Axion-DM 理論
July 5 2019 @ダークマター懇談会

高橋

史宜

（東北大）

1.導入

‣ ダークマターは新しい物理の直接的証拠‣ ダークマターは✓(i)冷たい（構造形成時に非相対論的）✓(ii)現在の宇宙のエネルギーの約1/4✓(iii)とても長生き⌧DM & 175 Gyr<latexit sha1_base64="p/8R/VjIWM1iVKDfFF8BclcmB8w=">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</latexit>

K. Enqvist, S. Nadathur, T. Sekiguchi and T. Takahashi,
arXiv:1906.09112 [astro-ph.CO].

(i),(ii): ダークマターの生成過程，宇宙の熱史に依る(iii): ダークマター粒子の性質で決まる．

✓なぜとても長生き？
•対称性で崩壊が禁止ないし抑制．
•とても相互作用が弱い．
•とても軽い．

✓なぜとても軽い？
•対称性で質量が抑制
例：pNG boson (axion), シフト対称性
sterile neutrino, カイラル対称性
hidden photon, ゲージ対称性

以下，ダークマター候補のアクシオンを考える．

2. QCDアクシオンとALP- QCDアクシオンは標準理論を超える新しい物理の有力な候補の一つ．
• 強いCP問題をダイナミカルに解決
Peccei, Quinn ̀77, Weinberg ̀78, Wilczek ̀78• ダークマターを説明可能
Preskill, Wise, Wilczek ̀83, Abbott, Sikivie, ̀83, Dine, Fischler, ̀83- Axion-like particle (ALPs)も同様にダークマター候補T ⌧ ⇤QCD

T

⇤QCD
✓i

a/fa

２つの大事なパラメター

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質量

軽ければ安定で

fa<latexit sha1_base64="8VWxl8waxMkjJPt3qPvZr8C/DN8=">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</latexit>

崩壊定数
相互作用の強さ / 1/fa
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DMに寄与

初期振幅を決めるのに大事．

どちらもアクシオンDMの存在量を決めるのに重要．

QCD axion

ALP

mφ / mama (T ) / ma
0

0

0

00

φL

aL
High TT0 ⟶T ⌧ ⇤QCD

massとHubbleがcomparableになると振動開始．

Low T

T

⇤QCD
✓i

a

a/fa

アクシオンの存在量
QCDアクシオン

⌦a h

2

2
' 0.14 ✓⇤<latexit sha1_base64="udty1hidEbKuEVkV9cYburm5vbU=">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</latexit>✓fa1012 GeV◆1.17“Classical axion window”: 108 GeV . fa . 1012 GeV<latexit sha1_base64="Jp6A6ifyvZK1KKUwV76HVl5Tn+Q=">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</latexit>

ALP

⌦' h
<latexit sha1_base64="WrQNJul6y/2mG5FKj4n2XHIqaEY=">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</latexit>2' 0.3 ✓⇤2⇣ m ⌘1/2 ✓
'

1 eV

f'
1012 GeV◆2

QCDアクシオンの相互作用•Gluonsa ↵sa ↵sa
LaGG = NDWGaµ⌫ G̃µ⌫ =Gaµ⌫ G̃aµ⌫
Fa 8⇡
fa 8⇡

Fa
deﬁnes the axion decay constant fa =. NDW: domain wall number
NDW
Identiﬁed(NDW=3)aFigure taken from 1210.3196

Hadronic/KSVZ axion
Kim ̀79, Shifman, Vainshtein, and Zakharov ̀80

DFSZ axion
Dine, Fischler, and Srednicki ̀81, Zhitnitsky ̀80

Yet unknown heavy

Ordinary SM quarks

quarks run in the loop.

run in the loop.

NDW = 3 or 6.

N.B. Both heavy and SM quarks, or only a part of SM quarks may run in the loop,
which help to avoid the domain wall problem by NDW = 1.

アクシオンの相互作用•Photons
La
ga

ga
=
aFµ⌫ F̃µ⌫ =
4
=

↵
2⇡fa

✓

E
N

◆
1.9

~ ·B
~
aE

ga

E and N are EM and color anomaly factorsof the PQ current.

•Electrons
Ce
Laee =@µ a ¯ e µ 5
2fa

C e megaee ⌘
fa

e

cos2
Ce =
3

=

igaee a ( ¯ e 5e) + · · ·for DFSZ axion.

Model-dependent. Coupling to electrons appear
only at loop-level in the hadronic axion.

•NucleonsX CN
LaN N =@µ a ¯ N µ 5
2fa
N =p,n

N

ga

c ↵
=
⇡fa

c =

X

<latexit sha1_base64="AuMLuLcwhz88SUD/aersqAa5dSw=">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</latexit>qi Q2ii

Taken from ̀Physics Beyond Colliders at CERN: Beyond the Standard Model Working Group Report,ʼ'arXiv:1901.09966 [hep-ex].

私の3. 最近のトピック

Topic 1: それは微調整ですか？
QCD axionはこの領域でとても軽い．
つまりfaが大きい．

⌦a h

2

' 0.14 ✓⇤2<latexit sha1_base64="udty1hidEbKuEVkV9cYburm5vbU=">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</latexit>✓fa1012 GeV◆1.17

fa=1016-17 GeVだとDMの存在量に合わせるためには，
初期振幅をO(10-3)くらいに小さくしないといけない．

cf.

物理学者の総数
地球上の総人口〜 10-4

Physics Today 17 Apr. 2015, “One Million Physicists”

Topic 1: それは微調整ですか？
実は，「自然な」初期値はインフレーションスケールに依存する．

1 2 2
V= m ϕ
2

Hinf
δϕ =
2π

ϕ

2
∼ Hinf/m

典型的な初期振幅は

2
Hinf
✓⇤ ⇠
ma (TGH )fa<latexit sha1_base64="CIzse/+D2REkNTHlbQUqJu4Ry3c=">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</latexit>

１より小さくなりうる．

となり，

The upper bound of the QCD axion window can be relaxedin low-scale inﬂation with Hinf ≲ ΛQCD .
Peter W. Graham, Adam Scherlis, 1805.07362,
FT, Wen Yin, Alan H. Guth, 1805.08763

Conventional axion
window, fa ≲ 1012 GeV

Hinf [GeV]

10

●

◆

■

θi = 1

θi = 0.1▲

θi = 0.01“Bunch-Davis distribution”

θrms =

1

0.1

0.01

2
Hinf
3
8π 2 fama(Tinf )

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▲
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■
i
◆
■
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◆
■
i
◆
■
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◆◆
■■
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◆◆
■■
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■
◆◆
■
r
m
●●
■
◆◆
s
r
■
ms
●●
■■
◆
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■
■■
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■
●●
■■
i
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■■
rms
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■
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●

θ ≃

θ =θ

0.126

θ

θ ≃

0.012

5θ

(10 %

tunin

g)

(1 %

tunin

g)

The axion window opens up to large fa

12

10

13

10

14

10

15

10

fa [GeV]

16

10

17

10

18

10

FT, Wen Yin, Alan H. Guth, 1805.08763

Topic 2:とにかく減らしたい

faがGUTスケールくらい大きいとアクシオンの量が多すぎる傾向．
減らす方法はいろいろ知られている．
• エントロピーを生成して薄める• Hidden monopoleを使ってWitten効果• Hidden photon生成
See Kitajimaʼs talketc.

QCDアクシオンをそれより軽い
ALPに転換させることが可能．
Kitajima and FT 1411.2011, Daido, Kitajima, and FT 1505.07670, 1510.06675,
Ho, Saikawa, and FT 1806.09551

QCD axion

mφ / mama (T ) / ma
0

0

0

00

φL

aL
High T

T0 ⟶

Low T

QCD axion + ALP with mφ < ma(T = 0)mφ / mama (T ) / ma
0

QCD axion

0

0

00

ALP

φL

aL
High T

T0 ⟶

Low T

QCD axion + ALP with mφ < ma(T = 0) + mass mixingmH (T ) / mamL (T ) / ma
0

0

0

a

a

 L ≃
0

High TaL00

 H  ≃ φL0a

 H ≃0a L  ≃ φL
0

aL
T0 ⟶

Low T

QCD axion + ALP with mφ < ma(T = 0) + mass mixingmH (T ) / mamL (T ) / ma00a

 H ≃

0

0

aL

00

Similar to MSW eﬀect
in neutrino physics!

a H  ≃ φL0a

 L  ≃ φL
0

The comoving number isthe adiabatic inv.

a

 L ≃
0

High T

aL
T0 ⟶

Low T

Axion coupling to photons
Axion-photon couplings (GeV-1 )

10-9

CAST

-10

10

ALPS II
IAXO

10-11
10-12
10-13
10-14

HB

1, Θ0

θ0

0

ΩDM h2 = 0.12

MADMAXADMXADMX (prospects)

ℰ/

0

ℰ/

.12

12

fa = 3 12
× 10 GeV
2 =0hfa /(10 GeV
φ12)
fa = 5 × 10 GeV .s. mΩLa+
v
γ
=
(
3,
5,
10
)
13
γ
f = 10 GeVℊ L
0

10

10-16

/3
8
=

0

0

-15

=0

CULTASK

0a

ABRACADABRA (Broad)

10-17

ALP DM )
<1
θ
0
,
φ
<
5
.
0
(
0

0

0

0

0

10-18

ABRACADABRA (Res)0ℊaγγ v.s. ma
0

10-19
10-11

10-10

10-9

10-8

0

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Axion mass (eV)
ALP coupling to photons can be enhanced by a few orders of magnitude.

Topic 3: ALPでインフラトン
インフラトンもダークマターも電気的に中性で宇宙のエネルギーの支配的成分であった．
V

F

F

Topic 3: ALPでインフラトン

⇢

V

F

Inﬂaton decays and disappears,

F

while DM must be produced

inﬂatonsomehow.

radiation?

DM

Scale factor

Topic 3: ALPでインフラトン
インフラトンもダークマターも電気的に中性で宇宙のエネルギーの支配的成分であった．
V

F

F

ALP inﬂaton = ALP DMg= O(10 11 ) GeV 1“ALP miracle”
Daido, FT and Yin, 1702.03284,1710.11107

IAXO collaboration, 1904.09155

Czerny, FT 1401.5212,
Czerny, Higaki, FT 1403.0410, 1403.5883•Axion hilltop inﬂation

Croon and Sanz, 1411.7809

Low-scale axion inﬂation can be realized with at least two
cosine terms: “Multi-natural inflation”

✓

✓

◆

◆◆

n
Vinf ( ) = ⇤ cos+✓+ const.
f
f
4
4
⇤
⇤
⇤4
4
2
⇠ 4
= V0
✓
+ ( m1) 2 + · · ·The inﬂaton mass at the fminimum,
2f , depends on n. f
4


cos
2
n

✓

<latexit sha1_base64="(null)">(null)</latexit>

Even n

-1

Odd n

1.5

1.5

1.0

1.0

0.5

0.5

0

1

2

3

4

5

-1

0

1

2

3

4

5

Small-scale structure

HDM constraint on

constraint on ALP CDM

thermalized ALP

CAST

10 -10

CDM

Telescopes

10 -9
HB

10 -11 ALPS-II

EBL

CMB τ

n

ax
io

X-ray

10 -14QC
D

10 -13

KS

VZ

10

-12

IAXO

Successful
reheating10 -4 10 -3 10 -2 10 -1 10 0mφ [eV]

10 1

10 2

Su

cc
inﬂ ess
fu
at
ion l

10 3

Telescopes

Inﬂaton = DM = ALP

10 -9
CAST

10 -10HB

10 -11 ALPS-II

axion helioscopes and laser

EBL

ion

VZ

ax

KS

10 -13

X-ray

within the reach of future

CMB τ

D

= O(10 11 ) GeV 1

IAXO

10 -14

QC

g

10

-12

10 -4 10 -3 10 -2 10 -1 10 0

experiments.

mφ [eV]

10 1

10 2

“An ALP miracle”*Plus, there is a preference for extra cooling of HB starsg= (0.29 ± 0.18) ⇥ 10 10 GeV 1

Ayala, Dominguez, Giannotti, Mirizzi and Straniero, 1406.6053, DESY- PROC-2015-02

10 3

4. まとめ•QCDアクシオン，ALPはダークマターの良い候補•どのパラメター領域が良いかは模型次第•よく言う微調整が必要な大きなfaの領域もインフレーションスケールが低ければOK.
•QCDアクシオンとALPのadiabatic conversionが起きると，普通はDMに足りないところでもALP DM可能．
•インフラトンとダークマターの統一模型 (ALP miracle)