sikivie - university of california, los angelesaxions are present in many models of...
TRANSCRIPT
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Axion Dark Matter : Motivation and Search Techniques
Pierre Sikivie
UCLA DM Conference February 17, 2016
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• Motivation
Axions solve the strong CP problem
Axions are present in many models of beyond-the-Standard Model physics Axions are a form of cold dark matter Axion BEC explains the existence and properties of caustic rings in galactic halos
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• Axion Search Techniques
the cavity haloscope the axion helioscope
shining light through walls NMR methods axion mediated long-range forces
LC circuit atomic transitions
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The Strong CP Problem 2
QCD 2... 32a agL G G µνµνθ π
= +
%
where arg ( ... )u tdm m mθ θ = − arg det ( )u dY Yθ= −
The absence of P and CP violation in the strong interactions requires
from upper limit on the neutron electric dipole moment
1010θ −≤
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If a symmetry is assumed,
relaxes to zero,
PQU (1)
2
2
1... .32 2
a a
a
a gL G G a af
µν µµν µπ
= + + ∂ ∂ + ..
%
and a light neutral pseudoscalar particle is predicted: the axion.
Weinberg, Wilczek 1978
�̄ =a
fa
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f f
a
a
γγ
610 GeVeVa
a fm 6 ;
= 0.97 in KSVZ model 0.36 in DFSZ model
gγ
Laf̄f = igfa
faf̄�5f
La�� = g�a
fa�E · �B
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The remaining axion window
laboratory searches
510 15101010 (GeV)af
(eV)am 1 510− 1010−
stellar evolution
cosmology
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Axion production by vacuum realignment
2 2 21 1 1 1
1
1
2
1
2( ) ( ) ( ) ( )a a at t t tt
n m a f α ; ;
GeVT ≥ 1 GeVT ≤ 1
V
a
V
a
1
0
3 76
0 1( ) ( )a aa aR
Rt tm mnρ −⎛ ⎞ ∝ ⎜ ⎟
⎝ ⎠ ;
initial misalignment angle
J. Preskill, M. Wise & F. Wilczek, L. Abbott & PS, M. Dine & W. Fischler, 1983
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Cold axion properties
• number density
• velocity dispersion • phase space density
5 347 31
3 12
( )4 10( )cm 10 GeV ( )
af a tn ta t
⎛ ⎞⋅ ⎛ ⎞ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠:
1
1
( )1( )
v( )a
a tm t a t
tδ
:
83 361
1234
3
(2 )( ) 1010 GeV( v)
a
a
fn tmππ
δ
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ : :N
if decoupled
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Bose-Einstein Condensation
if identical bosonic particles are highly condensed in phase space and their total number is conserved and they thermalize then most of them go to the lowest energy available state
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why do they do that?
by yielding their energy to the non-condensed particles, the total entropy is increased.
BEC preBEC
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the axions thermalize and form a BEC after a time
t < � t > �
the axion fluid obeys classical field equations, behaves like CDM
the axion fluid does not obey classical field equations, does not behave like CDM
�
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Quantum axion field dynamics
H =�
j
�ja†jaj +
�
ijkl
14�ijkla
†ka
†l aiaj
From self-interactions
From gravitational self-interactions
14!
�⇥4
� ⇥p3,⇥p4� ⇥p1,⇥p2 = �⇥
4m2V�⇥p1+⇥p2,⇥p3+⇥p4
� �p3,�p4g �p1,�p2 = �4⇥Gm2
V��p1+�p2,�p3+�p4
�1
|⇤p1 � ⇤p3|2+
1|⇤p1 � ⇤p4|2
⇥
O. Erken et al., PRD 85 (2012) 063520
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After , axions thermalize in the “condensed” regime
implies
�
t1
� >> �E
d
dtNl = i
�
ijk
12(�klija
†ia
†jakal � h.c.)
� � 14n�m�2 for
and for self-gravity
�⇥4
(⇥ � 1/�p)� � 4�Gnm2⇥2
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Thermalization occurs due to gravitational interactions
at time 1t
-1with v)l mδ= (
1 ( )( ) / ( ) ( )g a tt H t t a t −Γ ∝ ∝
2
2
Gmq
q
PS + Q. Yang, PRL 103 (2009) 111301
�g � 4�Gnm2l2
� 5 · 10�7H(t1)�
f
1012 GeV
⇥ 23
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Gravitational interactions thermalize the axions and cause them to form a BEC when the photon temperature
After that 1vm t
δ
:
3 3( ) / ( ) ( )g t H t t a t−Γ ∝
T� � 500 eV�
f
1012 GeV
⇥ 12
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Axion BEC thermalization has also been discussed by
• Saikawa and Yamaguchi, Phys. Rev. D87 (2015) 085010
• S. Davidson and Elmer, JCAP 1312 (2013) 034 • J. Berges and J. Jaeckel, Phys. Rev. D91 (2015)
025020
• A. Guth, M.P. Hertzberg and C. Prescod-Weinstein, Phys. Rev. D92 (2015) 103513
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Guth et al. write: " ... we conclude that while a Bose-Einstein condensate is formed, the claim of long-range correlation is
unjustified."
the axion BEC is inhomogeneous because it is gravitationally unstable. However it does have the long range correlations that are characteristic of BEC. The BEC correlation length is not to be identified with the scale of homogeneity.
homogeneity length scale
BEC correlation length
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Tidal torque theory
neighboring protogalaxy
Stromberg 1934; Hoyle 1947; Peebles 1969, 1971
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Tidal torque theory with ordinary CDM
neighboring protogalaxy
the velocity field remains irrotational
v 0∇× =ur r
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Tidal torque theory with axion BEC
v 0∇× ≠ur r
in their lowest energy available state, the axions fall in with net overall rotation
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simulation by Arvind Natarajan
in case of net overall rotation
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The caustic ring cross-section
an elliptic umbilic catastrophe
D -4
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On the basis of the self-similar infall model (Filmore and Goldreich, Bertschinger) with angular momentum (Tkachev, Wang + PS), the caustic rings were predicted to be
in the galactic plane with radii
was expected for the Milky Way halo from the effect of angular momentum on the inner rotation curve.
( )1,2,3...n =
maxj 0.18≅
rot max40kpc v j220km/s 0.18
nn
a ⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
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• Axion Search Techniques
the cavity haloscope the axion helioscope
shining light through walls NMR methods axion mediated long-range forces
LC circuit atomic transitions
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Axion dark matter is detectable
0Bur
γa
X
A/D FFT 0Bur001TME
ur
PS '83
La�� = g�a
fa�E · �B
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3v 10c
β − = :
2 21
2)ah m c βν = (1 +
1aQ ν−
1LQ ν−
ν
dPdν
2 /am hc
610aQ :
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Axion Dark Matter eXperiment see talks here by G. Carosi and B. Brubaker
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Gen 2 ADMX sensitivity
Will scan the lower-mass decade at or below DFSZ sensitivity
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Axion to photon conversion in a magnetic field
Theory
• P. S. ’83 • L. Maiani, R. Petronzio and E. Zavattini ’86 • K. van Bibber et al. ’87 • G. Raffelt and L. Stodolsky, ‘88 • K. van Bibber et al. ’89
Experiment • D. Lazarus et al. ’92 • R. Cameron et al. ‘93 • S. Moriyama et al. ’98, Y. Inoue et al. ’02 • K. Zioutas et al. 04 • E. Zavattini et al. 05
0Bur
γa
22
2 2sin
( )z
za
Lqg
af q
p γα
γπ 0
⎛ ⎞ ⎜ ⎟⎛ ⎞←→ = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎜ ⎟
⎝ ⎠
Β
x
with
conversion probability
2 2pl
2za
aE
mq
ω − =
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Tokyo Axion Helioscope
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CAST Collaboration: Phys. Rev. Lett. 112 (2013) 091302
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Shining light through walls K. van Bibber et al. ‘87 A. Ringwald ‘03 R. Rabadan, A. Ringwald and C. Sigurdson ‘05 P. Pugnat et al. '05 C. Robilliard et al. '07 A. Afanasev et al. '08 A. Chou et al. '08 K. Ehret et al. '10
0Bur
γ
x 0Bur
γa
x
rate 41
af∝
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Limits from "light through wall" axion searches
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(a)
(b)
Wall Photon DetectoraγLaser
L
B0
Magnet
B0
Magnet
L
Matched Fabry-Perots
IOLaser
MagnetMagnet
Photon Detectors
Resonantly Enhanced Axion-Photon Regeneration
F. Hoogeveen (1996); P.S., D. Tanner and K. van Bibber (2007)
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ALPS II at DESY
Expected sensitivity : 2 · 10�11 GeV�1
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PVLASLaser experiments
Solar search
HB StarsResonantly enhancedphoton regeneration
ma (eV)10-6 10-5 10-4 10-3 10-2
10-16
10-8
10-10
10-12
10-14
10-4
10-6
g aγγ
(GeV
-1)
Microwave cavity dark matter searches
Axion models
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Macroscopic forces mediated by axions
Theory:
J. Moody and F. Wilczek ’84 Experiment: A. Youdin et al. ’96 W.-T. Ni et al. ‘96
( )5ff ffa fa
mf
fL a i fg θγ + =
forces coupled to the f number density
forces coupled to the f spin density
1710fϑ− :background of magnetic forces
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NMR with long range axion field
th
A. Arvanitaki and A. Geraci, 2014
⇥ = �NB0
the rotating mass on the left produces an oscillating axion field
the oscillating axion field is an effective magnetic field in an NMR experiment
Hint =gfmf�f
faa(x) Hint =
gfmffa
⇥�a(x) · ⇥�
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de � 10�16 e cma(x)fa
the axion field induces an oscillating nuclear electric dipole moment
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Axion dark matter detection using an LC circuit
to re
PS, D. Tanner and N. Sullivan, 2013
circuit should be cooled to milli-Kelvin temperatures
⇥⇤� ⇥Ba = ⇥ja ⇥ ga�� ⇥B0(⇥x) �ta(⇥x, t)
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Axion dark matter detection using atomic transitions
- tune using the Zeeman effect - use laser techniques to count axion induced transitions - must cool to milli-Kelvin temperatures
PS 2014
Laf̄f = �gf2fa
⇥µa(x)f̄(x)�µ�5f(x)
f is electron, or nucleon
Haf̄f = +gf2fa
⇥�f · ⇥�aa
���
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Conclusions
• Axion dark matter is well motivated
• Axion dark matter can be detected over most of the plausible mass range