Axion

Georg G. Raffelt, Max-Planck 

Planck-Institut Axions 

für f 

Physik, München 

PONT d’Avignon, 21-25 25 April 2008, Avignon, France 

Georg Raffelt, Max-Planck-Institut für Physik, München, Germany 

PONT d‘Avignon, 21-25 April 2008, Avignon, France 

Motivation, Limits and Searches


Axion Physics in a Nut Shell 


Particle-Physics Physics Motivation 

CP conservation in QCD by 

Peccei-Quinn mechanism 

→ Axions a ~ π 0 

m π f π ≈ m a f a 

For f a ≫ f π axions are “invisible” 

and very light 

a 

γ 

γ 

Solar and Stellar Axions 

Axions thermally produced in stars, 

e.g. by Primakoff production 

γ 

a 

• Limits from avoiding excessive 

energy drain 

• Search for solar axions (CAST, Sumico) 

Cosmology 

Search for Axion Dark Matter 

In spite of small mass, axions 

are born non-relativistically 

(“non-thermal relics”) 

N 

Microwave resonator 

(1 GHz = 4 μeV) 

→ “Cold dark matter” 

candidate 

m a ~ 1-10001 

1000 μeV 

Cosmic 

String 

S 

a 

Primakoff 

conversion 

B ext 

γ


The CP Problem of Strong Interactions 


Characterizes degenerate 

QCD ground state (Θ( 

vacuum) 

Phase of Quark 

Mass Matrix 

Standard 

QCD Lagrangian 

contains 

a CP violating term 

L 

CP 

α 

= − 

s 

( 

Θ − 

arg det M 

) Tr G ~ 

q μν 

G 

8 

π 

14 4 

2 

4 4 

3 

0 

≤Θ≤ 

2 

π 

μν 

Induces a neutron 

electric dipole moment 

(EDM) much in excess 

of experimental limits 

d 

n 

≈ 

Θ 

10 

− 

16 

e cm 

≈ 

Θ 

10 

2 

μ 

n 

< 

3 

× 

10 

− 

26 

e 

cm 

Θ 

≲ 

10 −10 

Why so small


Dynamical Solution 


Peccei & Quinn 1977 - Wilczek 1978 - Weinberg 1978 

Θ 

Re-interpret as 

a dynamical variable 

(scalar field) 

L 

CP 

Θ → 

a(x) 

f a 

Pseudo-scalar 

scalar axion field 

Peccei-Quinn scale, 

Axion decay constant 

α 

s 

Tr(GG ~ 

α 

= − Θ ) 

a(x) 

L 

s 

Tr(GG ~ 

CP = − 

) 

8 

π 

8 

π 

f 

a 

V(a) 

Θ = 

0 

a 

Potential (mass term) 

induced by L CP drives 

a(x) to CP-conserving 

minimum 

CP-symmetry 

dynamically restored 

a 

gluon 

gluon 

Axions generically couple 

to gluons and mix with π 0 

⎛ 

Axion 

mass 

⎞ 

⎛ 

Pion 

mass 

⎞ 

f 

⎜ 

⎟ 

~ 

⎜ 

⎟ × 

π 

⎝ 

& couplings 

⎠ 

⎝ 

& couplings 

⎠ 

f a 

f 

π 

≈ 

93 

MeV 

Pion decay constant

Peccei-Quinn Mechanism Proposed in 1977 


PONT d‘Avignon, 21-25 April 2008, Avignon, France


The Pool Table Analogy 


P.Sikivie 

Sikivie, , Physics Today, Dec. 1996, pg. 22 

Gravity 

Pool table 

Symmetric 

relative 

to gravity




P.Sikivie 


Gravity 

Pool table 

Symmetric 

relative 

to gravity 

Floor 

inclined 

Symmetry 

broken




P.Sikivie 


Gravity 

Pool table 

Axis 

Symmetric 

relative 

to gravity 

Floor 

inclined 

Symmetry 

broken 

f a 

Symmetry 

dynamically 

restored 

(Peccei & Quinn 1977)




P.Sikivie 


Gravity 

Pool table 

Axis 

Symmetric 

relative 

to gravity 

Floor 

inclined 

Symmetry 

broken 

New degree 

of freedom 

Axion 

Θ _ 

(Weinberg 1978, Wilczek 1978) 

f a 

Symmetry 

dynamically 

restored 

(Peccei & Quinn 1977)


30 Years of Axions 



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)


Windows of Opportunity 


Axions 

Solve strong CP problem 

by Peccei-Quinn 

dynamical symmetry restoration 

Alternatives 

• Massless up-quark 

• Spontaneous CP violation 

• Θ = 

0 

set at some high energy scale 

(no radiative corrections) 

• Supersymmetric particles 

• Superheavy particles 

• Cosmic cold dark matter candidate 

• Sterile Neutrinos 

• Direct detection possible 

• 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) 

saw) 

• Proton decay 

• Neutron electric dipole moment 

• Deviation from Newton’s Law 

(e.g. large extra dimensions)


Axions as a Research Topic 


160 

140 

120 

100 

80 

60 

40 

20 

0 

1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 

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)

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 f a 

• Axions are the corresponding Nambu-Goldstone mode 

E ≈ f a 

V(a) 

• U PQ (1) spontaneously broken 

• Higgs field settles in 

“Mexican hat” 

a 

E ≈ Λ QCD ≪ f a 

V(a) 

• U PQ (1) explicitly broken 

by instanton effects 

• Mexican hat tilts 

• Axions acquire a mass 

_ 

Θ=0 

a


From Standard to Invisible Axions 


Standard Model 

All Higgs degrees of 

freedom are used up 

Standard Axion 

Weinberg 1978, Wilczek 1978 

• Peccei-Quinn scale f a = 

electroweak scale f ew 

• Two Higgs fields, 

separately giving mass 

to up-type quarks and 

down-type quarks 

Invisible Axion 

Kim 1979, Shifman, 

Vainshtein, Zakharov 1980, 

Dine, Fischler, Srednicki 1981 

Zhitnitsky 1980 

• Additional Higgs with 

f a ≫ f ew 

• 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


Axion Properties 


Gluon coupling 

(Generic property) 

Mass 

Photon coupling 

Pion coupling 

Nucleon coupling 

(axial vector) 

Electron coupling 

(optional) 

L 

m 

L 

g 

L 

L 

L 

aG 

a 

a 

a 

α 

= s 

GG ~ 

a 

a 

8 

π 

f 

= 

f 

a 

a 

0.6 eV 

/10 

7 

GeV 

C 

= N 

Ψ 

N 

γμ 

γ 

2f 

m 

f 

≈ 

π 

f 

Ψ 

∂ 

aN 5 N 

μ 

a 

C 

= e 

Ψ 

e 

γ 

μ 

γ 

2f 

Ψ 

∂ 

a 

a 

ae 5 e 

μ 

a 

π 

g 

a 

γ 

FF ~ r r 

γ = − a 

= 

g 

a 

γ 

E 

⋅ 

Baa 

4 

α 

⎛ 

E 

⎞ 

γ = 

⎜ 

− 

1. 

92 

⎟ 2 

π 

f 

⎝ 

N 

⎠ a 

π 

a 

C 

= 

a 

π 

( 

π 

0 

π 

+ 

∂ 

− 

...) 

μ 

μπ 

+ ∂ 

a 

f 

f 

a 

π 

a 

a 

a 

a 

π 

π 

G 

G 

γ 

γ 

π 

a 

N 

N 

e 

e

Supernova 1987A Energy-Loss Argument 



Neutrino 

sphere 

SN 1987A neutrino signal 

Neutrino 

diffusion 

Volume emission 

of novel particles 

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.) 

Late-time time signal most sensitive observable

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 f a 

• Axions are the corresponding Nambu-Goldstone mode 

E ≈ f a 

V(a) 

• U PQ (1) spontaneously broken 

• Higgs field settles in 

“Mexican hat” 

a 

E ≈ Λ QCD ≪ f a 

V(a) 

• U PQ (1) explicitly broken 

by instanton effects 

• Mexican hat tilts 

• Axions acquire a mass 

_ 

Θ=0 

a

Series of Papers on Axion Cosmology in PLB 120 (1983) 



Page 127




Page 133




Page 137


Killing Two Birds with One Stone 


Peccei-Quinn mechanism 

• Solves strong CP problem 

• May provide dark matter 

in the form of axions

Production of Cold Axion Population in the Early Universe 



Approximate axion 

cold dark matter density 

Ω 

a 

≈ 

7/6 

⎛ 

f 

12 a ⎞ ⎛1μeV 

⎞ 

0.5 

⎜ ⎟ ≈ 4 ⎜ ⎟ 

⎝ 

10 

GeV 

⎠ 

⎝ 

m 

a 

⎠ 

7/6 

Inflation after PQ symmetry breaking 

Reheating restores PQ symmetry 

Homogeneous mode oscillates after 

T ≲ Λ QCD 

Dependence on initial misalignment 

angle 

Ω 

∝ 

Θ 

a 

Θi 

• Cosmic strings of broken U PQ (1) 

form by Kibble mechanism 

• Radiate long-wavelength axions 

• Ω a 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 Λ I ≲ 10 13 GeV 

[Beltrán, García-Bellido & Lesgourgues 

hep-ph/0606107] 

ph/0606107] 

Inhomogeneities of axion field large, 

self-couplings lead to formation of 

mini-clusters 

Typical properties 

• Mass ~ 10 −12 

M sun 

• Radius ~ 10 10 cm 

• Mass fraction up to several 10%


Axions from Cosmic Strings 


Strings form by Kibble mechanism 

after break-down of U PQ (1) 

Small loops form by self-intersection 

Paul Shellard


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 ~ 10 −12 

M sun 

Radius ~ 10 10 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]

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 Θ i 

• 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 darkd 

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, 023505 (2006) [arXiv:astro-ph/0511774]

Axion Hot Dark Matter from Thermalization after Λ QCD 



Cosmic thermal degrees of 

freedom 

Freeze-out temperature 

L 

a 

π 

C 

= 

a 

f 

f 

a 

π 

π 

( 

π 

π π 

0 

π 

+ 

∂ 

μ 

π 

− 

− 

2 

π 

+ π 

+ 

0 

π 

π 

− 

− 

∂ 

∂ 

μ 

μ 

π 

π 

0 

+ 

) 

∂ 

μ 

a 

10 4 10 5 10 6 10 7 

f a (GeV) 

Cosmic thermal degrees of 

freedom at axion freeze-out 

π 

a 

C a 

1 

− 

z 

π 

= 

≈ 

0.094094 

3(1 

+ 

z) 

Chang & Choi, PLB 316 (1993) 51 

10 4 10 5 10 6 10 7 

f a (GeV)

Lee-Weinberg Curve for Neutrinos and Axions 



Axions 

log(Ω a ) 

Ω M 

Non-Thermal 

Relics 

CDM 

Thermal Relics 

HDM 

10 μeV 

10 eV 

log(m a ) 

Neutrinos 

& WIMPs 

log(Ω ν ) 

Ω M 

HDM 

Thermal Relics 

CDM 

10 eV 

10 GeV 

log(m ν )

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:0803.1585] 

Marginalizing over unknown neutrino hot dark matter component 

m a 

m a 

< 1.0 eV (95% CL) 

WMAP-5, LSS, BAO, SNIa 

< 0.4 eV (95% CL) WMAP-3, small-scale scale CMB, 

HST, BBN, LSS, Ly-α 

Hannestad, Mirizzi, Raffelt 

& Wong [arXiv:0803.1585[ 

arXiv:0803.1585] 

Melchiorri, Mena & Slosar 

[arXiv:0705.2695]


Axion Bounds 


10 3 10 6 10 9 10 12 [GeV] f a 

m a 

keV 

eV 

meV 

μeV 

Experiments 

Tele 

scope 

CAST 

Direct 

search 

ADMX 

Too much hot dark matter 

Too much 

cold dark matter 

Globular clusters 

(a-γ-coupling) 

Too many 

events 

Too much 

energy loss 

SN 1987A (a-N-coupling)

Experimental Tests of the Invisible Axion 



Primakoff effect: 

Axions-photon transitions in external 

static E or B field 

(Originally discussed for π 0 

by Henri Primakoff 1951) 

Pierre Sikivie: 

Macroscopic B-field B 

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

Search for Galactic Axions (Cold Dark Matter) 



DM axions 

m a = 1-10001 

1000 μeV 

Velocities in galaxy 

v a ≈ 10 −3 c 

Energies therefore 

E a ≈ (1 ± 10 −6 ) m a 

Microwave Energies 

(1 GHz ≈ 4 μeV) 

Axion Haloscope (Sikivie 1983) 

B ext ≈ 8 Tesla 

Microwave 

Resonator 

Q ≈ 10 5 

Power 

Frequency 

m a 

Axion Signal 

Thermal noise of 

cavity & detector 

Primakoff Conversion 

a 

γ 

B ext 

Cavity 

overcomes 

momentum 

mismatch 

Power of galactic axion signal 

2 

× 

−21 

V ⎛ B ⎞ Q 

4 10 

W 

3 

⎜ ⎟ 

⎝ 8.5T ⎠ 5 

0.22m 10 

⎛ 

m 

⎞⎛ 

× ⎜ a ⎟ 

⎜ 

⎝ 

2 

π 

GHz 

⎠ 

⎝ 

5 

× 

10 

ρ 

a 

− 

25 

g/cm 

3 

⎞ 

⎟ 

⎠


Axion Dark Matter Searches 


Limits/sensitivities, assuming axions are the galactic dark matter 

3 

2 

1 

1. Rochester-Brookhaven 

Brookhaven- 

Fermilab 

PRD 40 (1989) 3153 

5 

4 

2. University of Florida 

PRD 42 (1990) 1297 

3. US Axion Search 

(Livermore) 

ApJL 571 (2002) L27 

4. CARRACK I (Kyoto) 

preliminary 

hep-ph/0101200 

ph/0101200 

5. ADMX (Livermore) 

foreseen 

e.g. Rev. Mod. Phys. 

75 (2003) 777


ADMX (G.Carosi, Fermilab, May 2007) 














Renewed ADMX 

data taking has begun 

on 28 March 2008 

(Same day as CAST He-3 3 began)





Fine Structure in Axion Spectrum 


• Axion distribution on a 3-dim 3 

sheet in 6-dim 6 

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


Search for Solar Axions 


γ 

Primakoff 

production 

Sun 

a 

Axion flux 

Axion Helioscope (Sikivie 1983) 

a 

Axion-Photon 

Photon-Oscillation 

Magnet 

N 

S 

γ 

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, ...)


Tokyo Axion Helioscope (“Sumico”) 


~ 3 m 

S.Moriyama, M.Minowa 

Minowa, , T.Namba 

Namba, , Y.Inoue, Y.Takasu 

& A.Yamamoto, PLB 434 (1998) 147

Results and Plans of Tokyo Axion Helioscope (“Sumico”) 



S. Inoue at TAUP 07

Extending to higher mass values with gas filling 



Axion-photon transition probability 

⎛ g 

γB 

2 

a ⎞ 

⎛ 

⎞ 

= ⎜ ⎟ 

2 qL 

Pa 

→γ 

sin 

⎜ 

⎟ ⎝ 

q 

⎠ 

⎝ 

2 

⎠ Axion-photon momentum transfer 

m 

2 

m 

2 

a − γ 

q 

= 

2E 

Transition suppressed for qL ≳ 1 

Gas filling: Give photons a refractive 

mass to restore full transition strength 

(~ MSW effect) 

2 

4 

πα 

m 

γ = 

n 

e 

(n m 

e electron density) 

e 

Z 

m 

γ 

= 

28.9 eV 

ρ 

Gas 

A 

He 4 vapour pressure at 1.8 K 

ρ 

≈ 

0 .2 

× 

10 

− 

3 g 

cm 

− 

3 

m γ 

= 

0.26 

eV

LHC Magnet Mounted as a Telescope to Follow the Sun 




CAST at CERN 



CAST Focussing X-Ray X 

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-rayx 

satellite


Sun Spot on CCD with X-Ray X 

Telescope 



Limits from CAST-I I and CAST-II 


CAST-I I results: PRL 94:121301 (2005) and JCAP 0704 (2007) 010 

CAST-II results (He-4 4 filling): preliminary


Limits on Axion-Photon 

Photon-Coupling 


Axion-photon photon-coupling g aγ [GeV 

-1 ] 

10 -4 

10 -6 

10 -8 

10 -10 

10 -12 

10 -14 

10 -16 

Laser 

PVLAS expected 

Tokyo Helioscope 

CAST Sensitivity 

DM 

Search 

Future 

DFSZ model 

KSVZ model 

PVLAS 

Signature 

Helio 

seis 

mology 

+Gas 

Telescope 

Axion Line 

HB 

Stars 

10 -7 

10 -6 

10 -5 

10 -4 

10 -3 

10 -2 

10 -1 

1 10 100 

Axion mass m a [eV]



Alps 

Axion-like particles (ALPs) 

(Pseudo)-scalar scalar particles with a two-photon vertex


Particles with Two-Photon Coupling 


Particles with two-photon vertex: 

• Neutral pions (π( 

0 ), Gravitons 

• Axions (a) and similar hypothetical particles 

L 

a 

γ 

r 

= g 

γr E 

⋅ 

Baa 

a 

Two-photon 

decay 

Γ 

a 

γ 

= 

g 

2 

a 

γ 

m 

64 

π 

3 

a 

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 

Mouton-effect 

PVLAS experiment recently measured an 

effect ~ 10 4 larger than QED expectation 

(Signal now disproved)

Dimming of Supernovae without Cosmic Acceleration 



Axion-photon 

photon-oscillations oscillations in intergalactic B-field domains dim photon flux 

Effect grows linearly with distance 

Saturates at equipartition between photons and axions (unlike grey g 

dust) 

Mixing matrix 

Domain size ~ 1 Mpc 

Field strength ~ 1 nG 

a-γ-coupling ~ 10 −10 

GeV −1 

Axion mass < 10 −16 

eV 

2 

1 

2 

1 

⎛ 

pl 

ga 

B ⎞ 

− 

γ ⎛ 

10.8ne 

0.15ga 

B ⎞ 

⎜ 

ω ω 

⎟ 

⎜ 

ω 

γ 

−1 

= 

⎟ Mpc 

2 

ω 

⎜ 

2 

⎟ 

2 

4 2 

1 

ga 

B 

m 

⎜ 

a 0.15g 

a B 7.8 10 

− 

m 

− ⎟ 

γ 

⎝ γ × aω 

⎝ 

ω 

⎠ 

⎠ 

Photon energy ~ 1 eV 

Electron density 

~ 10 −7 cm −3 

(average baryon density) 

Chromaticity depends 

sensitively on assumed 

values and distribution 

of n e and B 

Csáki, Kaloper & Terning (hep-ph/0111311, ph/0111311, hep-ph/0112212, ph/0112212, astro-ph/0409596). Erlich & Grojean 

(hep-ph/0111335). ph/0111335). Deffayet, et al. (hep-ph/0112118). ph/0112118). Christensson & Fairbairn (astro-ph/0207525). 

Mörtsell et al. (astro-ph/0202153). 

Mörtsell & Goobar (astro-ph/0303081). Bassett (astro-ph/ 

0311495). Ostman & Mörtsell 

(astro-ph/0410501). Mirizzi, Raffelt & Serpico (astro-ph/0506078).


Cantatore 12 



The PVLAS Dichroism Signal 


PVLAS, PRL 96:110406 (2006), hep-ex/0507107 

ex/0507107


Latest PVLAS Results 


Zavattini et al., PRD 77:032006, 2008 [arXiv:0706.3419]


Photon Regeneration Experiments 


Single pass 

“Shining light through a wall” 

Resonant 

cavities on 

generation & 

regeneration 

side 

hep-ph/0701198 

ph/0701198


No Light Shining Through a Wall 


BMV Experiment, using a pulsed 

laser and pulsed magnetic field 

(Toulouse) 

Robilliard et al., arXiv:0707.1296 

GammeV Experiment 

with a variable baseline 

(Fermilab) 

Chou et al., arXiv:0710.3783

Technological Applications of PVLAS Particles 



arXiv:0704.0490v1 [hep-ph] 

ph]

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