Axion Dark Matter : Motivation and Search Techniques

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1 Axion Dark Matter : Motivation and Search Techniques Pierre Sikivie UCLA DM Conference February 17, 2016

2 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

3 Axion Search Techniques the cavity haloscope the axion helioscope shining light through walls NMR methods axion mediated long-range forces LC circuit atomic transitions

4 where The Strong CP Problem 2 g a a LQCD =... + G G % θ µν 2 µν 32π θ = θ = θ arg ( m m... m ) u d u d arg det ( Y Y ) t The absence of P and CP violation in the strong interactions requires θ from upper limit on the neutron electric dipole moment

5 If a U (1) PQ symmetry is assumed, 2 a g a aµν 1 µ L =... + G G% a a. 2 µν + µ +.. f 32π 2 a = a f a relaxes to zero, and a light neutral pseudoscalar particle is predicted: the axion. Weinberg, Wilczek 1978

6 m ; 6 a ev 6 10 GeV f a f a f L a ff = ig f a f a f 5 f γ γ L a = g a f a E B a g γ = 0.97 in KSVZ model 0.36 in DFSZ model

7 The remaining axion window 10 f a (GeV) ma (ev) laboratory searches cosmology stellar evolution

8 Axion production by vacuum realignment V V T 1 GeV a T 1 GeV a 1 a ; a ; a n m a f α ( t ) ( t ) ( t ) ( t ) t1 3 7 R ; m n t1 m ρa( t ) a a( ) R 0 1 a initial misalignment angle J. Preskill, M. Wise & F. Wilczek, L. Abbott & PS, M. Dine & W. Fischler, 1983

9 Cold axion properties number density nt () : 5 47 f 3 a at cm 10 GeV at ( ) 4 10 ( ) 3 velocity dispersion phase space density v( t) δ : 1 m t a 1 at ( 1) a() t if decoupled N 3 (2 π ) : nt () : 10 4π 3 m 3 ( δ v) a 61 f a GeV 8 3

10 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

11 why do they do that? by yielding their energy to the non-condensed particles, the total entropy is increased. prebec BEC

12 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

13 Quantum axion field dynamics H = From j 1 4! 4 p 3, p 4 p 1, p 2 = ja j a j + ijkl self-interactions 1 4 ij kl a k a l a ia j 4m 2 V p 1+ p 2, p 3 + p 4 O. Erken et al., PRD 85 (2012) From gravitational self-interactions p 3,p 4 g p 1,p 2 = 4 Gm2 V 1 p 1 +p 2,p 3 +p 4 p 1 p p 1 p 4 2

14 After t 1, axions thermalize in the condensed regime >> E d dt N l = i ijk 1 2 ( kl ij a i a j a ka l h.c.) implies 1 4 n m 2 for 4 and 4 Gnm 2 2 for self-gravity ( 1/ p)

15 Thermalization occurs due to gravitational interactions PS + Q. Yang, PRL 103 (2009) Gm 2 q 2 q g 4 Gnm 2 l H(t 1 ) with l = ( mδ v) f GeV t at time Γ g ()/ t H() t ta() t 1 at ()

16 Gravitational interactions thermalize the axions and cause them to form a BEC when the photon temperature T 500 ev f GeV 1 2 After that 1 δ v : mt 3 3 Γ ()/ () () g t H t t a t

17 Axion BEC thermalization has also been discussed by Saikawa and Yamaguchi, Phys. Rev. D87 (2015) S. Davidson and Elmer, JCAP 1312 (2013) 034 J. Berges and J. Jaeckel, Phys. Rev. D91 (2015) A. Guth, M.P. Hertzberg and C. Prescod-Weinstein, Phys. Rev. D92 (2015)

18 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

19 Tidal torque theory neighboring protogalaxy Stromberg 1934; Hoyle 1947; Peebles 1969, 1971

20 Tidal torque theory with ordinary CDM neighboring protogalaxy ur r v = 0 the velocity field remains irrotational

21 Tidal torque theory with axion BEC ur r v 0 in their lowest energy available state, the axions fall in with net overall rotation

22 simulation by Arvind Natarajan in case of net overall rotation

23 The caustic ring cross-section D-4 an elliptic umbilic catastrophe

24 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 ( n =1, 2,3... ) a n 40kpc vrot jmax = n 220km/s 0.18 j 0.18 was expected for the Milky Way max halo from the effect of angular momentum on the inner rotation curve.

25 Axion Search Techniques the cavity haloscope the axion helioscope shining light through walls NMR methods axion mediated long-range forces LC circuit atomic transitions

26 Axion dark matter is detectable a γ PS '83 L a = g a f a E B X ur B0 ur ETM 001 ur B0 A/D FFT

27 1 2 2 hν = m c (1 + β a 2 ) β v = : c 10 3 dp dν Qa 1 ν Q : a 6 10 ma c 2 / h ν 1 QL ν

28 Axion Dark Matter experiment see talks here by G. Carosi and B. Brubaker

29 Gen 2 ADMX sensitivity Will scan the lower-mass decade at or below DFSZ sensitivity

30 Axion to photon conversion in a magnetic field p a conversion probability x ur B0 2 qzl sin α gγ 2 ( a γ ) 2 = Β0 π fa qz 2 2 ma ωpl qz = 2 with E a γ 2 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

31 Tokyo Axion Helioscope

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33 CAST Collaboration: Phys. Rev. Lett. 112 (2013)

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36 Shining light through walls K. van Bibber et al. 87 A. Ringwald 03 γ a γ R. Rabadan, A. Ringwald and C. Sigurdson 05 x ur B0 x ur B0 P. Pugnat et al. '05 C. Robilliard et al. '07 A. Afanasev et al. '08 rate 1 f a 4 A. Chou et al. '08 K. Ehret et al. '10

37 Limits from "light through wall" axion searches

38 Resonantly Enhanced Axion-Photon Regeneration (a) Laser γ B 0 a Wall B 0 Photon Detector Magnet Magnet L L (b) Photon Detectors Laser IO Magnet Magnet Matched Fabry-Perots F. Hoogeveen (1996); P.S., D. Tanner and K. van Bibber (2007)

39 ALPS II at DESY Expected sensitivity : GeV 1

40 Laser experiments PVLAS g aγγ (GeV -1 ) Solar search Resonantly enhanced photon regeneration HB Stars Axion models Microwave cavity dark matter searches m a (ev)

41 Macroscopic forces mediated by axions ( γ + θ ) f L f a f i f 5 f f a f = g m f a Theory: J. Moody and F. Wilczek 84 forces coupled to the f spin density background of magnetic forces forces coupled to the f number density ϑ f : Experiment: A. Youdin et al. 96 W.-T. Ni et al. 96

42 NMR with long range axion field A. Arvanitaki and A. Geraci, 2014 H int = g f m f f a(x) H f int = g f m f a the rotating mass on the left produces an oscillating axion field th = N B 0 f a a(x) the oscillating axion field is an effective magnetic field in an NMR experiment

43 the axion field induces an oscillating nuclear electric dip d e e cm a(x) f a

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45 Axion dark matter detection using an LC circuit PS, D. Tanner and N. Sullivan, 2013 to re B a = j a g a B0 ( x) ta( x, t) circuit should be cooled to milli-kelvin temperatures

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47 Axion dark matter detection using atomic transitions PS 2014 L a ff = g f 2f a µ a(x) f(x) µ 5f(x) f is electron, or nucleon a H a ff =+ g f 2f a f a - tune using the Zeeman effect - use laser techniques to count axion induced transitions - must cool to milli-kelvin temperatures

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50 Conclusions Axion dark matter is well motivated Axion dark matter can be detected over most of the plausible mass range