暗黒物質の検出に向けて
中山和則（東北大 & QUP/KEK）
2023/5/17 @ 大阪公立大セミナー

目標
専門外の人、これから学ぶ人に、最近の暗黒物質の研究について雰囲気を伝える

目次
1. 素粒子標準模型と暗黒物質
2. 暗黒物質の様々な検証方法
3. 暗黒物質検出と物性物理1. 素粒子標準模型と暗黒物質

素粒子標準模型
物質場
クォーク・レプトンx３世代

ヒッグス場
ゲージ場・物質場に質量を与える

ゲージ場
強い相互作用弱い相互作用
電磁相互作用を媒介[Figure from Wikipedia]

素粒子標準模型
標準模型：以下のラグランジアンを持つ場の量子論<latexit sha1_base64="dJTxF1PvqBSf+yT5yqSSKOgZVuM=">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</latexit>

L=

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ゲージ場
物質場＋ゲージ相互作用

V( )

ヒッグス場

ゲージ場の質量+ h.c.

湯川相互作用

物質場の質量この世界のほとんど全てを正しく記述する“神の数式”

標準模型の問題点
宇宙論的問題

暗黒物質
物質反物質非対称性
インフレーション

理論的問題

階層性問題
強いCP問題世代構造 ゲージ構造
量子重力

標準模型は究極理論ではない！

lensing

暗黒物質の観測的証拠
Evidence ofdarkmatterCMB
anisotropy
銀河の回転曲線
重力レンズ

Rotation curve of galaxy

Rotationcurve of galaxy
銀河団の衝突Bullet cluster

Gravitational
lensing2010年2月25日木曜日

Bullet cluster

CMB anisotropy

Bullet cluster

暗黒物質の観測的証拠
宇宙背景放射宇宙のエネルギーの割合
通常の物質 ~5%

暗黒物質
~25%
暗黒エネルギー~70%[Planck (2018)]

暗黒物質について分かっていること
単位

宇宙の全エネルギーの約２０％

1 GeV<latexit sha1_base64="38QAK8erEi6fpJH37n6gK86/HAI=">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</latexit><latexit sha1_base64="aF3/+2K3wnhYgPiqZWvEhBrtesc=">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</latexit>

地球近傍では質量密度 ⇢ ' 0.4 GeV/cm

3

質量 10

eV

3

eV

9

GeV = 10 eV“冷たい” （速度が小さい）
22<latexit sha1_base64="Qhh64a6ZoSWsutydmDycSPNHT5g=">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</latexit>

meV = 10

重力を及ぼす<latexit sha1_base64="I5Owkb/b5mmxntsUNzcmqQveDQY=">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</latexit>〜陽子１個の質量1052TeV = 10eV（ほぼ全く決まってない！）

雲を掴むような話

12

eV など

暗黒物質の研究
理論的動機

暗黒物質のモデル

強いCP問題
大統一理論？ 弦理論？ etc …

階層性問題

初期宇宙での生成過程
現在の存在量と合致するか？
宇宙の構造形成がうまくいくか？

実験・観測との関係

今日の地上実験（加速器実験、直接検出実験 …）

主題

宇宙観測（宇宙線、宇宙背景放射、重力波、星の進化 …）
新たな実験手法の提案

MSSM

Figure by T.Tait

NMSSM

R-parity
violating

Supersymmetry

WIMPless DM
HiddenSector DM

Gravitino DM

mSUGRA
Self-Interacting
DM

pMSSM
Q-balls
Technibaryons

Dark Photon

Asymmetric DM

Dirac
DM

R-parity
Conserving

Light
Force Carriers

Extra Dimensions

Dynamical
DM

Warm DM

Sterile Neutrinos

Axion DM

Theories of
Dark Matter?

Solitonic DM
Quark
Nuggets

UED DM
6d

Warped Extra
Dimensions

5d

RS DM
T-odd DM

Little Higgs
暗黒物質の模型はO(100)(1000以上？)あると思われる
QCD Axions

暗黒物質の代表的な模型
WIMP (Weakly-Interacting Massive Particle)
典型的には質量 1TeV 程度で、弱い相互作用程度の相互作用の大きさを持つ
超対称性理論のニュートラリーノなどが代表例

標準模型の階層性問題を解決

アクシオン
典型的には質量 1μeV - 1meV 程度で、相互作用はすごく弱い
標準模型の強いCP問題を解決[Peccei, Quinn (1977)]

ALP (Axion-Like Particle), ダークフォトン
典型的には質量 << 1eV で、相互作用はすごく弱い弦理論から多数のALP, ダークフォトンが予言される？

[Arvanitaki et al. (2009)]

（重力以外の）相互作用の強さ

広大なパラメータ領域を探索するために、様々な実験・観測のアイデアが必要！
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（重力以外の）相互作用の強さ
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WIMP

Axion
質量

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2. 暗黒物質の様々な検証方法
2-1. WIMP暗黒物質
2-2. アクシオン暗黒物質

WIMP暗黒物質の直接・間接検出
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暗黒物質のフラックス

4⇠ 10 cm

2

s

1

✓

3

10 GeVm◆

暗黒物質が検出器中の原子にたまにぶつかる
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2

⇣

m mN
mN
2
E⇠
v
⇠
100
keV
(m + mN )2
100 GeV⌘

暗黒物質

電離、シンチレーション、温度上昇など相互作用の大きさ（散乱断面積）の情報が得られる

原子核

液体キセノンの場合

XENON実験

LZ実験waveforms from isolated S1 and S2 pulses and applying
the WIMP analysis selections. The selection efficiency
is thenapplied to UDT single-scatter-likeevents to con暗黒物質-核子
散乱断面積への上限
strain the accidentals rate.

colors as given in the legend. Background compon
8
B solar neutrinos and accidentals are included inare too small to be visible in the plot.

Wino暗黒物質の予言��� �����

nest model. The background component unc�����
are included as constraint terms
inacombined�����background model to the data, ��
the result of wh���
shown in Table I.
Above the smallest tested WIMP mass ofthe best-fit number of WIMP events is zero, andare thus
consistent with the background-only hy�����Figure 5 shows the 90 % confidence level uppe
the spin-independent WIMP-nucleon cross secta function of mass. The minimum of the limit c
m = 30 GeV/c2 with a limit of SI = 6.5 ⇥ 1
For WIMP masses between �����������
19 GeV/c2 and 2
backgroundfluctuations produce a limit which
�����
�
��
a critical discovery power threshold, ⇡crit =���������������
for these masses the reported limit is set to
equivalent
to
⇡
[54].
The
background
model
crit
Figure 6: Wino-proton SI scattering cross section. Blue dashed and red sasafunctionofreconstructedenergy
are
shown
[LZ
collaboration(2022)][Hisano,Ishiwata,
Nagata(2015)]
resentLO
and
NLO
results,
respectively,
withcorresponding
bands
show
FIG. 5. The 90 % confidence limit (black line) for the spinand
the
data
agree
with
the
background-onlymuncertainties.
Gray
band
shows
uncertainty
resulting
from
the
input
error.
independent WIMP cross section vs. WIMP mass. The

WIMP暗黒物質の直接・間接検出
間接検出
暗黒物質はたまに対消滅する
対消滅<latexit sha1_base64="AblIDrqCqLQqStP3LrlbNw0+CH4=">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</latexit>

e , p̄

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銀河系内成分＋銀河外成分
質量・対消滅断面積に制限±,⌫

IceCube

AMS-02Fermi
HESS
Super-Kamiokande適当な質量・断面積を仮定した場合の予言

ガンマ線

陽電子

[K.Nakayama, PhD thesis]

様々な宇宙線
観測データから
暗黒物質模型に対して制限が付く

ニュートリノ（銀河系外）

ニュートリノ（銀河中心）

宇宙論・天体物理からの制限
宇宙背景放射[Padmanabhan, Finkbeiner (2005)]

初期宇宙での暗黒物質の対消滅

高エネルギー光子・電子

水素, ヘリウムの再結合を阻害
10-23

宇宙背景放射に影響

宇宙背景放射観測
から排除

10-24

10-25

10-26

10-27
1

[Kanzaki, Kawasaki, Nakayama (2009)]

10

100

1000

104

[Kawasaki, Nakatsuka, Nakayama, Sekiguchi (2021)]

FIG. 6. CMB constraints on the annihilation cross section for four DM annihilation channels. W

宇宙論・天体物理からの制限
太陽からのニュートリノ
暗黒物質はたまに太陽の中の水素と散乱してエネルギーを失い太陽内部に溜まっていく
溜まった暗黒物質は対消滅してニュートリノを出す⌫<latexit sha1_base64="hprXbtHtZUFmo7qk3nhUemgEZFs=">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</latexit>

Super-Kamiokande, IceCubeなどから強い制限

中性子星のheating
暗黒物質の対消滅が中性子星を温める
中性子星の温度に下限が与えられる[Kouvaris (2008), Baryakhtar et al. (2017),
Fujiwara, Hamaguchi, Nagata, Zheng (2022)]

低い温度の中性子星が見つかれば、断面積に上限が与えられる

2. 暗黒物質の様々な検証方法
2-1. WIMP暗黒物質
2-2. アクシオン暗黒物質

アクシオン/ダークフォトン暗黒物質
典型的なアクシオン/ダークフォトン暗黒物質： m ⌧ 1 eV<latexit sha1_base64="IF2Ep8VIxoXFd/nqmNetjPDwXWc=">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</latexit>

質量が軽い

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アクシオン暗黒物質： a(~x, t) = a0 cos(m(t~v · ~x))

~
~
H(~
x
,
t)
=
H
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このような振動場の下での特徴的な反応を探す~v · ~x))アクシオン暗黒物質 直接探索
Axion haloscope[Sikivie (1983)]

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L=

ga
µ⌫
e
aFµ⌫ F '4~~⇤E = ga äB0
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g a aE

CavityCavity 周波数とアクシオン質量が等しいとき、共鳴が起こる
周波数をスキャンすることで、広いアクシオン質量領域を探索

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Axion

Photon

10°9

104

CAST

Neutron StarsRADES

QUAX-ag

HAYSTAC

CAPP

ADMX

| gagg

UF

CAPP

10°14

CAPP

10°13

GrAHalRBF

10°12

HAYSTAC

10°11

ORGAN

ORGAN

10°10

°
1
| [GeV ]ADMX experiment103

Frequency [MHz]

E

44/
=
N
/

3

KSVZ

E/ N

DFSZ
= 5/3

10°15
Dine ’17
Bonati ’16

Buschmann ’21

Klaer ’17

Ballesteros ’17

Buschmann ’20

Petreczky ’16

Berkowitz ’15

10°6

10°5

m a [eV]Borsanyi ’16
Co ’20
Fleury ’15

10°4[AxionLimits, C.O’Hare ]ensures a return path for the Meissner screening current; seediscussion in main text.

アクシオン暗黒物質
直接探索(KSVZ model [19, 20]). Thus, in the presence of a static
CASPErmagnetic background B0 , there is an axion-sourced effective current

ABRACADABRA [Kahn, Safdi,Thaler (2016)][Budker et al. (2013)]Je↵ = gap2⇢DM cos(ma t)B0 .

(5)

アクシオン暗黒物質が核スピンの歳差運動を励起This e↵ective currentアクシオンが振動磁場を励起
then sources a real magnetic field,
oscillatingatfrequency
m
,
that
is
perpendicular
to
B
.
a
0
（~核磁気共鳴）22
Our proposed design is shown schematicallyin Fig. 1.
3
InThe
this Letter,
present first results
staticwe magnetic
fieldfromB0 is generated by a constant
ABRACADABRA-10 cm, probing the axion-photon
coupling
g
forin
ADM
in the frequency range
current
a superconducting
wire wrapping a toroid, andf 2 [75 kHz, 2 MHz], corresponding to R
axion massesm the
2 [3.1 ⇥
10 , 8.3 e↵ective⇥ 10 ] eV.rThis current
mass range is is detected with a superconaxion~
Bexthighly motivated for QCD axions, where the axion decay
SQUID
constantlies near the
GUT scale andis easilyducting
pickuploop
inthe
toroidhole.
Intheabsenceofacompati~
pickupM
ble with pre-inflationary Peccei-Quinn (PQ) breaking inloop
a varietyof models,
includingunified theories[16] is no magnetic flux throughaxion
DM(orgrandnoise),
therehor
stringcompactifications
[17,
18],
and
such
low-mass~⇤
BWith
E
0 Additionally,
theloop. [19].
axion DM, there will be an osaxions
may pickup
be favored anthropicallysuch light ALPs may explain the previously-observed
cillatingmagnetic
throughtransparency
anomalyof the Universe
toflux
TeV gammaFigure
1. A (gapped)
toroidal geometrytogenerate a staticthe pickup loop proporrays [20–23],
thoughinp
this
ALPredis notrequired
1. Left: Rendering of the ABRACADABRA-10 cm
magneticfield
B . case
The thedashedcircleshows the FIG.
location
FIG. 1. Experimental setup. (a) The sample
wasa cylindrical
ferroelectric
PMN-PT
crystalwithdiameter
0.46
cmprimarytionalto⇢.
This
designisinspiredbycryogenic
cursetup.
The
magnetic
field
is al.
drivenby 1,280
super[Ouellet
et(2018)]tobe
DM.
Recently,
this
mass
range
has
gatheredsigof
thesuperconducting
pickuploop
ofradius
r

R.
The
gap
DM
[Aybasetal.
(2021)]and thickness 0.50 cm. It was electricallynificant
polarized
along the cylinder
axis, 12,indicatedthe blackarrow.
The
conducting
experimental
interest
24–28]with
toscreening
namea current;
ensures a return
path [11,for the Meissnersee windings around a POM support frame (green).
pickup coil and the cancellation coil were coaxialwith comparatorsand the axis (CCCs)of the Helmholtz[21],coil
The axion-induced
field
a superconducting
whichareis measured
usedbyfor
meato suppress broadening due to chemical shifts and increase T substantially [51]. T in
discussioninmain text. review.
few,rentor see[29] thefor acrystal,comprehensive
Furthermore, excitationaa~ ext is colinear with the sample magnetization, M~ . Theexperiment. The applied magnetic field B~ ⇤ is perpendicular to B
~ ext . The SQUID pickup loop is arranged to measure the transverse
crystal E
.

2

2

10

9

0

アクシオン暗黒物質 間接探索
<latexit sha1_base64="6GxVzwAoyfcEFhxt0pk2FY/OO4A=">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</latexit>

アクシオンは２光子へ崩壊

a<latexit sha1_base64="wwh4x8xJFoxOe45dwRJcLaWWyvI=">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</latexit><latexit sha1_base64="6GxVzwAoyfcEFhxt0pk2FY/OO4A=">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</latexit>⌧ ⇠ 10

22

sec

✓

1 eV
m

◆3 ✓

10

9

GeV
ga

1 ◆2

可視・赤外背景放射に寄与
望遠鏡による天文観測が暗黒物質探索に使える！

[Nakayama,Yin (2022)]a

5. × 10-10
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Horizontal branch star cooling

5. × 10-11

HST 0.85μm (this work))

HST 0.606μm (this work-11

1. × 10

5. × 10-12

背景光の非等方性の観測から特に強い制限

Telescope

1. × 10-12
5

10Reionization

15

20

25

30

m[eV][Nakayama,Yin (2022)]b
Figure 3:[Mitchell-Wynne et al., (2015)]

Same figure as Fig. 2 but we assume the ALP is the dominant cold DM, i.e.

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アクシオン-光子結合に対する制限

L=

ga
µ⌫
e
aFµ⌫ F
4

 [“AxionLimits”, C.O’Hare,
https://cajohare.github.io/AxionLimits/]

✏µ⌫L = Fµ⌫ H
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ダークフォトン結合定数に対する制限

 [“AxionLimits”, C.O’Hare,
https://cajohare.github.io/AxionLimits/]

ion, we numerically show the evolution of Abelian-Higgs string networks with
ype and near-global-type cases. First, we focus on the scaling behavior for theng length. Then, we show the emission of dark photons from the string network.

del重力波とダークフォトン暗黒物質

ダークヒッグス場によりider the Abelian-Higgs model in the hidden sector with the dark U(1) gauge
ダークフォトンが質量を持つ
iven by thefollowing Lagrangian,⇤L = (Dµ ) D

µ

1
µ⌫
Fµ⌫ F
4

4

(| |

2

2 2

v ),

(1)

the dark Higgs field, Dµ = @µ ieAµ is the covariant derivative operator with Aµ
ark photon初期宇宙で自発的対称性の破れ
field, Fµ⌫ = @µ A⌫ @⌫ Aµ is the field strength tensor, e, and v areon the string loops may also emit high-energy particles [67,68]. See also Refs. [69–71]
whereeffi[Kitajima, Nakayama (2022)]
位相欠陥(cosmic
string)の生成oton/Higgs emission from local-type strings has also been reported. Phenomenology/cosmology
ngs due to heavy particle radiation have been discussed in Refs. [72–77].
Cosmic string がダークフォトンを生成 [Long, Wang (2019)]
Figure2 は同時に重力波も生成
Cosmic string

The vertical dotted line correspon

背景重力波スペクトル10-1

ΩGW(f)

10

-4

10

10

10

EPTA
NANOGravSKA
LISA
DECIGO
LIGO/Virgo
ET

-7

-10

(a)

地上重力波検出器(v, m) =(a) : (1014(b) : (10(c)

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(b )

-13

パルサータイミング

12(c) : (10

-16

10

-16

10

-13

13

10

-10

10

-7

10

-4

10

-1

10

2

10

5

10

8

GeV, 1014eV)

GeV, 1010eV)

GeV, 105eV)[Kitajima, Nakayama (2022)]

f [Hz]

重力波でダークフォトン暗黒物質シナリオの一つを検証可能いろんな種類の暗黒物質に対して、いろんな観測方法が考案されている

先に進むには
これまでの手法をさらに突き詰める
新しいアイデアを考える
この後は、最近のアイデア（のごく一部）を紹介します3. 暗黒物質検出と物性物理

暗黒物質と物質との反応
暗黒物質（重い場合）

原子核

電子

暗黒物質（軽い場合）
準粒子

X)

真空中の粒子の分散関係

r2s

固体中の準粒子の分散関係

D. Electronic density of states

The density of states is given by—10

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computed by numerical means.

logarithmic

A

r

98
X

U, K

X

マグノン (YIG)
V. Cherepanov et a!., The saga of YIG

where the sum is over wave vector and~_c 2 k 2 + m2

TABLE II. Eigenvalues for diamond-structu
conductors at I', X, andL. Energies are in0-Compound

Point

Level

Ge

Local

Nonlocal-12.53-12.36

-12.6

-0.2

k
<latexit sha1_base64="FOMZxfc43M3H67RghN5ire6FdxM=">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</latexit>

—10
—12

pC

1464

D Strauch and B Dorner,Q~~‘uriioJ

0.00
4. 17

0.00
4.10

0.9

3.43

3.22

-8.
-2.

-7.
-2.

-8.
-3.

1.22

1.17

1.1

~g,rIoo]

1

Fig. 4. Magnon spectra for the symmetric directions k [1101, [100] and for the values of the exchange constants (

フォノン

10

The spectrum ~d1 (k) is not linear and anisotropic only27
in the vicinity69of the edge of
6zone. This part of the spectrum is not universal, it depends on all the values of excha
1ad, Jdd, and faa. Nevertheless, the volume of that part 99of the Brillouin
86 zone where2adeviates from the linear behavior (1.30) is negligibly small for most quantities.

(GaAs)

固体中には様々な準粒子が存在
暗黒物質との反応に利用可能

1.4.2. Ferromagnon and ant~ferromagnonmodes
In an overview of the spectra it strikes one that the antiferromagnetic
branch17
55Wai (k)-10
3parallel to the ferromagnetic branch wdl(k) and they both are not noticeably pertu
multiple crossing of other branches. In the language of
24perturbation96theory this m61eigenvectors of the FM and AFM modes are practically unmixed with the other6
Neglecting such an intermixing, we can obtain simple analytical expressions for th~~a1 (k) and ~d1 (k) of the FM and AFM branches over the entire Brillouin zone. T
43assume that in (1.15) the oscillation amplitudes of all eight a and all twelve d sp
X(a
2. 15
2.23
0.7
1=
= a8,a9 == a20) and obtain

-10.

-7.

2

~

-7.

-1.
-1.

—10

r

-9.
-6.

Z

X

U, K

WAVE VECTOR k

4. 1
FIG. 1. Band structures 0 for Si, Ge, and e-Sn. da.In
da*i-j~=Aiat+Biaf~—i-~-=B1a,+D1a,
2. Phononnonlocal.
dispersion curves for GaAs.
The experimental data at i=1,...,8,j=9,...,20.
T = 12 K are given
the case of silicon two results are Figure
presented:

固体電子による暗黒物質の吸収
暗黒物質が電子を励起状態にE（光による励起と同じような原理）[Hochberg, Lin, Zurek (2016)]

典型的な半導体のギャップ

暗黒物質

伝導体
荷電子帯

エネルギー ~ 1eV

k1eVより重い暗黒物質であれば可能
超伝導体のギャップ ~ 1meV

[Hochberg et al (2015), Hochberg, Lin, Zurek (2016)]

Dirac 物質のギャップ ~ 10meV [Hochberg et al (2017), Geilhufe, Kahlhoefer, Winkler (2019)]

4
ダークフォトン暗黒物質の場合

102

10

10

ZrTe5

Al

SC

10 14

12

13

Vector DM

13

XENON10/100

10

11

10

Ge
10

10

10

Pseudoscalar DM

WD

10 2

15

ZrTe5
10

Si
Z
S
F
D

10 3

10

Ge

SC

Si

10

9

Al

gaee

アクシオン暗黒物質の場合

Si

16

Ge

Z
V
S
K

10 1
1
m [eV]

10

102

10 3

10 2

10 1
1
m [eV]

10102[Mitridate et al. (2021)]

m Refs. [10, 68].) 95 % C.L. projected constraints on scalar (left), pseudoscalarフォノンによる暗黒物質の吸収
ギャップエネルギー以下でも光が吸収されることがある（光学）フォノンを励起
典型的なフォノンエネルギー ~ 0.1eV
0.1eV
程度のダークフォトン暗黒物質検出などに有効
1464
D Strauch and B Dorner
10

ー
格子イオン

2

0

Figure 2. Phonon dispersion curves for GaAs. The experimental data at T = 12 K are givenby the crosses; the experimental uncertainty is typically 0.02 THz (less than the height of the

＋

ー

＋

~
E

ダークフォトン暗黒物質の場合

軽い散乱型の暗黒物質の場合

3
6

10

Stellarconstraints

10 10

2
[cm
]
e

les

SC

phononexcitationeexcitation

Dirac material

10 18
10 3

Ge

10

10

1

In

10 40
10 42
10

44

10

46

r
a
l
l
te

S

10 48

1 kg-yr, GaAs
2

Freeze

36

10 38

Si

10

10

Molecu

Al

10 14

16

10 34

Direct detection
constraints

10 12

32

10

0

10

1

10

2

mA [eV]

10 3

10 2

10 1

XENON10
DarkSide 50
XENON100
SuperCDMSSENSEI
DAMIC
10
102

1
m [MeV]

Si
Ge
CsI
Al2O3
CaWO4
SiO2
InSb

103

104

Figure 1. Projected reach from single phonon excitations (dashed) and electron transitions (solid) for DM scattering mediate
FIG. 2. Reach for absorption of dark photon DM, in termsby a kinetically mixed light dark photon (the smallest-gap target InSb su↵ers from slow convergence in the electronic transitio
at m < 1 MeV, for which we show results of the two most accurate runs with solid and dotted curves, seof the kinetic mixing parameter  for kg-year exposure.calculation
Appendix A 1 for details). Nuclear recoils (not shown) can also probe this model, but the conclusion on which targets ar
Shaded regions are stellar constraints [48, 49], and directsuperior is the same as for the light hadrophilic mediator model. A detector threshold of 1 meV is used for the phono
calculations, and all transitions with energy deposition greater than the band gaps are included in electron excitations. Th[Knapen, Lin, Pyle, Zurek (2017)]

fi

detection constraints from DAMIC [50], Xenon10 [46, 51],

[Grif n et al., (2019)]

Snowmass2021 - Letter of Interest
The TESSERACT Dark Matter Project

SPICE-HeRALD project

TESSERACT project➢ Managed by LBNL for DOE-HEP➢ Different targets with complementary DM
sensitivity➢ All using TES readout➢ ~40 people from 8 institutes➢ Includes SPICE (polar crystals) and

Kamioka Cryolab development

HeRALD (superfluid helium) experiments

Kamioka Cryolab project2

Dec 14, 2022

QUP Low Temperature — M. Garcia-Sciveres

6[Talk by M. Garcia-Sciverse]

12
L = (@µ a)
2

1 2 2
ma a + (i/
@
2

@µ a
me ) +
2fµ

5,

マグノンによる暗黒物質の吸収where denotes the electron and f is of the order of the Peccei-Quinn symmetry

et theal (1989),
Chigusa,the
Moroi,
Nakayama(2020)] Ha
scale. Then, in the non-relativistic[Barbieri
limit ofelectron,totalinteraction
アクシオン-電子相互作用of the material isX1@µ a µ
~
~
H
=
ra(~
x
)
·
S
L=
int
`
`,
5
f `
2f
YIG
~` is the electron spin at each cite ` (see Appendix A).
アクシオンの勾配は振動磁場のように振る舞う
where S
Below we treat the axion as a classical background described bya(~x, t) = a cos(m t m ~v · ~x + ),スピンのゆらぎの量子化＝マグノン
磁性体のスピン波（マグノン）を励起

電子スピンの歳差運動を引き起こす
0

a

a a

wikipedia

Ferromagnetism and Antijerromagnetism
スピンのゆらぎ＝スピン波with ✓
va ⌧ 1. This treatment is valid within the axion coherence time ⌧a ⇠
12

p

3

Note that ma a0 = 2⇢DM , with ⇢DM ⇠ 0.3 GeV/cm being the energy density othe following, the location of the ferromagnetic material is chosen to be close to~x ⇠ 0. Then, the interaction Hamiltonian becomes
Figurc 9m
A spinwave
on X
a line of spins.
The spins viewed in perspective. (b) Spins viewed
a
v
a
0
a
~ is drawn through the ends of the spin vectors.
from ahow, showing
wavclcngth. The wave
(a)

UII~

アクシオン暗黒物質の場合

ダークフォトン暗黒物質の場合

Figure 1: Sensitivity plot for SNR = 3 underT=
10years.
Left:
Sensitivity
of
the
total
[Chigusa,
Moroi,
Nakayama(2020)]
Figure 2: Sensitivity of the magnon (left) and cav
magnon detector on the axion-electron couplinggaee as a function of the axion mass ma .
We use M= 1 kg and T= 10 years. The
target

total

-20

Readout line. From this measurement we obtain a sysp
7
i
tem
noise
temperature
T
=
1.0
K,
and
a
gain
of
70.4
dB
n
4
QUAX
Use
of
Qubit
JPAexperimentfrom D1 to Readout (see Fig. 2). In our setup, the couTABLE I. Parameters determined in the experiment. The error ranges indicate the 95% confidence interval.
pling
of D1
can bewhere gq m is the coupling strength
betweenthe varied
Kittel of 8 dB, thus we estimate aT
D1the qubitParameter
S
SymbolValue cavity
Microwave
mode and[28, 34–36].
calibration
uncertainty
of
16%.
We
measuredthe
JPAg
Dressed magnon frequency!m/2⇡
7.94962 GHz
Combining Eqs. (12), (15)
and
(16),
the
Hamiltonian(n =0)
gain, thetem!cavity
ac-Stark-shifted
qubitHEMTs
frequency noise temperature, and!q the/2⇡7.99156 GHz#of the hybrid quantum
system,including the e↵ective(n =0)
Broadened
qubit
linewidth/2⇡Tab. I. The
0.78 ± 0.03 MHzqperature
to
get
the
noise
budgetdetailed
inaxion-induced e↵ective
field,
is given by
Probemagnetic
cavity-mode
linewidth
p /2⇡
3.72 ± 0.03 MHz!
⇣ 0.12⌘Magnonlinewidth
1.3 ± 0.3 MHzK
di↵erence
may
be
due
to
unaccounted
losses, or
m /2⇡
"
↵
↵
2
D2 Ĥ /~ = ! ĉ † ĉ +Qubit–probe-mode† dispersive†shift
0.8 ± 0.2 MHz
%eff
$q-m
q p /2⇡!
q̂
q̂ + temperature
q̂ q̂
tot
m
q non-precise
control.
Qubit–magnon-mode
dispersiveshift
1.5 ± 0.1 MHz
2
2
YIG
q m /2⇡
Superconducting
FerrimagneticspMagnetmw-cavityp+ gq m (q̂ †Probe-modeĉ + q̂ĉ † ) +occupancyge↵ ĉ† e i!a t + ĉei!a t.
Source(17)ngp

0.22 ± 0.17
qubit

crystalEstimatedN
Quantum noise
0.50 K∼ 1/2π ω∼ 2/2π ω∼ 0/2π ω∼ 3/2πω
0.12 Kqqnoiseqq Thermal
FIG. 1. Schematic
illustration of the detector. A spheri10
work
HEMTs noisecal ferrimagnetic
0.25 K crystal and aThis
transmon-type superconduct-

Here,

5

cs of the apparatus. The cavity is reported 0.2 Ba sin ✓ p~ge↵ = 2µB
N,
(18)
10
n YIG spheres are in black, and the blue4
ing qubit are coherently
coupled through a microwave cav10
ermeated by a uniform magnetic field. The
Data
ity. Thee↵ectivemagnetic
fieldof the axion DM coherImproved
stats.
is the e↵ective coupling
constant
betweenaxionsandExpected
total
0.87
K
10
m temperature HEMT amplifiers are A1 and 0.15
ently drives the uniform spin-precession mode (Kittel mode)
magnons, which corresponds toFitthe strength of the co10in the ferrimagnetic
crystal with an e↵ective coupling connd the JPA ports are the herent
signal magnon(s), idlerdrive.
(i)
10 strong
Measured total stantTn ge↵0.99
CAST. InKthedispersive regime, each magnon exuperconducting cables are Let
brown,
theredus consider the dispersive
regime corresponding
10 mode shifts the resonance frequency of the0.1
cited in the Kittel
thermometers, SO is a source
to a oscillator,
detuning and!m between the qubit freWhite dwarf coolingq m ⌘ !qqubit by 2 qThem10+measured
a , where noiseq m is the dispersive shift and
TABLE
I:
Noise
budgetoftheapparatus.
ghown with their reductionquency
factor!qinand
dB.
theAs
frequency of the Kittel mode !m . This
giant
=
!
!a10is the Red
detuning
between the frequency !a ofamiscompatible
withtheestimatedone.
is muche calibration of the system
gainlarger
and thannoisethe coupling strength gq m such thatthe axion-induced
10 e↵ective magnetic field and the frequency
0.05
g
ion
the
exchangeofenergybetweenthetwosystemsishighly!
thein the ground state |gi.
Z axqubitS
ined by injecting signals in the SO line. The
m of the Kittel mode withFD
10
suppressed[28]. For this limit, the total Hamiltonian of
the HS is given in termsof an e↵ective
To double check the accuracy of the result,wemeasure
10
10
10
Eq.
(17)
can
be
rewritten
asortional to Acal . The errors are within the0thethermal noise of the HS. The noise di↵erence for Log!1 ma [eV]. See text for further details.
1
0
†
†
−8
−9

Log gaee~
Qubit spectrum S(ωs) (arb.)

−7

−10

QUAX 2018−6

QUAX 2020

G. Flower (2019)

−5

−11

−12
−13
−14
−15
−16

−5

−4

it

on ando↵ qtheand light blue)Ĥtot /~ ' !m ĉ ĉ +!
˜ q ˆz +ĉ ˆz resonance (dark bluem ĉJPA
FIG.
4.spectroscopy
Constraints on frequency
the coupling [39].
constantgthis
aee between
2
where
!
is
the
In
sub0.01s[Ikeda,Ito,
Miuchi,
Soda,
Kurashige,
Shikano(2020)][QUAX
collaboration(2020)]
gives
the
noise
added
by
the
hybridmode(orangecurve),
axions and electrons. The region excluded by this work†withi!
a tpresenti!
at
4: Exclusion plot at 95% CL on the axion-electron coupling+obtained
theprototype(excluded
regionreported
section,ananalytical model for the qubit spectrum inge↵ ĉ e
+ ĉe
,
(19)
with 95% confidence is shown in red. The mass range ismetry
⌅
0
0
0
1
1
1
0
1
1
1

固体中のアクシオン準粒子
トポロジカル絶縁体[Kane, Mele (2005), Fu, Kane, Mele (2007)]✓ = 0 : normal insulator↵e d e µ⌫
L = ✓ Fµ⌫ F
Conventional ν=0
insulator
1
2
3 4⇡4
5
6
7 ✓8= ⇡ : topologicalInsulator

E

8
Conduction Band

⇧
(a)
(b)
0
0
Z
0
Z
0
Z
0
Z
EF
1
Z
0
Z
0
Z
0
Z
0
磁性体における“アクシオン”の存在可能性
0
0
0
0
Z
0 Z2 Z2 Z
Quantum[Wilczek
spin(1987)]
1Z
0
0
0
Z
0 Z2 Z2
Hall insulator ν=1
Valence Band
✓
!
✓(t,
~
x
)
0
Z2 Z
0
0
0
Z
0 Z2
−π /a
0
k −π /a1
Z2 Z2 Z000
Z
000 Z2 Z2 Z
0
0
0
Z
FIG.
5 Edge states in the quantum [Hasan,
spin Hall
insulator.
(a)
トポロジカル磁性体における“アクシオン”
Mele (2010)]
1Z
0 Z2 Z2 Z000shows the interface between a QSHI and an ordinary insulator,and (2009)](b) shows the edge state dispersion in the graphene
00 Fe-dopedZ
0 Z2 Bi2Se3Z2 Z
0[Li, Wang,
0
Qi,
Zhang
model,
in
which
up
and
down
spins
propagateinopposite
1
00
Z
0 Z2 Z2 Z
0
directions.
<latexit sha1_base64="3/Cz1i6qa/+4N5fwYFeGHn/IakI=">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</latexit>interest at each site. The model Hamiltonian is gi
iefly review the Fu-Kane-Mele-Hubbard model on the diamond lattice. We
X
X[Sekine,
Nomura(2014)]
4†
f-filling例：Fu-Kane-Mele-Hubbard
case, i.e., there is only one 模型
electron at the electronHorbitalsofourtij ci cj + i 2
0 =ah site. The model Hamiltonian is given by H = H0 + HU :
hi,ji
hhi,
X
X
X
4
†
†
1
2
~
~
HU = Uni" ni# ,H0 =tij ci cj + i 2
ci ~ · (dij ⇥ dij )cj ,
(4.1)
a
i
hi,ji
hhi,jiiX
FULL PAPERS
FULL PAPERS
HU = Uni" ni# ,
(4.2)
7
i

shownthatthat
hown
outthetheposposut
2121 In anse.
7
e. In ansite
interacte interacel,
theexisexis, theorphasephasehas
haseseofofthreethreeond lattice,mondlattice,asasa amodel
model
eproperties
properties
ane-Mele- Fig. 1. (Color online) (a) A diamond lattice, which consists of two subKane-MeleFig. 1. (Color online) (a) A diamond lattice, which consists of two subhis(red(redandandblue),
and andeacheachsublatticeforms
a fccalattice.
(b) Thethismodel,
model, lattices
latticesblue),
sublatticeforms
fcc lattice.
(b)first
The first
Brillouinzone
of aoffcc
lattice.
Green
circles
represent
the Xthepoints.
merge.
Brillouin
zone
a fcc
lattice.
Green
circles
represent
X points.
merge.
etoelectric

3 Dirac points in Brillouin zone

この模型では反強磁性マグノン〜 “アクシオン”~k固体アクシオンを利用した暗黒物質検出[Marsh et al (2018), Chigusa, Moroi, Nakayama (2021)]

WidebandTHz
Source

E THz

1
µ⌫
e
L ⇠ (ga a + Ca ↵) Fµ⌫ F
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Source PowerAQ MaterialN

暗黒物質から固体アクシオンへの変換
a

↵,
E
B0

S

B0

z
x

f [THz]By|Ty| Function
Transmission

固体アクシオンは暗黒物質アクシオンと同じ形の電磁相互作用を持つ

1

0

0

E

Detector

B0

d

Be

[Schutte-Engel et al. (2021)]

Figure 6: Proposed transmission experiment B
to detect thEsource power spectrum. Centre: Transmission experiment c

アクシオン暗黒物質の場合

ダークフォトン暗黒物質の場合

ensitivity of the magnon to the ALP DM in the ma vs. ga plane. The orange
Figure2:
SensitivityofthemagnontotheDMhiddenphoton
in
the
m
vs.
✏
H
n corresponds to the sensitivity of the -mode (↵-mode) with u~0 v~0 = 10,
color
and
line
style
convention
andtheexperimental
set
up
are
the
same
as
tho
[Chigusa,
Moroi,
Nakayama(2021)]
t-dashed line in each region shows the sensitivity of the corresponding mode
3 The gray region is a combination of existing constraints, while the mag
in
Fig.
1.
= 1. We postulate the target volume V = (10 cm) and the magnetic field暗黒物質検出と物性物理
物質の種類によって色んな準粒子が存在する
比較的軽い暗黒物質の検出に向いている
吸収型の暗黒物質：1 meV ~ 1 keV ぐらい
散乱型の暗黒物質：1 keV ~ 1 GeV ぐらい

暗黒物質の種類によって、反応のし易さが違う
アクシオン … 電子/核子スピンと結合

マグノン

ダークフォトン … 電子/核子電荷と結合

フォノン

こうしたアイデアに基づいた実験計画も進行中

erial engineering
37
on eﬃciency
37
ge state eﬃciency
37
ptical eﬀects on NV charge state eﬃciency
38
al eﬀects on NV charge state eﬃciency
38
ダイヤモンドセンサー
synthesis and high pressure high temperaturet
39
Nitrogen-Vacancy(NV)
中心の
irradiation
41
sure high temperatureannealing42
電子の量子状態を制御
mmon impurities in synthetic or treated single
amond
43(２電子のspin triplet state)ial orientation452017), and industrial vector m2017).

量子センサーと暗黒物質検出

磁場、温度、圧力などの
sensing techniques45
cho magnetometry
高感度センサーとして利用45

c phase magnetometry
45
ssisted upconversion
magnetometry45
アクシオン暗黒物質検出へ応用
es for the strong NV -NV interaction regime 46

b

a

V
N

¯¯ ]
NV || [111

[Chigusa, Hazumi, Herbschleb, Mizuochi, Nakayama, (2023)]

FIG. 1 Overview of the nitrogenmagnetic resonance (NMR) (Wuplanetary science (Glenn et al.,
tor magnetometry (Grosz et al.,

NV中心による磁場検出
Ramsey sequence:

バイアス磁場

初期状態： |0i<latexit sha1_base64="FvQNAwqFf1Q1/xea7GF+kgcGXvU=">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</latexit>b

6&& ' ,2&.45

most magnetic sensing applica
π/2-パルス:
Hamiltonian describing the NVof the hyperfine states.
1
the +presencep In(|0i|+1i)of a magneti~ = (0, 0, Bz
2internuclear
axis Bby8:. .

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Free precession!" # $%
;:

. .

87
.

9

(

0

ge µ B
磁場があると状態のD+
B!" # '% 2.87GHz

B(z)
H0 /h = @時間発展に影響( ) *+,-./01h00π/2-パルス!" # &

with eigenstates |ms = 0i, |mmagnetic-field-dependent
tran
終状態を読み出す（蛍光）

パルスfor the NV ground state spin in
FIG. 2 Energy level diagram
the presence of an axial magnetic field Bz and ignoring nuclear

ogen-vacancy (NV) center quantum-⌫± = D ±

µ

~
~
¯
L
=
g
√∞
∞
√
!
H
=
ra
·
Se ,
ter that interacts
with the5 electron spinaee
eff like a magnetic≤ of
2m ematter Let us discuss effectsm
Effects of darke darkµ∫mat-

"
Note
that,
since
typically
∞
(4)
e
Rø
R
≤e
e
ø e
°i 0 Heff d t
1
~
~
~
'
I°i
H
d
t
.
Un
field. An example is the axion a(~
x , t ), whoseeff
L =interaction° F µ∫ H La- ! e Note
Heff =
(
r
£
H
)
·
S
.
(5
0
e
S(±)
=
cos
µ
+
that,
since
typically∞
ter that interacts with the electron spin like2 a magnetic off-diagonalmRe elements
R
2
ø e
of
(8)
a
grangianandtheresultingeffective
Hamiltonian
are
given
ø
~
°i
H
d
t
eff
with
S
being
the
electron
spin.
Anotherexampleisthedarkeeff d t . U
0e' I°i 0 H
field.e An example is the axion a(~
x , t ), whose interaction La- besafely neglected.interactio
For m øby [20]In
bothcases,
theeffective
dark
matter-electron
photonHµand(~x , tthe) withthe kinetic
with arethegiven
Standard
off-diagonal elements of (8) agrangianresultingeffectivemixing
Hamiltonian
nents
are
important.
Then,
we
Note
that
±
takes
ra
Hamiltonianisexpressedas
アクシオン
be safely neglected. For m øby [20]@µ a[21],µModelphotong aee~"¯ ∞5 √ ! Heff =ø,althoughinea
L = g aee√∞ra · ~
Se ,
(4)
DM
nents
are
important.
Then,
w
ef
2m
m
~
~
∞
B
e
1
H
=
∞
B
·
S
cos(mt+±),(6ez≤@eµ a µ∫
≤e
e
e
g
eff
eff
aee
as
ø
ø
ø
.
To
take
µ
DM
S(±)
=
cos
µ
+
sin
µ
~
~
~
~
~
"
¯
LL==
g aee
√∞
∞
√
!
H
=
ra
·
S
,
(4)
° F µ∫ H 5 !
Heff(r £ He ) · S e .
(5)
eff =
2
m
e
2m
m
~
∞e B
e
e
1
2 electronmwith S e being the
spin. Anotherexample
is
the
dark
the
average
of
an
ar
e
z
with

暗黒物質のNV中心への影響

S(±) =
cos µ + sin µ
photon~Hµ (~x , t ) with the kinetic mixing with the Standard
2
m
(
with
S ecases,
being theelectron
spin.
Anotherexample is thedark
g aee Note that ± takes random valu
In
both
the
effective
dark
matter-electroninteractionp
ダークフォトン≠~v
foraxion,
Model
photon [21],DMe~~photon
H
(
x
,
t
)
with
the
kinetic
mixingwith
theStandardøDM , ¢although in each Ramseyµ is expressed as
B eff = 2Ω DM £ °(7Hamiltonian
Note
that
±
takes
randomvalu≤ ~v DMas£ øĤø øfor .dark
photon,≤ [21],µ∫≤eModel photon
To take account oDM~~~øDM , although in each Ramse
L = ° F µ∫ H!
Heff =(r £ H ) · S e .
(5)~eff · ~2 ≤ Heff = ∞e BmtheaverageofanarbitraryfuneScos(mt
+
±),
(6)
≤e
e
as ø ømass,
øDM . Totakeaccountµ∫
wheremdenotesthedarkmatterv
thetypica~~~DM
L = ° F µ∫ H!
Heff =(r £ H ) · S e .
(5)
h
i
Since
S
=
0,
the
st
Z
2
m
the
averageofanarbitraryfuneIn both cases, the effective dark matter-electroninteraction
dark matter
velocity,Ω DM the dark matter energy
densit≠Æ1
暗黒物質が電子に及ぼす
“磁場”
with
typicalsizedafof¥theHamiltonianisexpressedasaroundtheEarth,±
anarbitrary
phase
of
the
dark
matte
Z
In both cases, the effective
darkmatter-electroninteraction
2º
(g
≠
Æ
0
1
~
~
lated
as
aee
oscillation,
and
Ĥ
¥
H
/|
H
|
the
direction
of
the
dark
pho
f
¥
Hamiltonian
expressed
as
pis
~
v
for
axion,
p
~
~
DM
H
=
∞
B
·
S
cos(mt
+
±),
(6)
e
2º
e
e
°8
eff
eff
~
°
¢
B eff = 2Ω DM £ton field. We can estimate (7)2Ω DM v DM ' 1.3 £ 10 qT fo
hSi
Since
=
0,
the
standard
de
~
≤
v
£
Ĥ
for
dark
photon,~~≠3°3
Heff = ∞e B eff ·DM
S e cos(mt
+
±),
(6)
Ω
=
0.4
GeV/cm
and
v
=
10
[1].
For
reference,
th
2
DM
DM
with
S
typicalsize=of0,thematterSince hSi
thedarkstandard°1dede Broglie wavelength of the dark matter is ∏ = (mv ) 'アクシオンダークフォトンmagnetic field as weak as4¢B sp '

ø/T2§

∞e

e
p

µ

12 ∂1/2 µ10' 13 fTN
N øt obs

0.5 µsø∂1/2 µ

1s
t obs

∂1/2

(1

where the exponential factor represents the sensitivity lo
according to the spin dephasing with a relaxation time T§
This factor makes ø ª T2 /2 to be the optimal choice to ma
imize the sensitivity [39], which is assumed on the righhand side.
The sensitivityondarkmattermodelsisestimate
q≠ Æ
°
¢
§
°ø/T2
eff 2
2
S e
= ¢S sp . We replace B zbby solving

2
B eff/3 to take into account the randomness of the dire~eff . The resulting sensitivities on g aee for ation of B
FIG. 1:ion
Theandreach
NV-centeron dark≤ offordiamonddark photon
aremagnetometry
shown in Fig.
1. W
mattermodels.
(Top)
The
case
of axiondark mattersetups:
coupling[Chigusa, Hazumi,
Herbschleb,
Mizuochi,Nakayama,(2023)]
draw
three
lines
for
three
experimental(Nwith, t obs )electron. 12(Bottom) The
12 case of dark
20 photon dark matter with ki(10 , 1 s), (10 , 1 year), (10 , 1 year) with ø = 0.5 µs. Th

まとめ
暗黒物質の研究は多岐に渡る
今日紹介したものはほんの一部！

検出のための色んなアイデアが求められている
宇宙物理・物性物理の応用や、検出器のテクノロジーの進展など
たぶんまだ誰も思い付いていないアイデアがたくさんある