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間仁田侑典 (京都大学)

重力波検出器を用いた

超軽量暗黒物質の�スピンの探査

理論懇2023

December 25, 2023

Based on 2310.10646 [hep-ph] with H. Takeda, K. Aoki, T. Fujita, and S. Mukohyama

Credit: The Virgo Collaboration/CCO 1.0

2 of 24

1

1. 超軽量暗黒物質は

重力波検出器を用いて探査できる

2. 複数台の相互相関で�超軽量暗黒物質のスピンが区別できる

3. 現在のスピン1超軽量暗黒物質の結合定数の�上限は28倍悪くなる

Credit Caltech/MIT/LIGO Lab

Credit LVK collaboration

Credit: The Virgo Collaboration/CCO 1.0

Yusuke Manita (Kyoto U)

Let me show the basic features of the ULDM. ULDM is a dark matter model with a really tiny mass in the range of 10^-22 to 1 eV. The typical mass of WIMP particle is like GeV, so the ULDM has literally light mass.

I will show you four features of the ULDM.

First, the ULDM must be a bosonic particle because the fermionic particles are not possible to be dense enough like inside the dark matter halo, due to the Pauli blocking. So, the spin of the ULDM must be an integer like 0, 1, and 2.

Second, the ULDM has a typical length scale called Compton wavelength. The Compton wavelength is large because the mass is tiny, thus it can be regarded as a classical wave which oscillates at Compton wavelength.

Thirdly, the ULDM is a non-relativistic wave because the local speed of DM is about 10^-3 in the unit of the speed of light.

Fourth, the ULDM has a long coherent time. For example, in the case of the mass is about 10^-12eV, the cohrenttime scale is about 7700 seconds.

So, in the GW detectors, the ULDM signal looks almost monochromatic wave with the Compton wave length, and it is almost coherent signal within the coherent time scale correspond to the dB wavelength.

3 of 24

2

1. 超軽量暗黒物質は

重力波検出器を用いて探査できる

2. 複数台の相互相関で�超軽量暗黒物質のスピンが区別できる

3. 現在のスピン1超軽量暗黒物質の結合定数の�上限は28倍悪くなる

Credit Caltech/MIT/LIGO Lab

Credit LVK collaboration

Credit: The Virgo Collaboration/CCO 1.0

Yusuke Manita (Kyoto U)

Let me show the basic features of the ULDM. ULDM is a dark matter model with a really tiny mass in the range of 10^-22 to 1 eV. The typical mass of WIMP particle is like GeV, so the ULDM has literally light mass.

I will show you four features of the ULDM.

First, the ULDM must be a bosonic particle because the fermionic particles are not possible to be dense enough like inside the dark matter halo, due to the Pauli blocking. So, the spin of the ULDM must be an integer like 0, 1, and 2.

Second, the ULDM has a typical length scale called Compton wavelength. The Compton wavelength is large because the mass is tiny, thus it can be regarded as a classical wave which oscillates at Compton wavelength.

Thirdly, the ULDM is a non-relativistic wave because the local speed of DM is about 10^-3 in the unit of the speed of light.

Fourth, the ULDM has a long coherent time. For example, in the case of the mass is about 10^-12eV, the cohrenttime scale is about 7700 seconds.

So, in the GW detectors, the ULDM signal looks almost monochromatic wave with the Compton wave length, and it is almost coherent signal within the coherent time scale correspond to the dB wavelength.

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超軽量暗黒物質とは？

超軽量暗黒物質は質量が10^-22eVから10eVの暗黒物質模型。整数スピンを持つ。

3

ボゾン

超軽量暗黒物質はボゾン粒子(整数スピン粒子)によって構成される

軽いフェルミオン粒子はパウリの排他原理のためにハロー中心のように高密度にならないから。

非相対論的

超軽量暗黒物質は質量に対応するコンプトン波長（周波数）で振動する。

超軽量暗黒物質は比較的長い時間、コヒーレントに振動する。

スピン0

スピン1

スピン2

有質量スカラー粒子: アクシオン、モジュライ、ディラトン.

有質量ベクトル粒子: ダークフォトン

有質量テンソル粒子: 有質量グラビトン、bigravityなどの修正重力に由来

超軽量暗黒物質の特徴

(Tremaine & Gunn 1979)

(YM+, 2023)など

Yusuke Manita (Kyoto U)

Let me show the basic features of the ULDM. ULDM is a dark matter model with a really tiny mass in the range of 10^-22 to 1 eV. The typical mass of WIMP particle is like GeV, so the ULDM has literally light mass.

I will show you four features of the ULDM.

First, the ULDM must be a bosonic particle because the fermionic particles are not possible to be dense enough like inside the dark matter halo, due to the Pauli blocking. So, the spin of the ULDM must be an integer like 0, 1, and 2.

Second, the ULDM has a typical length scale called Compton wavelength. The Compton wavelength is large because the mass is tiny, thus it can be regarded as a classical wave which oscillates at Compton wavelength.

Thirdly, the ULDM is a non-relativistic wave because the local speed of DM is about 10^-3 in the unit of the speed of light.

Fourth, the ULDM has a long coherent time. For example, in the case of the mass is about 10^-12eV, the cohrenttime scale is about 7700 seconds.

So, in the GW detectors, the ULDM signal looks almost monochromatic wave with the Compton wave length, and it is almost coherent signal within the coherent time scale correspond to the dB wavelength.

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重力波検出器による超軽量暗黒物質探査

超軽量暗黒物質はLIGOなどの重力波検出器で検証できる。

4

もし超軽量暗黒物質が標準模型粒子と相互作用すれば、�質量m~10^-12eVの超軽量暗黒物質は重力波検出器に振動するシグナルを残す

DMハロー

2. 超軽量暗黒物質は波動的性質を持つ

1. 重力波検出器は腕の長さの変化に�敏感

3. 私たちは暗黒物質密度の高い領域に住んでいる

Nakatsuka et.al.(2023)

Yusuke Manita (Kyoto U)

Let me show the basic features of the ULDM. ULDM is a dark matter model with a really tiny mass in the range of 10^-22 to 1 eV. The typical mass of WIMP particle is like GeV, so the ULDM has literally light mass.

I will show you four features of the ULDM.

First, the ULDM must be a bosonic particle because the fermionic particles are not possible to be dense enough like inside the dark matter halo, due to the Pauli blocking. So, the spin of the ULDM must be an integer like 0, 1, and 2.

Second, the ULDM has a typical length scale called Compton wavelength. The Compton wavelength is large because the mass is tiny, thus it can be regarded as a classical wave which oscillates at Compton wavelength.

Thirdly, the ULDM is a non-relativistic wave because the local speed of DM is about 10^-3 in the unit of the speed of light.

Fourth, the ULDM has a long coherent time. For example, in the case of the mass is about 10^-12eV, the cohrenttime scale is about 7700 seconds.

So, in the GW detectors, the ULDM signal looks almost monochromatic wave with the Compton wave length, and it is almost coherent signal within the coherent time scale correspond to the dB wavelength.

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重力波検出器における超軽量暗黒物質シグナルの生成

2つの効果によって超軽量暗黒物質のシグナルが生成される。

5

インプット�ミラー

検出器の腕の模式図

エンド�ミラー

レーザー

検出器はレーザーの�光路長を測定する。

レーザーの往復時間内に鏡が振動するため、行きと帰りで腕長が異なる(Morisaki+,2021)

2つの鏡は空間的に離れているので、振動がズレて、有効的に�腕長が変化。重力波で支配的。

有限時間効果

有限空間長効果

Yusuke Manita (Kyoto U)

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スピンによる2つの効果の違い

6

スピン0、スピン1

スピン2

For

無視できる

差動運動

同相運動

鏡

鏡の応答

Yusuke Manita (Kyoto U)

8 of 24

7

1. 超軽量暗黒物質は

重力波検出器を用いて探査できる

2. 複数台の相互相関で�超軽量暗黒物質のスピンが区別できる

3. 現在のスピン1超軽量暗黒物質の結合定数の上限は28倍悪くなる

Credit Caltech/MIT/LIGO Lab

Credit LVK collaboration

Credit: The Virgo Collaboration/CCO 1.0

Yusuke Manita (Kyoto U)

Let me show the basic features of the ULDM. ULDM is a dark matter model with a really tiny mass in the range of 10^-22 to 1 eV. The typical mass of WIMP particle is like GeV, so the ULDM has literally light mass.

I will show you four features of the ULDM.

First, the ULDM must be a bosonic particle because the fermionic particles are not possible to be dense enough like inside the dark matter halo, due to the Pauli blocking. So, the spin of the ULDM must be an integer like 0, 1, and 2.

Second, the ULDM has a typical length scale called Compton wavelength. The Compton wavelength is large because the mass is tiny, thus it can be regarded as a classical wave which oscillates at Compton wavelength.

Thirdly, the ULDM is a non-relativistic wave because the local speed of DM is about 10^-3 in the unit of the speed of light.

Fourth, the ULDM has a long coherent time. For example, in the case of the mass is about 10^-12eV, the cohrenttime scale is about 7700 seconds.

So, in the GW detectors, the ULDM signal looks almost monochromatic wave with the Compton wave length, and it is almost coherent signal within the coherent time scale correspond to the dB wavelength.

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問題と答え

重力波検出器のシグナルで超軽量暗黒物質のスピンを区別できるか？

8

手順1. 3台以上の検出器で、複数の相互相関関数を計算する。

手順2. ORFの検出器組み合わせの依存性でスピンを区別する。

答えできる!

問題

Overlap Reduction Function

相互相関において、検出器の�位置や向きの情報を持つ量

a,bは検出器を表す

Yusuke Manita (Kyoto U)

10 of 24

超軽量暗黒物質シグナルにおけるORF

有限時間効果と有限空間長効果のORFは位置・向き依存性が異なる。

9

H: LIGO-Hanford

L: LIGO-Livingston

V: Virgo

K: KAGRA

地球

Yusuke Manita (Kyoto U)

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スピン2と1の判別可能性

10

重質量

軽質量

ケーススタディー

仮定：LIGOの2台が何らかの�超軽量暗黒物質のシグナルを捉えた.

スピン判別の指標:

易

難

判別

スピン1

スピン2

支配的な効果

LIGOの~1-100倍の�感度なら区別できる

同じ効果

違う効果

難

LIGOはスピン1の感度は0�シグナルはスピン2!

LIGOの~1/10倍の�感度でも区別できる

易

Yusuke Manita (Kyoto U)

Let's consider the spin distinguishability with ORF. We define the indicator of distinguishability as the difference between the SNR of spin-1 ULDM and that of spin-2 ULDM.

As a case study, we suppose that a signal is detected through the cross-correlation analysis between LIGO-Livingston and LIGO-Hanford,

Then we got this plot, which is representing the distinguishability normalized by the observed SNR by Livingston and Hanford.

At the low-frequency region, about lower than 30 Hz, since the effective ORF for spin-1 and spin-2 ULDM is the same, the distinguishability is low.

On the other hand, at the high-frequency region, about higher than 30 Hz, since the finite time light traveling effect dominates, the distinguishability of spin is high.

The reason why it has a divergence here is that the SNR of Livingston and Hanford becomes zero because the finite time light traveling effect and conventional effect is balancing at this point.

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スピン1と0の判別可能性

11

重質量

軽質量

スピン1

スピン2

支配的な効果

LIGOの~1-100倍の�感度なら区別できる

同じ効果

難

LIGOはスピン0と1の感度�が0になる2つのピーク

LIGOの~1-100倍の�感度なら区別できる

易

ケーススタディー

仮定：LIGOの2台が何らかの�超軽量暗黒物質のシグナルを捉えた.

スピン判別の指標:

難

同じ効果

易

難

判別

Yusuke Manita (Kyoto U)

Let's consider the spin distinguishability with ORF. We define the indicator of distinguishability as the difference between the SNR of spin-1 ULDM and that of spin-2 ULDM.

As a case study, we suppose that a signal is detected through the cross-correlation analysis between LIGO-Livingston and LIGO-Hanford,

Then we got this plot, which is representing the distinguishability normalized by the observed SNR by Livingston and Hanford.

At the low-frequency region, about lower than 30 Hz, since the effective ORF for spin-1 and spin-2 ULDM is the same, the distinguishability is low.

On the other hand, at the high-frequency region, about higher than 30 Hz, since the finite time light traveling effect dominates, the distinguishability of spin is high.

The reason why it has a divergence here is that the SNR of Livingston and Hanford becomes zero because the finite time light traveling effect and conventional effect is balancing at this point.

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12

1. 超軽量暗黒物質は

重力波検出器を用いて探査できる

2. 複数台の相互相関で�超軽量暗黒物質のスピンが区別できる

3. 現在のスピン1超軽量暗黒物質の結合定数の上限は28倍悪くなる

Credit Caltech/MIT/LIGO Lab

Credit LVK collaboration

Credit: The Virgo Collaboration/CCO 1.0

Yusuke Manita (Kyoto U)

Let me show the basic features of the ULDM. ULDM is a dark matter model with a really tiny mass in the range of 10^-22 to 1 eV. The typical mass of WIMP particle is like GeV, so the ULDM has literally light mass.

I will show you four features of the ULDM.

First, the ULDM must be a bosonic particle because the fermionic particles are not possible to be dense enough like inside the dark matter halo, due to the Pauli blocking. So, the spin of the ULDM must be an integer like 0, 1, and 2.

Second, the ULDM has a typical length scale called Compton wavelength. The Compton wavelength is large because the mass is tiny, thus it can be regarded as a classical wave which oscillates at Compton wavelength.

Thirdly, the ULDM is a non-relativistic wave because the local speed of DM is about 10^-3 in the unit of the speed of light.

Fourth, the ULDM has a long coherent time. For example, in the case of the mass is about 10^-12eV, the cohrenttime scale is about 7700 seconds.

So, in the GW detectors, the ULDM signal looks almost monochromatic wave with the Compton wave length, and it is almost coherent signal within the coherent time scale correspond to the dB wavelength.

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スピン1の超軽量暗黒物質の制限

LIGO-Virgo-KAGRAコラボレーションは、LIGOの2台の相互相関によって、�スピン1の超軽量暗黒物質の結合定数に上限を与えた。

13

R. Abbott et al. Phys. Rev. D 105, 063030 (2021)

相互相関HL

線より上は禁止

Yusuke Manita (Kyoto U)

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ORFの取り扱い

LIGOの2台では、有限時間効果と有限空間長効果のORFの値はかなり異なることに注意して解析する必要がある。

14

有限空間長効果のORF

有限時間効果のORF

LVK�論文

我々の論文

相互相関関数

ORF

LIGOの2台の向きは、差動運動の応答には最適で、�同相運動の応答に最悪�→2つのORFは大きさがかなり違う

Yusuke Manita (Kyoto U)

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スピン1の超軽量暗黒物質の制限の修正

ORFを正しく取り扱うと、現在の制限は最大28倍悪化する。

15

線より上は禁止

相互相関HL

相互相関HL(修正)

R. Abbott et al. Phys. Rev. D 105, 063030 (2021)のFig.3に変更を加えた。

Yusuke Manita (Kyoto U)

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まとめ

16

1. 超軽量暗黒物質は

重力波検出器を用いて探査できる

2. 複数台の相互相関で�超軽量暗黒物質のスピンが区別できる

3. 現在のスピン1超軽量暗黒物質の結合定数の�上限は28倍悪くなる

Credit Caltech/MIT/LIGO Lab

Credit LVK collaboration

Credit: The Virgo Collaboration/CCO 1.0

今後の課題

VirgoやKAGRAを用いたスピン1の相互相関解析�KAGRAの向き・位置はスピン1の探査と相性が良い。
宇宙の重力波検出器による超軽量暗黒物質のスピンの探査�少ない台数の検出器でスピンを区別できるか?別の時刻データとの相互相関?

Yusuke Manita (Kyoto U)

Let me show the basic features of the ULDM. ULDM is a dark matter model with a really tiny mass in the range of 10^-22 to 1 eV. The typical mass of WIMP particle is like GeV, so the ULDM has literally light mass.

I will show you four features of the ULDM.

First, the ULDM must be a bosonic particle because the fermionic particles are not possible to be dense enough like inside the dark matter halo, due to the Pauli blocking. So, the spin of the ULDM must be an integer like 0, 1, and 2.

Second, the ULDM has a typical length scale called Compton wavelength. The Compton wavelength is large because the mass is tiny, thus it can be regarded as a classical wave which oscillates at Compton wavelength.

Thirdly, the ULDM is a non-relativistic wave because the local speed of DM is about 10^-3 in the unit of the speed of light.

Fourth, the ULDM has a long coherent time. For example, in the case of the mass is about 10^-12eV, the cohrenttime scale is about 7700 seconds.

So, in the GW detectors, the ULDM signal looks almost monochromatic wave with the Compton wave length, and it is almost coherent signal within the coherent time scale correspond to the dB wavelength.

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Several cross-correlations

17

Ideally, we can distinguish ULDM spin with three or more detectors.

Currently, there are 4 (or more) ground-based detectors (LVK), thus 6 (or more) combinations of cross-correlations can be considered.

Yusuke Manita (Kyoto U)

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Coupling between ULDM and SM

The coupling with SM depends on the spin. Thus, the way to generate signals differs by its spin.

18

Spin-0

Through its dilatonic coupling to SM, ULDM fluctuate the fundamental constants such as fine structure constant and fermion mass.

[Spin-0] - Y. V. Stadnik & V. V. Flambaum, PRL 114, 161301 (2015) - Y. V. Stadnik & V. V. Flambaum, PRA 93, 063630 (2016) - A. A. Geraci+, PRL 123, 031304 (2019) - H. Grote & Y. V. Stadnik, PRR 1, 033187 (2019) - S. Morisaki & T. Suyama, PRD 100, 123512 (2019) - C. Kennedy+, PRL 125, 201302 (2020) - E. Savalle+, PRL 126, 051301 (2021) - S. M. Vermeulen+, Nature 600, 424 (2021) GEO600 data analysis

[Spin-1] - P. W. Graham+, PRD 93, 075029 (2016) - A. Pierce+, PRL 121, 061102 (2018) - H-K Guo+, Commun. Phys. 2, 155 (2019) LIGO O1 data analysis - Y. Michimura, T. Fujita, S. Morisaki, H. Nakatsuka, I. Obata, PRD 102, 102001 (2020) - D. Carmey+, New J. Phys. 23, 023041 (2021) - J. Manley+, PRL 126, 061301 (2021) - S. Morisaki, T. Fujita, Y. Michimura, H. Nakatsuka, I. Obata, PRD 103, L051702 (2021) - LIGO-Virgo-KAGRA Collaboration, arXiv:2105.13085 LIGO/Virgo O3 data analysis

[Spin-2] Y.Manita, K. Aoki, T. Fujita, S. Mukohyama, Phys.Rev.D 105 8, 084038 (2022) - J. M. Armaleo, D. Lopez Nacir, and F. R. Urban, JCAP 04, 053 (2021)

Spin-1

U(1)_B or U(1)_L-B gauge boson leave a signal by pushing the mirrors through the Coulomb-like force.

Spin-2

Since it originates from the gravity sector, it universally couples to matter fields.

Thus, it leaves a signal in GW detectors like GW.

D=B or B-L

Yusuke Manita (Kyoto U)

More precisely, the ULDM within the mass range of 10^-14 to 10^-11 eV can be detectable in grand-based GW detectors.

The typical frequency of the signal is given by the Compton wave length, thus the dark matter mass with 10^-12 eV corresponds to 242Hz. It’s in a LIGO band. So, it may be possible to leave the signal in the grand based detectors like LIGO.

So, all the ULDM within this mas range is expected to leave a signal. But, technically speaking the way to leave the signal are different for each spin.

The spin-0 ULDM such as QCD axion and ALP leaves a signal by fluctuate the fundamenral constants like a fine structure constant and the fermion masses.

The spin-1 ULDM such as dark photon leaves a signal by pushing the mirror through the new Coulomb force.

The spin-2 ULDM is originating from the gravity sector, so is universally couples to all the matter files like the usual gravity field. Thus it leaves a signal in the gravitational wave detectors in the same way as the usual gravitational waves.

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Question

Can we distinguish spin of ULDM by the signal from GW detectors?

19

The methods for separating non-tensorial polarizations in SGWB are not applicable. This is because the frequency width of the signal is too narrow to distinguish the differences in the ORF.

Overlap reduction function (ORF)

Power spectrum

SGWB

[A.Nishizawa, A. Taruya, K.Hayama, S. Kawamura, M. Sakagami, 2009]

Cross correlational signal�of two detectors

Yusuke Manita (Kyoto U)

21 of 24

SNR

20

Spin-0

Spin-1

Spin-2

Finite-time effectが支配的

Yusuke Manita (Kyoto U)

22 of 24

Spin-2 and spin-1

21

Yusuke Manita (Kyoto U)

23 of 24

Spin-0 and spin-1

22

Yusuke Manita (Kyoto U)

24 of 24

問題と答え

重力波検出器のシグナルで超軽量暗黒物質のスピンを区別できるか？

23

手順1. 複数台の検出器で、複数の相互相関関数を計算する。

手順2. ORFの検出器組み合わせの依存性でスピンを区別する。

答えできる!

問題

Overlap Reduction Function

相互相関において、検出器の�位置や向きの情報を持つ量

スピン2

スピン1

スピン0

a,bは検出器を表す

Pは定数(パワースペクトル)を表す。

Yusuke Manita (Kyoto U)