Axion-DM 理論

高橋　史宜 （東北大）

July 5 2019 @ダークマター懇談会

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

(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．

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

⌧DM & 175Gyr<latexit sha1_base64="p/8R/VjIWM1iVKDfFF8BclcmB8w=">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</latexit>

✓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．

- 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．

a✓ia/fa

T ⌧ ⇤QCD

T � ⇤QCD

•強いCP問題をダイナミカルに解決

•ダークマターを説明可能Peccei, Quinn `77, Weinberg `78, Wilczek `78

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

2. QCDアクシオンとALP

２つの大事なパラメター

質量 崩壊定数

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

相互作用の強さ / 1/fa<latexit sha1_base64="ys1hZceePpWSi+XQYAbC+lPh4MQ=">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</latexit>

軽ければ安定で DMに寄与

どちらもアクシオンDMの存在量を決めるのに重要．

初期振幅を決めるのに大事．

mφ 0/0mama(T)0/00ma

aL

φL

T0 ⟶High T Low T

QCD axion

a✓ia/fa

T ⌧ ⇤QCD

T � ⇤QCD

massとHubbleがcomparableに なると振動開始．

ALP

アクシオンの存在量QCDアクシオン

ALP

⌦ah2 ' 0.14 ✓2⇤

✓fa

1012 GeV

◆1.17

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⌦'h2 ' 0.3 ✓2⇤

⇣ m'

1 eV

⌘1/2✓

f'1012 GeV

◆2

<latexit sha1_base64="WrQNJul6y/2mG5FKj4n2XHIqaEY=">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</latexit>

“Classical axion window”: 108 GeV . fa . 1012 GeV<latexit sha1_base64="Jp6A6ifyvZK1KKUwV76HVl5Tn+Q=">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</latexit>

•Gluons

defines the axion decay constant 　 . NDW: domain wall number

Figure taken from 1210.3196

Hadronic/KSVZ axion

Yet unknown heavy quarks run in the loop.

DFSZ axion

Ordinary SM quarks run in the loop.

Dine, Fischler, and Srednicki `81, Zhitnitsky `80Kim `79, Shifman, Vainshtein, and Zakharov `80

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.

a

Identified(NDW=3)

LaGG = NDWa

Fa

↵s

8⇡Gaµ⌫G̃

aµ⌫ =

a

fa

↵s

8⇡Gaµ⌫G̃

aµ⌫

NDW = 3 or 6.

fa =Fa

NDW

QCDアクシオンの相互作用

•Photons

•Electrons

•Nucleons

La�� =ga��4

aFµ⌫ F̃µ⌫ = �ga�� a ~E · ~B

ga�� =↵

2⇡fa

✓E

N� 1.9

◆

Laee =Ce

2fa@µa

� ̄e�

µ�5 e

�= �igaeea ( ̄e�5 e) + · · ·

gaee ⌘Ceme

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

LaNN =X

N=p,n

CN

2fa@µa

� ̄N�µ�5 N

�

E and N are EM and color anomaly factors of the PQ current.

アクシオンの相互作用

Ce =cos2 �

3for DFSZ axion.

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

ga� =c�↵

⇡fa<latexit sha1_base64="AuMLuLcwhz88SUD/aersqAa5dSw=">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</latexit>

c� =X

i

qiQ2i

3. 最近のトピック私の

QCD axionはこの領域でとても軽い． つまりfaが大きい．

⌦ah2 ' 0.14 ✓2⇤

✓fa

1012 GeV

◆1.17

<latexit sha1_base64="udty1hidEbKuEVkV9cYburm5vbU=">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</latexit>

Topic 1: それは微調整ですか？

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”

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．

Topic 1: それは微調整ですか？

ϕ

V =12

m2ϕ2

δϕ =Hinf

2π

∼ H2inf /m

典型的な初期振幅は ✓⇤ ⇠ H2

inf

ma(TGH)fa<latexit sha1_base64="CIzse/+D2REkNTHlbQUqJu4Ry3c=">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</latexit>

となり，

１より小さくなりうる．

The axion window opens up to large fa

The upper bound of the QCD axion window can be relaxed in low-scale inflation with .Hinf ≲ ΛQCD

Peter W. Graham, Adam Scherlis, 1805.07362, FT, Wen Yin, Alan H. Guth, 1805.08763

●●●●●●●

●●●●●●●●

●●●●●●●●

●●●●●●●●

●●●●●●●●

●●●●●●●●

●●●

●

■■■■■■■

■■■■■■■■

■■■■■■■■

■■■■■■■■

■■■■■

■

◆◆◆◆◆◆◆

◆◆◆◆◆◆◆◆

◆◆◆◆◆◆◆

◆

▲▲▲▲▲▲▲

▲

1012 1013 1014 1015 1016 1017 1018

0.01

0.1

1

10

fa [GeV]

Hinf[GeV]

FT, Wen Yin, Alan H. Guth, 1805.08763

θi = 1 θi = 0.1 θi = 0.01

θi = θrms

θi ≃ 0.126 θrms (10 % tuning)

θi ≃ 0.0125 θrms (1 % tuning)

Conventional axion window, fa ≲ 1012 GeV

θrms =3

8π2

H2inf

fama(Tinf)

“Bunch-Davis distribution”

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．

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

• 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 etc. See Kitajima’s talk

mφ 0/0mama(T)0/00ma

aL

φL

T0 ⟶High T Low T

QCD axion

mφ 0/0mama(T)0/00ma

aL

φL

T0 ⟶High T Low T

QCD axion

ALP

+ ALP with mφ < ma(T = 0)QCD axion

High T Low T

mH(T)0/0mamL(T)0/00ma

� 0aL � ≃ aL

� 0aL � ≃ φL� 0aH � ≃ φL

� 0aH � ≃ aL

T0 ⟶

+ mass mixing+ ALP with mφ < ma(T = 0)QCD axion

High T Low T

mH(T)0/0mamL(T)0/00ma

� 0aL � ≃ aL

� 0aL � ≃ φL� 0aH � ≃ φL

� 0aH � ≃ aL

T0 ⟶

+ mass mixing+ ALP with mφ < ma(T = 0)QCD axion

Similar to MSW effect in neutrino physics!

The comoving number is the adiabatic inv.

CAST

IAXO

ADMXADMX0(prospects)

CULTASK

MADMAX

ABRACADABRA0(Broad)

ABRACADABRA0(Res)

HBALPS II

ℰ/= 0

ℰ/= 8

/3

ℊaγγ 0v.s.0ma

ℊLγγ0v.s.

0mL

ALP DM(0.50<0θφ,0 0<01)

θ0 1, Θ0 0ΩDMh2 = 0.12

fa 0/(1012 0GeV)

= (3, 5, 10)

10-110-210-310-410-510-610-710-810-910-1010-11

10-9

10-10

10-11

10-12

10-13

10-14

10-15

10-16

10-17

10-18

10-19

Axion mass (eV)

Axion

-photoncouplings

(GeV

-1 )

Axion coupling to photons

fa = 3 × 1012 GeVfa = 5 × 1012 GeVfa = 1013 GeV

Ω a+φh2 = 0.12

ALP coupling to photons can be enhanced by a few orders of magnitude.

Topic 3: ALPでインフラトン

V

F�F�

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�

?

Inflaton decays and disappears, while DM must be produced somehow.

inflaton

radiation

DM

⇢

Scale factor

Topic 3: ALPでインフラトン

Daido, FT and Yin, 1702.03284,1710.11107

V

F�F�

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．

ALP inflaton = ALP DMg��� = O(10�11)GeV�1

“ALP miracle”

Topic 3: ALPでインフラトン

IAXO collaboration, 1904.09155

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

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

Croon and Sanz, 1411.7809

Vinf(�) = ⇤4

✓cos

✓�

f+ ✓

◆�

n2cos

✓n�

f

◆◆+ const.

= V0 � ��4 � ✓⇤4

f�+ (� 1)

⇤4

2f2�2 + · · · � ⇠ ⇤4

f4

-1 1 2 3 4 5

0.5

1.0

1.5

0 -1 1 2 3 4 5

0.5

1.0

1.5

0

Even n Odd n

The inflaton mass at the minimum, , depends on n.m�<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

KSVZ

QCD axion

IAXOALPS-II

10-4 10-3 10-2 10-1 100 101 102 103

CAST HB

10-14

10 -13

10 -12

10 -11

10 -10

10 -9

m [eV]φ

CMB τ

EBL

X-ray

Telescopes

Successful inflation

Successful reheating

CDM

Small-scale structure constraint on ALP CDM

HDM constraint on thermalized ALP

g��� = O(10�11)GeV�1

Inflaton = DM = ALP

within the reach of future axion helioscopes and laser experiments.

KSVZ

QCD axion

IAXOALPS-II

10-4 10-3 10-2 10-1 100 101 102 103

CAST HB

10-14

10 -13

10 -12

10 -11

10 -10

10 -9

m [eV]φ

CMB τ

EBL

X-ray

Telescopes

*Plus, there is a preference for extra cooling of HB stars

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

g��� = (0.29± 0.18)⇥ 10�10 GeV�1

“An ALP miracle”

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)