1. Georg G. Raffelt, Max-Planck-Institut für Physik, München
Axions
Georg G. Raffelt, Max-Planck-Institut für Physik, München
Motivation, Limits and Searches
Axions
PONT d’Avignon, April 2008, Avignon, France

2. Axion Physics in a Nut Shell
Particle-Physics Motivation
CP conservation in QCD by
Peccei-Quinn mechanism
For fa ≫ fp axions are “invisible”
and very light
 Axions a ~ p0
mpfp  mafa g a
Solar and Stellar Axions
Axions thermally produced in stars,
e.g. by Primakoff production
Limits from avoiding excessive
energy drain
Search for solar axions (CAST, Sumico) a g
Cosmology
Cosmic
String
In spite of small mass, axions
are born non-relativistically
(“non-thermal relics”)
 “Cold dark matter”
candidate
ma ~ meV
Search for Axion Dark Matter S N g a
Bext
Microwave resonator
(1 GHz = 4 meV)
Primakoff
conversion

3. The CP Problem of Strong Interactions
Characterizes degenerate
QCD ground state (Q vacuum)
Phase of Quark
Mass Matrix
Standard
QCD Lagrangian
contains
a CP violating term
Induces a neutron
electric dipole moment
(EDM) much in excess
of experimental limits
Why so small ? ≲

4. Dynamical Solution
Peccei & Quinn Wilczek Weinberg 1978
Re-interpret as
a dynamical variable
(scalar field)
Peccei-Quinn scale,
Axion decay constant
Pseudo-scalar axion field a
V(a)
Potential (mass term)
induced by LCP drives
a(x) to CP-conserving
minimum
CP-symmetry
dynamically restored
Axions generically couple
to gluons and mix with p0
gluon a
Pion decay constant

5. Peccei-Quinn Mechanism Proposed in 1977

6. P.Sikivie, Physics Today, Dec. 1996, pg. 22
The Pool Table Analogy
P.Sikivie, Physics Today, Dec. 1996, pg. 22
Gravity
Pool table
Symmetric
relative
to gravity
Axis
Symmetry
dynamically
restored
(Peccei & Quinn 1977)
New degree
of freedom
 Axion Q _
(Weinberg 1978, Wilczek 1978) fa
Symmetry
broken
Floor
inclined

7. 30 Years of Axions

8. The Cleansing Axion Frank Wilczek “I named them after a laundry
detergent, since they clean up
a problem with an axial current.”
(Nobel lecture 2004, written version)

9. Windows of Opportunity
Axions
Alternatives
Solve strong CP problem
by Peccei-Quinn
dynamical symmetry restoration
Massless up-quark
Spontaneous CP violation
set at some high energy scale
(no radiative corrections)
Cosmic cold dark matter candidate
Direct detection possible
Supersymmetric particles
Superheavy particles
Sterile Neutrinos
Many others …
(but usually not experimentally
accessible)
Search for new physics at E ≫ TeV
in low-energy experiments
(Axions Nambu-Goldstone boson of
spontaneously broken symmetry)
Neutrino masses (see-saw)
Proton decay
Neutron electric dipole moment
Deviation from Newton’s Law
(e.g. large extra dimensions)

10. Axions as a Research Topic
Papers in SPIRES that cite one of the two original Peccei and Quinn papers or
Weinberg’s or Wilczek’s paper or with “axion” or “axino” in their title
(total of 3186 papers up to 2007)

11. Axions as Pseudo Nambu-Goldstone Bosons
The realization of the Peccei-Quinn mechanism involves a new chiral
U(1) symmetry, spontaneously broken at a scale fa
Axions are the corresponding Nambu-Goldstone mode
E  fa
UPQ(1) spontaneously broken
Higgs field settles in
“Mexican hat” a
V(a)
E  LQCD ≪ fa
UPQ(1) explicitly broken
by instanton effects
Mexican hat tilts
Axions acquire a mass a
V(a)
Q=0 _

12. From Standard to Invisible Axions
Standard Model
Standard Axion
Weinberg 1978, Wilczek 1978
Invisible Axion
Kim 1979, Shifman,
Vainshtein, Zakharov 1980,
Dine, Fischler, Srednicki 1981
Zhitnitsky 1980
All Higgs degrees of
freedom are used up
Peccei-Quinn scale fa =
electroweak scale few
Two Higgs fields,
separately giving mass
to up-type quarks and
down-type quarks
Additional Higgs with
fa ≫ few
Axions very light and
and very weakly
interacting
No room for axions
Axions quickly ruled out
experimentally and
astrophysically
New scale required
Axions can be
cold dark matter
Can be detected

13. Axion Properties g p a e G Gluon coupling (Generic property) a Mass
Photon coupling g a
Pion coupling a p
Nucleon coupling
(axial vector) N a
Electron coupling
(optional) e a

14. Supernova 1987A Energy-Loss Argument
Neutrino
sphere
SN 1987A neutrino signal
Neutrino
diffusion
Late-time signal most sensitive observable
Emission of very weakly interacting
particles would “steal” energy from the
neutrino burst and shorten it.
(Early neutrino burst powered by accretion,
not sensitive to volume energy loss.)
Volume emission
of novel particles

15. Axions as Pseudo Nambu-Goldstone Bosons
The realization of the Peccei-Quinn mechanism involves a new chiral
U(1) symmetry, spontaneously broken at a scale fa
Axions are the corresponding Nambu-Goldstone mode
E  fa
UPQ(1) spontaneously broken
Higgs field settles in
“Mexican hat” a
V(a)
E  LQCD ≪ fa
UPQ(1) explicitly broken
by instanton effects
Mexican hat tilts
Axions acquire a mass a
V(a)
Q=0 _

16. Series of Papers on Axion Cosmology in PLB 120 (1983)
Page 127

17. Series of Papers on Axion Cosmology in PLB 120 (1983)
Page 133

18. Series of Papers on Axion Cosmology in PLB 120 (1983)
Page 137

19. Killing Two Birds with One Stone
Peccei-Quinn mechanism
Solves strong CP problem
May provide dark matter
in the form of axions

20. Production of Cold Axion Population in the Early Universe
Approximate axion
cold dark matter density
Inflation after PQ symmetry breaking
Homogeneous mode oscillates after
T ≲ LQCD
Dependence on initial misalignment
angle
Reheating restores PQ symmetry
Cosmic strings of broken UPQ(1)
form by Kibble mechanism
Radiate long-wavelength axions
Wa independent of initial conditions
Isocurvature fluctuations from large
quantum fluctuations of massless
axion field created during inflation
Strong CMBR bounds on isocurvature
fluctuations
Scale of inflation required to be
very small LI ≲ 1013 GeV
[Beltrán, García-Bellido & Lesgourgues
hep-ph/ ]
Inhomogeneities of axion field large,
self-couplings lead to formation of
mini-clusters
Typical properties
Mass ~ Msun
Radius ~ 1010 cm
Mass fraction up to several 10%

21. Axions from Cosmic Strings
Strings form by Kibble mechanism after break-down of UPQ(1)
Small loops form by self-intersection
Paul Shellard

22. Axion Mini Clusters
The inhomogeneities of the axion field are large, leading to bound objects,
“axion mini clusters”. [Hogan & Rees, PLB 205 (1988) 228.]
Self-coupling of axion field crucial for dynamics.
Typical mini cluster properties:
Mass ~ Msun
Radius ~ 1010 cm
Mass fraction up to several 10%
Potentially detectable with
gravitational femtolensing
Distribution of axion energy density.
2-dim slice of comoving length 0.25 pc
[Kolb & Tkachev, ApJ 460 (1996) L25]

23. Inflation, Axions, and the Anthropic Principle
Late inflation scenario of axion cosmology
Initial misalignment angle constant in our patch of the universe
Dark matter density determined by the initial random number Qi
Is different in different patches of the universe
Dark matter fraction not calculable from first principles
Random number chosen by process of spontaneous symmetry breaking
Natural case for applying anthropic reasoning for the observed dark
matter density relative to baryons
Linde, “Inflation and Axion Cosmology,” PLB 201:437, 1988
Tegmark, Aguirre, Rees & Wilczek,
“Dimensionless constants, cosmology and other dark matters,”
PRD 73, (2006) [arXiv:astro-ph/ ]

24. Axion Hot Dark Matter from Thermalization after LQCD
Cosmic thermal degrees of
freedom
Freeze-out temperature
104
105
106
107
fa (GeV)
Cosmic thermal degrees of
freedom at axion freeze-out p a
Chang & Choi, PLB 316 (1993) 51
104
105
106
107
fa (GeV)

25. Lee-Weinberg Curve for Neutrinos and Axions
log(Wa)
log(ma) WM
10 eV
10 meV
CDM
HDM
Axions
Thermal Relics
Non-Thermal
Relics
log(Wn)
log(mn) WM
10 eV
CDM
HDM
10 GeV
Neutrinos
& WIMPs
Thermal Relics

26. Axion Hot Dark Matter Limits from Precision Data
Credible regions for neutrino plus axion hot
dark matter (WMAP-5, LSS, BAO, SNIa)
Hannestad, Mirizzi, Raffelt & Wong
[arXiv: ]
Marginalizing over unknown neutrino hot dark matter component
ma < 1.0 eV (95% CL)
WMAP-5, LSS, BAO, SNIa
Hannestad, Mirizzi, Raffelt
& Wong [arXiv: ]
ma < 0.4 eV (95% CL)
WMAP-3, small-scale CMB,
HST, BBN, LSS, Ly-a
Melchiorri, Mena & Slosar
[arXiv: ]

27. Too much hot dark matter
Axion Bounds
103
106
109
1012
[GeV] fa eV
keV
meV ma
Experiments
Tele
scope
CAST
Direct
search
ADMX
Too much hot dark matter
Too much
cold dark matter
Globular clusters
(a-g-coupling)
Too many
events
Too much
energy loss
SN 1987A (a-N-coupling)

28. Experimental Tests of the Invisible Axion
Primakoff effect:
Axions-photon transitions in external
static E or B field
(Originally discussed for p0
by Henri Primakoff 1951)
Pierre Sikivie:
Macroscopic B-field can provide a
large coherent transition rate over
a big volume (low-mass axions)
Axion helioscope:
Look at the Sun through a dipole
magnet
Axion haloscope:
Look for dark-matter axions with
A microwave resonant cavity

29. Search for Galactic Axions (Cold Dark Matter)
Power
Frequency ma
Axion Signal
Thermal noise of
cavity & detector
Power of galactic axion signal
Microwave Energies
(1 GHz  4 meV)
DM axions
Velocities in galaxy
Energies therefore
ma = meV
va  10-3 c
Ea  (1  10-6) ma
Axion Haloscope (Sikivie 1983)
Bext  8 Tesla
Microwave
Resonator
Q  105
Primakoff Conversion g a
Bext
Cavity
overcomes
momentum
mismatch

30. Axion Dark Matter Searches
Limits/sensitivities, assuming axions are the galactic dark matter
4. CARRACK I (Kyoto)
preliminary
hep-ph/ 4
3. US Axion Search
(Livermore)
ApJL 571 (2002) L27
1. Rochester-Brookhaven-
Fermilab
PRD 40 (1989) 3153
2. University of Florida
PRD 42 (1990) 1297
5. ADMX (Livermore)
foreseen
e.g. Rev. Mod. Phys.
75 (2003) 777 5 3 2 1

31. ADMX (G.Carosi, Fermilab, May 2007)

32. ADMX (G.Carosi, Fermilab, May 2007)

33. ADMX (G.Carosi, Fermilab, May 2007)

34. ADMX (G.Carosi, Fermilab, May 2007)
Renewed ADMX
data taking has begun
on 28 March 2008
(Same day as CAST He-3 began)
ADMX (G.Carosi, Fermilab, May 2007)

35. ADMX (G.Carosi, Fermilab, May 2007)

36. Fine Structure in Axion Spectrum
Axion distribution on a 3-dim sheet in 6-dim phase space
Is “folded up” by galaxy formation
Velocity distribution shows narrow peaks that can be resolved
More detectable information than local dark matter density
P.Sikivie
& collaborators

37. Search for Solar Axions
Axion Helioscope (Sikivie 1983) g
Magnet S N a
Axion-Photon-Oscillation
Primakoff
production
Axion flux a g
Sun
Tokyo Axion Helioscope (“Sumico”)
(Results since 1998, up again 2008)
CERN Axion Solar Telescope (CAST)
(Data since 2003)
Alternative technique:
Bragg conversion in crystal
Experimental limits on solar axion flux
from dark-matter experiments
(SOLAX, COSME, DAMA, ...)

38. Tokyo Axion Helioscope (“Sumico”)
S.Moriyama, M.Minowa, T.Namba, Y.Inoue, Y.Takasu
& A.Yamamoto, PLB 434 (1998) 147

39. Results and Plans of Tokyo Axion Helioscope (“Sumico”)
S. Inoue at TAUP 07

40. Extending to higher mass values with gas filling
Axion-photon transition probability
Axion-photon momentum transfer
Transition suppressed for qL ≳ 1
Gas filling: Give photons a refractive
mass to restore full transition strength
(~ MSW effect)
(ne electron density)
He4 vapour pressure at 1.8 K

41. LHC Magnet Mounted as a Telescope to Follow the Sun

42. CAST at CERN

43. CAST Focussing X-Ray Telescope
From 43 mm  (LHC magnet aperture) to ~3 mm 
Signal/background improvement > 100
Signal and background simultaneously measured
One spare mirror system from the failed Abrixas x-ray
satellite

44. Sun Spot on CCD with X-Ray Telescope

45. Limits from CAST-I and CAST-II
CAST-I results: PRL 94: (2005) and JCAP 0704 (2007) 010
CAST-II results (He-4 filling): preliminary

46. Limits on Axion-Photon-Coupling
10-4
10-6
10-8
10-10
10-12
10-14
10-16
10-7
10-5
10-3
10-2
10-1 1 10
100
Axion mass ma [eV]
Axion-photon-coupling gag [GeV-1]
KSVZ model
DFSZ model
Axion Line
PVLAS expected
Tokyo Helioscope
Laser
PVLAS expected
Tokyo Helioscope
Helio
seis
mology
PVLAS expected HB
Stars
+Gas
CAST Sensitivity DM
Search
Telescope
PVLAS
Signature
Future
CAST Sensitivity
+Gas

47. Axion-like particles (ALPs)
(Pseudo)-scalar particles with a two-photon vertex

48. Particles with Two-Photon Coupling
Particles with two-photon vertex:
Neutral pions (0), Gravitons
Axions (a) and similar hypothetical particles
Two-photon
decay
Photon
Coalescence
Primakoff
Effect
Conversion of photons into
pions, gravitons or axions,
or the reverse
Magnetically
induced vacuum
birefringence
In addition to QED
Cotton-Mouton-effect
PVLAS experiment recently measured an
effect ~ 104 larger than QED expectation
(Signal now disproved)

49. Dimming of Supernovae without Cosmic Acceleration?
Axion-photon-oscillations in intergalactic B-field domains dim photon flux
 Effect grows linearly with distance
 Saturates at equipartition between photons and axions (unlike grey dust)
Mixing matrix
Domain size ~ 1 Mpc
Field strength ~ 1 nG
a-g-coupling ~ GeV-1
Axion mass < eV
Photon energy ~ 1 eV
Electron density
~ 10-7 cm-3
(average baryon density)
Chromaticity depends
sensitively on assumed
values and distribution
of ne and B
Csáki, Kaloper & Terning (hep-ph/ , hep-ph/ , astro-ph/ ). Erlich & Grojean
(hep-ph/ ). Deffayet, et al. (hep-ph/ ). Christensson & Fairbairn (astro-ph/ ).
Mörtsell et al. (astro-ph/ ). Mörtsell & Goobar (astro-ph/ ). Bassett (astro-ph/
). Ostman & Mörtsell (astro-ph/ ). Mirizzi, Raffelt & Serpico (astro-ph/ ).

50. Cantatore 12

51. The PVLAS Dichroism Signal
PVLAS, PRL 96: (2006), hep-ex/

52. Zavattini et al., PRD 77:032006, 2008 [arXiv:0706.3419]
Latest PVLAS Results
Zavattini et al., PRD 77:032006, 2008 [arXiv: ]

53. Photon Regeneration Experiments
“Shining light through a wall”
Single pass
Resonant
cavities on
generation &
regeneration
side
hep-ph/

54. No Light Shining Through a Wall
BMV Experiment, using a pulsed
laser and pulsed magnetic field
(Toulouse)
Robilliard et al., arXiv:
GammeV Experiment
with a variable baseline
(Fermilab)
Chou et al., arXiv:

55. Technological Applications of PVLAS Particles
arXiv: v1 [hep-ph]