m [GeV]
March. 17, 2015
300
350
400
38
Indirect detection
Cosmic ray from the DM annihilation.
Indirect signals
DM
We discuss the neutrinos from the annihilation of captured DM in the Sun.
ν
IceCUBE
Semi-annihilation
φ
In our model, the semi-annihilation
process produces
a monochromatic neutrino.
Mayumi Aoki
φR
ηR
χ
Exploring the dark sector
N
η0
ν
νLi
March. 17, 2015
χ
η0
cα
NR
νLj
39
Indirect detection
Single component DM : χ
- Time evolution of nχ in the Sun
nχ : Number of DM in the Sun
C : Capture rate in the Sun.
CA : Annihilation rate CA=<σv>/Veff
ṅ = C
C A n2
χ
χ
SM
χ
SM
q
χ
q
0
$ XX ) =
CA (
! XX 0 )v >
Ve↵
< (
Veff : Effective Volume of the Sun
Veft = 5.7 ⇥ 1027
✓
100 GeV
m
- At the time of birth of the Sun the nχ were zero.
- The nχ increase with time and approach the fixed point values.
◆3/2
cm3
Fixed point at C=CA nχ2
→ equilibrium → The number of DM reaches its maximal value.
- DM annihilation rate :
Γ = CA nχ2/2 = C/2
- Neutrino production rate :
Γν = 2Γ Br(χχ→XX’νν)
Mayumi Aoki
Exploring the dark sector
March. 17, 2015
40
TABLE I. data
Results
the combination
independent
sets. Th
om the combination of the three independent
sets. from
The upper
90% limits of
onthe
thethree
number
of signal data
events
, the
WIMP
annihilation
Sun !A , the muon
flux "
neutrino flu
ation rate in the Sun !A , the muon flux
neutrino
flux "" ,rate
andin
thethe
WIMP-proton
scattering
cross
sections
$90
$ and
$ and
s"
# $ (seelevel,
(spin
independent,
dependent,errors.
!SD;p )The
at the
90% confidence
confidence
level,!including
sensitivity
"
the incl
SI;p ; spin systematic
p ; spin dependent, !SD;p ) at the 90%
text) is shown for comparison.
parison.
Indirect detection
!A
IceCUBE (2013)
(s"1 )
$90
s
#m$%
"
"$
"2 "1
(GeV=c
(km"2
y"1 ) 2 ) (kmChannel
y )
#$
"
!A
""
!SI;p
!SD;p "$
"2 "1
2
$90
(km
y ) (s"1 ) (cm2 )(km"2 y"1 ) (cm(km
) "2 y"1 )
s
"4
9:27 &$þ &10
"4
1:21 &$þ &10
# 5
1:04 $bb10
"3
2:84 &$þ &10
# 4
1:80 $bb10
1:19W$þ W
10"3
# 3
5:91 $bb10
4:15W$þ W
10"2
# 3
1:45 $bb10
2:23W$þ W
10"2
# 3
1:02 $bb10
1:85W$þ W
10"2
# 2
5:99 $bb10
1:66W$þ W
10"2
# 2
3:47 $bb10
1:58W$þ W
10"2
# 2
3:26 $bb10
4
15
"40
162 $ 102:46
$ 1:08
1025 $ 105:26
$ 10
2:35
1:29
$ 9:27
10"38$ 104
4
14
"42
70.2 $ 101:03
$ 6:59
1024 $ 101:03
$ 10
1:02
1:28
$ 1:21
10"39$ 104
4
15
"39
128 $ 101:99
$ 1:28
1026 $ 105:63
$ 10
6:29
2:49
$ 1:04
10"37$ 105
3
13
"42 $ 10
19.6 $ 101:20
$ 1:03
1023 $ 104:82
1:17
2:70
$ 2:84
10"40$ 103
4
14
"40 $ 10
55.2 $ 101:75
$ 1:51
1025 $ 102:06
5:64
3:96
$ 1:80
10"38$ 104
3
12
"43 $ 10
16.8 $ 103:35
$ 6:01
1022 $ 101:49
1:23
2:68
$ 1:19
10"40$ 103
3
13
"41 $ 10
28.9 $ 101:82
$ 3:30
1024 $ 107:57
6:34
1:47
$ 5:91
10"38$ 103
2
10
"43 $ 10
29.9 $ 102:85
$ 1:67
1021 $ 103:04
9:72
1:34
$ 4:15
10"40$ 102
3
12
"42 $ 10
19.8 $ 101:27
$ 7:37
1023 $ 101:85
4:59
5:90
$ 1:45
10"39$ 103
2
10
"43
25.2 $ 108:57
$ 1:45
1020 $ 101:46
$ 10
2:61
1:57
$ 2:23
10"40$ 102
2
12
"42
30.6 $ 104:12
$ 6:98
1022 $ 108:53
$ 10
1:52
7:56
$ 1:02
10"39$ 103
2
10
"43
23.4 $ 106:13
$ 3:46
1020 $ 101:19
$ 10
1:62
4:48
$ 1:85
10"40$ 102
2
11
"42
30.4 $ 101:39
$ 7:75
1022 $ 104:33
$ 10
5:23
1:00
$ 5:99
10"38$ 102
2
10
"42
22.2 $ 107:79
$ 3:44
1020 $ 101:09
$ 10
1:65
5:02
$ 1:66
10"39$ 102
2
11
"41 $ 10
26.1 $ 104:88
$ 2:17
1021 $ 102:52
1:89
3:16
$ 3:47
10"38$ 102
2
10
"41 $ 10
22.8 $ 108:79
$ 1:06
1020 $ 101:01
1:77
1:59
$ 1:58
10"38$ 102
2
11
"41 $ 10
26.4 $ 106:50
$ 4:89
1020 $ 102:21
1:63
7:29
$ 3:26
10"38$ 102
IceCube Collaboration
25 131302
Phys.Rev.Lett.
110 (2013)
162
2:46
$ 1013,
5:26 20
$ 104
1:03 $ 1024
1:03 35
$ 104
26
WW
XX’νν
1:99→
$ 10
5:63 35
$ 104
1:20 $ 1023
4:82 50
$ 103
1:75 $ 1025
2:06 50
$ 104
3:35 $ 1022
1:49 100
$ 103
1:82 $ 1024
7:57 100
$ 103
2:85 $ 1021
3:04 250
$ 102
1:27 $ 1023
1:85 250
$ 103
8:57 $ 1020
1:46 500
$ 102
4:12 $ 1022
8:53 500
$ 102
6:13 $ 1020
1:19 1000
$ 102
1:39 $ 1022
4:33 1000
$ 102
7:79 $ 1020
1:09 3000
$ 102
4:88 $ 1021
2:52 3000
$ 102
8:79 $ 1020
1:01 5000
$ 102
6:50 $ 1020
2:21 5000
$ 102
70.2
χχ→
128
19.6
55.2
16.8
28.9
29.9
19.8
25.2
30.6
23.4
30.4
22.2
26.1
22.8
26.4
-38
MSSM incl. XENON (2012) ATLAS + CMS (2012)
DAMA no channeling (2008)
CDMS (2010)
CDMS 2keV reanalyzed (2011)
CoGENT (2010)
XENON100 (2012)
log10 (
-42
-43
-44
IceCube 2012 (bb)
-45
+
(
-46
+ -
-
IceCube 2012 (W W )
for m <mW = 80.4GeV/c2)
1
/ cm2 )
-41
-36
SD,p
SI,p
/ cm2 )
-40
log10 (
-39
2
3
4
SUPER-K (2011) (b b)
+ SUPER-K (2011) (W W )
-37
-38
-39
IceCube 2012 (bb)
+
-
IceCube 2012 (W W )
-40
log10 ( m / GeV c-2 )
MSSM incl. XENON (2012) ATLAS + CMS (2012)
DAMA no channeling (2008)
COUPP (2012)
Simple (2011)
PICASSO (2012)
-35
(
+ -
for m <mW = 80.4GeV/c2)
1
2
3
4
The
Theinupper
limits on $scross
Uncertainties
neutrino-nucleon
sections
forhypothesis
sigeutrino-nucleon cross sections for sigfor each
signal
are upp
nal
simulations
arise in thetoparametrization
of the CTEQ6then 41
conve
in the parametrization
of the CTEQ6then converted
limits on the
neutrino
to muon converMayumi Aoki Exploring the dark sector
March. 17, 2015
distribution
used in NUSIGMA
sion
on functions as used in NUSIGMADIS
rate and,functions
throughasDarkSUSY
[9], to[24].
limits on
therate a
[24].partonsion
log10 ( m / GeV c-2 )
Indirect detection
Multicomponent DM : φR, χ, NR
ṅi = Ci
CA (ii ! SM)n2i
Standard
X
mi >mj
CA (ii ! jj)n2i
CA (ij ! k⌫)ni nj
Conversion
Semi-annihilation
φR
- Since CN=0, the nN cannot increase.
- φχ→Nν is the only ν production process.
⌫
=
2
/(4⇡R
)
⌫
R : the distance to the Sun
- The IceCUBE limit is at least 103 times
larger than these results.
(1,300)
10
Exploring the dark sector
(m
0
R
-(m +m ) , M1)=(1,500)[GeV]
R
8
107
106
(10,300)
(10,500)
105
104
Mayumi Aoki
ν
109
Neutrino Flux [km-2year-1]
- Neutrino flux :
! N ⌫)n n
= CA (
ηR
χ
- Monochromatic ν production rate :
⌫
N
150
200
250
300
350
m [GeV]
March. 17, 2015
400
450
500
42
Summary
- The origin of neutrino masses and the nature of dark matter are two
in pressing open questions.
- It would be interesting to consider the possibility in which these two
problems are related.
- Radiative seesaw model with DM
• Symmetry
→ guarantees the radiative neutrino mass and the stability of the DM.
• The model has a predictive power.
- Radiative seesaw model with multicomponent DM
• Two-loop extension of the Ma model
Three-component (N, χ, φR) DM system
- 0Nh2 is reduced by the semi-annihilation processes.
- The predicted σSI will be covered by XENON1T.
- The monochromatic neutrino is produced by the semi-annihilation.
- The neutrino flux from the Sun is enhanced by the resonant effect.
Mayumi Aoki
Exploring the dark sector
March. 17, 2015
43