Proceedings of the XXIX PHYSICS IN COLLISION, Fermilab Preprint# FERMILAB-CONF-09-498-E 1

Experimental probes of axionsAaron S. Chou

Fermi National Accelerator Laboratory, Wilson and Kirk Roads, Batavia, IL 60510-5011, U.S.A

AbstractExperimental searches for axions or axion-like parti-

cles rely on semiclassical phenomena resulting from thepostulated coupling of the axion to two photons. Sen-sitive probes of the extremely small coupling constantcan be made by exploiting familiar, coherent electro-magnetic laboratory techniques, including resonant en-hancement of transitions using microwave and opticalcavities, Bragg scattering, and coherent photon-axion os-cillations. The axion beam may either be astrophysicalin origin as in the case of dark matter axion searchesand solar axion searches, or created in the laboratoryfrom laser interactions with magnetic fields. This noteis meant to be a sampling of recent experimental results.

1. IntroductionAxion models are motivated by the strong CP

problem–the apparent vanishing of the CP- and T-violating electric dipole moment (EDM) of the neutron.The total EDM is expected to receive contributions fromboth the TeV electroweak scale, via the quark spin, andfrom the GeV QCD scale, via the spatial distribution ofthe quark wavefunction within the neutron. It is difficultto understand how these two contributions could can-cel to such precision to produce a CP-conserving QCDground state without fine-tuning of parameters.

The axion model of Peccei, Quinn, Weinberg, andWilczek [1, 2, 3, 4] offers a dynamical solution to thestrong CP problem by introducing a new scalar fieldwhich rolls within its potential into a state of minimumaction, a CP-conserving QCD vacuum state. Any im-balance between the contributions to the EDM from theTeV and GeV scales is absorbed into the scalar fieldvalue. The quantized excitations of the scalar field aboutthe potential minimum are called axions.

The complex scalar potential starts as a Higgs-likeMexican hat potential, with symmetry-breaking scale f .A massless Goldstone boson lives in the circular mini-mum of this potential at radius f in field space. Duringthe QCD phase transition, instanton effects give a lineartilt to this potential, lifting it by an amount Λ4

QCD on oneside. The degeneracy of the circular minimum is lifted,and the Goldstone boson starts rolling towards its min-imum. While rolling, a portion of the energy from thequark-gluon plasma is stored temporarily as potentialenergy. The quantized excitations about the potentialminimum are called axions, and have mass

ma ≈ Λ2QCD/f. (1)

When the minimum is reached, the original potentialenergy can be released as quanta of cold axions whichcould make up all or part of the inferred cold dark matterdensity of the universe.

The usually quoted search window for axions is10−6 eV < ma < 10−2 eV. Axions with ma > 10−2 eVare disfavored by the supernova SN1987A cooling ratevia the direct coupling of axions to fermions, suppressedby 1/f , which is then linked to mass via Eq. 1. Axionswith ma < 10−6 eV may remain cosmologically frozenfor too long before the potential energy density is con-verted into quanta, thus overproducing the cold dark

Fig. 1. The Peccei-Quinn symmetry is broken at some high massscale f , resulting in a Higgs-like potential. The potential istilted by instanton effects during the QCD phase transition,causing the Goldstone boson to roll towards a unique mini-mum. The quanta of small excitations about this minimumare called axions, and have mass ma = Λ2

QCD/f .

Fig. 2. (Left) While by design, axions are coupled to quarksand gluons, they also obtain couplings to two photons viatriangle anomaly diagrams. These effective couplings allowconversions between axions and photons, in the presence ofbackground electromagnetic fields. (Right) In Primakoff scat-tering, the axions convert into photons by interacting with theCoulomb field of a charged fermion.

matter density. However, the total initial potential en-ergy depends on the random QCD misalignment anglewhich describes where the original Goldstone boson wassitting in its circular potential before the potential wastilted. If the field was originally already sitting closeto the eventual minimum of the potential, then totalamount of potential energy available for conversion intodark matter is restricted, and lower values of ma areallowed.

The natural coupling of axions a to gluons or quarks istransferred to a coupling g to the photon field strengthF via an anomaly diagram.

L ≈ α

8πfF F̃ ≡ −1

4gaF F̃ = ga ~E · ~B. (2)

This electromagnetic coupling represents the best exper-imental hope to discover axions. For agnostic, model-independent searches, the experimental results are typi-cally presented in the two-dimensional parameter spaceof photon coupling g vs axion mass ma.

2. Axion Dark Matter Search (ADMX)The ADMX experiment is based on the axion halo-

scope idea of Sikivie. This idea is based on the modifica-tion to the Maxwell equations due to the photon-axioninteraction. In particular:

~∇× ~B − ∂t~E = −g ~B∂ta. (3)

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FERMILAB-CONF-09-498-E

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In the presence of a constant background field B0, thecurl term vanishes, and the electric field follows thetime evolution of the axion field, with amplitude sup-pressed by gB0. Due to the low dark matter halo ve-locity v ≈ 200 km/s, the cold dark matter axions areexpected to form a classical background field with co-herence length greater than 100m, much larger than thesize of a typical detector. In the presence of a laboratorymagnetic field, this spatially constant background axionfield will drive an oscillating electric field with microwavefrequency Ea ≈ ma. Using a microwave cavity, this elec-tric field can be built up coherently, with a quality factorlimited by the intrinsic energy spread of the axions. Thiskinetic energy spread is expected to be ∆E/E ≈ 10−6

for halo axions which have thermalized into a Maxwelliandistribution, or as small as ∆E/E ≈ 10−11 for cold flowsof dark matter which are entering the galaxy and havenot yet thermalized.

The ADMX experiment [5, 6, 7] uses a meter-scale mi-crowave cavity suffused with a 8 T field generated by asolenoidal magnet. Cavity power at the level of 10−23 Wcan be detected using antennas amplified by HEMTs or,in a recent upgrade, by SQUID magnetometers. The res-onant frequency of the cavity can be tuned by insertingdielectric rods into the cavity. The very small energyspread of the dark matter axions implies that millions oftrials are necessary to scan the cavity frequency througha range of axion masses, thus limiting the integrationtime at each step in frequency to be on the scale of min-utes. So far, no excess power has been detected abovethermal noise in any of the trials. These results can beinterpreted in two ways. First, if axions are assumed tobe the dominant component of cold dark matter, thenthis sets the normalization of the background axion fieldamplitude, and a non-observation of electric field givesan upper limit on the coupling g. Alternatively, if thecoupling g is assumed to be that predicted by one of thepopular models of axions such as the DFSZ or KSVZmodel, then an upper bound can be set on the densityof dark matter axions, which may contribute just a frac-tion of the total cold dark matter density. The presentresults constrain the model in which KSVZ-type axionsare the dominant form of dark matter.

Experimental scaling laws may be derived from theDicke radiometer equation which specifies the signal tonoise ratio

S

N=

Psignal

kTnoise

√t

∆ν(4)

where t is the integration time and ∆ν is the frequencybandwidth, and the expected cavity signal power

Psignal ∝g2B2

0QρaV

ma(5)

where Q is the limiting quality factor, ρa is the axiondark matter energy density, and V is the volume of thecavity. For a fixed S/N requirement, these two equationsyield a scan rate

dν

dt∝ B4

0V 2

T 2noise

(6)

for fixed sensitivity to coupling g, or a sensitivity to smallcouplings

g ∝

√Tnoise

B20V

(7)

for fixed scan rate. The current activity in ADMX isto reduce the system noise temperature Tnoise. The 2K

Fig. 3. In the presence of a background magnetic field, photonscan oscillate into axions and vice-versa. This leads to thephenomenon of light shining through walls, where photons canpenetrate opaque regions in the guise of axions. In the case ofsolar axion searches, the light source is the core of the sun, andthe wall is the outer plasma layers of the sun. In laser axionsearches, the wall is a reflective mirror or beam dump. Foranomalous transparency observed from astrophysical sources,the wall is the bath of extragalactic background photons.

HEMT-amplified sensors in the initial phase of the ex-periment have been replaced with SQUID magnetome-ters which currently have a noise temperature of 0.4K.A further upgrade will add a dilution refrigerator to re-duce the SQUID noise temperature to 0.1K. This noisereduction will allow the scan rate to be increased by afactor of ∼ 250, thus allowing more rapid coverage ofthe preferred range of masses for dark matter axions inthe 10−6 eV− 10−5 eV range. Extending this techniquetowards higher masses will require the design and de-velopment of smaller cavities and higher frequency, lownoise sensors.

3. Axion-photon oscillationsThe axion-photon interaction also manifests itself in

the semiclassical equations of motion of a propagatingaxion-photon system. Again, in the presence of a back-ground magnetic field B0, Eq. 2 becomes an off-diagonalterm in a bilinear mass matrix, and induces transitionsbetween photon flavor states (polarized along the direc-tion of B0) and axion flavor states. In analogy withneutrino mixing, the transition probability is given by

Pγ↔a = sin2(2θ) sin2

((m2

a −m2γ)L

4ω

)(8)

where m2a and m2

γ are the diagonal elements of the massmatrix, ω is the total energy of the wave, and the mix-ing angle θ is defined implicitly by the ratio of the off-diagonal elements to the diagonal elements

tan(2θ) =2gB0ω

m2a −m2

γ

. (9)

In the limit of small mixing angle and magnetic lengthslong compared to the natural oscillation length,

L � Losc ≡2ω

m2a −m2

γ

, (10)

the sines in Eq. 8 can be replaced by their arguments,and the conversion probability simplifies to

Pγ↔a ≈14(gB0L)2. (11)

This is referred to as the coherent limit, in which themixed amplitude monotonically grows with propagationdistance. Experiments have their maximum sensitivityto g when operating in this limit.

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Fig. 4. Summary of experimental results from microwave cav-ity searches for dark matter axions (assuming axions saturatethe dark matter density), helioscope searches from CAST, andBragg scattering search from CDMS. Helioscope prospects arebright as new magnets with B0L ≈ (14T )(15m) are devel-oped for future accelerators projects. Also shown is the up-per bound on g from star cooling of horizontal branch stars,the weak lower bound on ma from overproducing dark mat-ter, and the diagonal band representing typical QCD axionmodels.

4. Solar axion searches via oscillationExperiments such as the CERN Axion Solar Telescope

(CAST) [8, 9] or the Tokyo Axion Helioscope (Sumico)[10] use the sun as a possible source of keV energy axions.These axions can then be converted into detectable keVx-rays via oscillations within laboratory magnetic fields.At larger values of g, axions would be copiously producedin the hot core of the sun by Primakoff scattering, usingthe axion-photon interaction vertex. The axions wouldhave a blackbody-like spectrum reflecting the tempera-ture of the production region. The mean free path forreconversion into photons is longer than the radius of thesun, and so these axions free stream out, contributing tothe cooling of the sun. The total axion flux is estimatedto be Φa = 3.67 × 1011 cm−2s−1(g/10−10 GeV−1)2 andis proportional to g2. For g > 10−10 GeV−1, the cool-ing rate becomes inconsistent with the observed age ofstars. For the 9T, 9.3m accelerator dipole magnet with14.5 cm2 aperture used by the CAST experiment, thereconversion probability is

Pa→γ = 1.7× 10−17

(B0L

9T · 9.3m

)2(g

10−10 GeV−1

)2

,

(12)indicating that sensitivity beyond the star cooling limitis possible with reasonable integration time. The signalrate for coherent oscillation is given by

Rsignal = AΦaPa→γ ∝ Ag2(gB0L)2 (13)

where A is the collecting area. A variety of x-ray de-tectors have been used, including PIN photodiodes bythe Sumico experiment, and MicroMegas, TPCs, and x-ray telescopes to tightly focus the spot size on low noiseCCDs. All of these detectors have an intrinsic back-ground rate Rbkgd, and so in the absence of signal, the

upper limit on the signal rate scales as the square rootof integration time tint and gives the design equation

glimit ∝(

Rbkgd

tint

)1/8 1(B0L)1/2A1/4

, (14)

applicable to searches for axions of sufficiently lowmass to satisfy the coherence condition Eq. 10. TheCAST experiment has achieved the world’s best model-independent sensitivity to the photon coupling g <8.8 × 10−11 GeV−1, which slightly extends the upperbound from star cooling arguments.

The current effort in both CAST and Sumico is toextend the coherent sensitivity to larger axion mass byincreasing the effective mass of the photon to reduce themomentum difference between photons and axions andincrease the coherent oscillation length Losc in Eq. 10. Agas of neutral helium introduced into the magnet borewill look like a plasma to x-ray photons, which can re-solve the individual electrons in the atoms. The effectivephoton mass is then equal to the Debye frequency

mγ ≡√

4παne

me≈

√0.02

P [mbar]T [K]

[eV/c2] (15)

where ne is the electron number density, and P and T arethe pressure and temperature of the gas. Sumico uses a4T, 2.3m magnet of 3.1 cm2 aperture. The B × L is anorder of magnitude smaller than CAST, and so the de-tector is intrinsically less sensitive. However, the shorterlength allow Sumico to naturally probe towards largeraxion masses while remaining the coherent limit. Fur-thermore, the smaller magnetic field allows operation ofthe magnet at higher temperature T ≈ 6 K which allowshigher pressure levels of He4 gas and correspondinglyhigher mγ . For magnetic field 9.3T, the CAST super-conducting magnet must be operated at 1.8K at whichincreased pressure values would cause the He4 gas to con-dense. Instead, CAST must use the more expensive He3

gas to reach higher pressure levels. Both experimentsaim to probe towards eV mass axions by performing ascan in steps of gas pressure to optimize the detectorfor finite bandwidth steps in axion mass. Since eachtrial necessarily uses less integration time than the lowermass coherent data runs, the sensitivity to g is somewhatpoorer, and both experiments can only probe in a regionof parameter space disfavored by star cooling, and bythe SN1987A energy loss rate. However, this region hasnever been directly tested using sources as well-modeledas the sun and surprises may be in store.

Future efforts on CAST will be focused in reducingdetector background rates, and utilizing larger aperture,higher field accelerator magnets as they are developedfor future accelerator projects. Already, the backgroundrates of the MicroMegas detectors have been improvedby an order of magnitude by using better shielding, andlow radioactivity materials. If 14 T, 15 m magnetsbecome available it may be possible for an upgradedCAST experiment to achieve sensitivity at the level ofg ≈ 5× 10−12 GeV−1.

5. Solar search via Bragg scatteringSimilarly, a search for solar axions has been conducted

using the Cryogenic Dark Matter Search (CDMS) de-tectors [11]. The detection technique is now Bragg-likescattering in which the amplitudes for Primakoff scat-tering from individual electrons in an ordered Germa-nium crystal lattice add coherently for orientations of

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the beam and the crystal lattice which satisfy the usualBragg condition. The coherence enhances the scatteringprobability by factors up to ∼ 1000. In this scatter-ing process, the axion is converted into an x-ray photonwhich immediately deposits energy into the crystal in theform of ionization and heat. Nuclear recoil events canbe rejected using the ratio of ionization and phonon sig-nals, using the standard CDMS WIMP search technique.However, these axion-induced γ events cannot be distin-guished from other β or γ events on the basis of signalrisetime. A background rate of ∼ 1.5 count/day/kg/keVfrom electromagnetic events in both the surface and bulkof the crystals is seen, in an analysis window of 2.5-8 keVenergy, as measured by the phonon signal. To focus thesearch for an axion beam from the sun, a maximum like-lihood analysis is performed to look for excess event ratesas a function of measured energy and time of day, whichdetermines the instantaneous deviation from the Braggangle as a function of energy. No excess was detectedin a 443.2 kg-day sample, resulting in an upper limitg < 2.4× 10−9 GeV−1, independently of axion mass upuntil the kinematic limit ma < Tsun ≈ 104 K. Devel-opment of lower background detectors such as a solidxenon crystal, are underway and could further improvethis limit by an order of magnitude.

6. Laser axion searchesSeveral experiments have also been conducted using

lasers as axion sources. The laser beam is directed intoa transverse magnetic field B0 in which an axion beam isgenerated by the photon-axion oscillation process. Thepreferential depletion of one component of polarizationwith respect to the B0 direction can manifest itself asa rotation of the net polarization of the laser beam.An anomalous detection of such polarization rotationwas published but later retracted by the PVLAS experi-ment [12]. The inferred coupling was unexpectedly largeg ≈ 2 × 10−6 GeV−1, and inspired the development ofa number of new experiments (GammeV, BMV, LIPSS,ALPS, OSQAR), to verify this signal.

All of these experiments are based on the idea of shin-ing light through walls. A laser beam is sent into atransverse magnetic field where a tiny fraction of thelaser photons is converted into axions. An opaque wallis inserted into the laser path to block or deflect the un-converted photons. Being very weakly-interacting, theaxion beam passes unhindered through the wall and intoa second magnetic field region beyond where they oscil-late back into photons. The regenerated photons, whichhave apparently passed right through the wall, can be de-tected with a low noise photodetector. The probabilityfor photon oscillation and reconversion has two factorsof Eq. 11

Pregen =116

(gB0L)4, (16)

assuming equal B0L on both sides of the wall. Forbackground-free single photon detection, the sensitivityto low rates scales linearly with integration time tint, andthe sensitivity to the coupling scales as

glimit ∝1

B0Lt1/4int

. (17)

If background subtraction is required, then the sensitiv-ity to g scales as t

−1/8int .

As an example, the GammeV experiment [13] hasachieved nearly background-free operation by using apulsed 1064 nm laser which produced 20 Hz of 5 ns pulseswhich went into a 5T dipole magnet from the Tevatron

Fig. 5. By placing an optical cavity around the axion genera-tion region, the initial laser beam can be recycled and passedmany times through the magnetic field. The produced ax-ion beam is also shaped by the curvature of the mirrors. Asecond optical cavity is placed around the photon regenera-tion region, with curvature matched to the divergence of theaxion beam. Regenerated standing waves can then build upcoherently over the lifetime of the cavity, resulting in a largeenhancement in the number of regenerated photons.

accelerator. A beam-blocking mirror is inserted into themagnet bore to divide the 6m length into axion produc-tion and photon regeneration regions, each of which iscontained in a separately isolated vacuum system. Us-ing timing circuits with ∼ 1 ns precision, the search forregenerated photons can be performed in 10 ns windowsin coincidence with the pulse arrival times. The back-ground ∼ 100 Hz dark rate of a cooled photomultipliertube the produces an accidental coincidence rate of only2×10−5 Hz and allows 15 hours of background free run-ning. No excess signal has been seen, resulting in a limitof g < 3.5 × 10−7 GeV−1. This limit for odd-parityparticles, and a similar limit achieved for even-parityparticles achieved by rotating the initial laser polariza-tion by 90◦, completely rule out the explanation for thePVLAS anomaly in terms of axion-like particles. Theseresults are the current best laser limits on the axion-photon coupling, but are unfortunately still far from theastrophysical limits from star cooling and solar searches.Further sensitivity to g via this technique is limited bythe availability of stronger and longer magnets.

7. Cavity-enhanced photon regenerationAn ingenious proposal has recently been made to co-

herently enhance the photon regeneration rate using highfinesse Fabry-Perot optical cavities [14, 15]. A cavityis placed around the axion-generating magnet in orderto recycle the photon beam, or equivalently to increasethe instantaneous power within the cavity by a factor ofF/π. The finesse F is roughly equal to the number ofmirror reflections a photon makes before it escapes fromthe cavity. The curvature of the cavity mirrors also de-termines the transverse Gaussian profile of the trappedstanding wave. As long as the momentum differencebetween axions and photons is small, ∆m2/2ω � ω,the produced axion beam will have approximately thesame transverse momentum distribution as the photonbeam. The resulting Gaussian axion beam will undergodiffraction-limited expansion as it leaves the cavity andpasses through an opaque wall. Beyond this wall, asecond cavity is placed around the photon-regeneratingmagnet. The curvature of the mirrors is matched tothe shape of the expanding axion beam so that any re-generated electromagnetic field can efficiently populatea standing wave in the second cavity. If the relativephase between the two cavities can be maintained, thenthe standing wave electric field will build up coherentlyin the second cavity, again over approximately F reflec-tions and gives an enhancement of F2 in photon num-ber. In effect, axions generated from multiple reflectionsin the first cavity all contribute coherently to the pho-

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ton standing wave in the second cavity, resulting in thislarge “wavefunction-squared” enhancement in the totalcavity power. The regenerated photon signal can thenbe seen as the regenerated photons leak out through theend mirror. If the cavity losses which determine F aredominated by transmission through this end mirror, thenthe instantaneous leaked photon rate is suppressed bya factor of 1/F . The net result is that the regeneratedphoton rate is coherently enhanced by a factor of F2, po-tentially an extremely large number. For a laser photonrate Rlaser, the number of detectable regerated photonsis

Nregen = (Rlasertint)116

(gB0L)4(Fπ

)2

. (18)

Optical heterodyne detection can be used to sense theregenerated field which has been transmitted out fromthe second cavity. A secondary laser is phase-locked tothe axion-generating laser, but at a fixed, stable fre-quency offset, ω2 = ω1 + ∆ω. The regenerated photonsat frequency ω1 are focused onto a photodiode wherethey overlap with the beam from the second laser whichserves as the local oscillator (LO). The RF beat fre-quency then has power proportional to

√RregenRLO. In

this way, the photon flux RLO of the LO laser amplifiesthe regenerated photon signal. The amplification fac-tor can be made almost arbitrarily large until the shotnoise of the LO laser dominates the total noise of thedetection system. In this shot-noise-limited regime, aheterodyne detection system has single-photon sensitiv-ity, and quantum-limited noise performance. The noiseoriginates from the zero-point fluctuations of the statesbeing mixed to produce the beat signal. It obeys an ex-act upper bound of 2 photons per integration time, anddoes not have a Poisson tail. Subtraction of a constantPoisson background rate is therefore not necessary, andthe sensitivity of the technique scales as

glimit ∝1

(Rlasertint)1/4(B0L)(F)1/2. (19)

Several experimental groups around the world are ex-ploring an implementation of the cavity-enhanced pho-ton regeneration technique. As an example, a proposedFermilab experiment would use a configuration of 6+6Tevatron dipole magnets, each operating at 5 T, giv-ing a 36 m baseline for each conversion region. WithF ≈ 105, this experiment would have sensitivity tog ≈ 2 × 10−11 GeV−1. Just as with solar searches, thissensitivity can be improved with higher field magnetswhich may become available in the future. The mag-netic length can also be extended up to several hun-dred meters before the ∼ 10 cm aperture diameter oftypical accelerator magnets starts to clip the Gaussiancavity modes. With these future devices, it may be pos-sible to reach sensitivity to photon couplings as low asg ≈ 6× 10−13 GeV−1.

8. Extragalactic axionsRecent astrophysical observations indicate the possi-

bility of a new axion-like particle with photon couplingg ≈ 10−11 GeV−1 within the reach of the next genera-tion of oscillation experiments. The universe is opaque tohigh energy photons which can pair-produce on the gasof photons composing the extragalactic background light(EBL). The EBL consists of photons from all sourcesincluding the cosmic microwave background and red-shifted starlight from the first stars. Anomalous trans-parency has been reported in observations by various

Fig. 6. The new idea of using optical cavities to coherently en-hance the photon regeneration rate will improve laser searchsensitivity by several orders of magnitude to cover a regionof parameter space suggested by recent astrophysical observa-tions of anomalous transparency of the universe to high energyphotons. Shown here are the laser limits of a no-cavity config-uration from GammeV, compared to the gains in sensitivitythat could be made with cavities of finesse F = 104 − 105,combined with longer magnetic baselines B0L.

air Cherenkov telescopes of TeV photons from distantblazars [16]. TeV photons can scatter efficiently on thenear-infrared background photons of micron wavelengthwith interaction length of several hundred Mpc, givenpreliminary estimates of the EBL spectral density. How-ever, the spectra of TeV blazars at distanes of hundredsof Mpc do not exhibit the expected exponential suppres-sion in flux. The lack of flux suppression in most blazarobservations has been used as a tool to directly constrainthe EBL spectral density to below the levels implied bydirect satellite observations. These satellite observationsmay indeed be problematic due to possible contamina-tion from isotropically scattered sunlight with the solarsystem.

However, another explanation for the perhaps anoma-lous transparency of the universe to TeV gamma rays isthat TeV photons may be converted to energetic axionsin the magnetic fields of the astrophysical sources. Theaxions may then shine through the “wall” of extragalac-tic background light before oscillating back into photonsin the galactic magnetic field. Because photon-axionoscillations only affect a single polarization component,the lack of obvious spectral features in the TeV spectra,due to the attenuation of the unconverted component,then requires very efficient conversion and regenerationof photons. Recalling Eq. 11, O(1) probabilities requiresg ≈ 1/(B0L). Observations from the Pierre Auger Ob-servatory indicate that ultra-high-energy cosmic rays arevery likely protons which are accelerated in extragalacticastrophysical sources [17]. In order to contain the pro-tons while accelerating them, the sources must have mag-netic field regions which satisfy B0L = ECR ≈ 1020 eVfor the highest energy cosmic rays. In a somewhat mirac-ulous coincidence, some models of the galactic magneticfield also give a comparable magnetic baseline for thepoloidal magnetic field [18], B0L ≈ (6µG) · (4 kpc) =3× 1019 eV. So an axion model with g ≈ 10−11 GeV−1

would predict efficient conversions via oscillation bothat the source, and in the galaxy [19, 20]. This mecha-nism is expected to be effective at photon energies upto 1 TeV, above which magnetic birefringence due toquantum electrodynamics sufficiently alters the photon

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Fig. 7. Constraints from WMAP data on the joint parameterspace of Peccei-Quinn scale f and the inflation scale HI . Up-per bounds on the tensor-to-scalar ratio and of isocurvaturecomponent of the CMB power spectrum constrain this pa-rameter space.

dispersion relationship such that the effective photon-axion mixing angle becomes small [21]. An alternativemodel has photons oscillating into axions in intergalac-tic magnetic domains of nG field strength and Mpc scale[22].

9. Cosmic Microwave Background observationsCMB observations have also been used to constrain

the joint axion and inflaton parameter space [23]. Theresults depend on whether the axion symmetry breakingscale f is greater than or less then the Hubble rate duringinflation HI . If f < HI then the Peccei-Quinn symmetrybreaks after inflation, leading to the formation of topo-logical axionic strings. This scenario is more likely forlarger values HI > 1014 GeV in which the primordialspectrum of gravity waves may be observable via theirimprint of B-mode polarization patterns on the CMB.In this case, determination of HI via CMB polarizationplaces an upper bound on f .

However, if f > HI , then the entire cosmological hori-zon contained a single mean misalignment angle Θ fromwhich the Goldstone boson field started rolling duringthe QCD phase transition. This misalignment angle de-termines what fraction of energy from the quark-gluonplasma is converted into axionic potential energy, and ul-timately into cold dark matter axions. However, scalarperturbations of the Goldstone boson field due to in-flation generate local deviations in Θ with Gaussianvariance δΘ2 ∝ (HI/f)2. Because these perturbationsdo not inject more energy, but instead determine howthe local energy density is partitioned, they give rise toisocurvature perturbations on the CMB spectrum. TheCMB spectrum, measured most recently by WMAP, ismost consistent with a spectrum of adiabatic perturba-tions with very little isocurvature component. The CMBspectrum therefore places an upper bound on δΘ2 andhence on the parameter space of f and HI . A posi-tive detection of isocurvature would imply a fairly lowHI < 108 GeV for natural models of axion dark mat-ter with f < 1013 GeV. If isocurvature measurementsare ambiguous, then determination of f via direct axiondark matter searches would exclude a range of HI .

10. SummaryThe outlook for the experimental axion field is bright.

A variety of techniques have been proposed and imple-mented, using semiclassical methods to overcome the

suppression of quantum amplitudes by the large Peccei-Quinn scale. Recent breakthroughs in sensor technol-ogy, magnet development, and experimental configura-tion, promise order of magnitude improvements in sensi-tivity to the photon-axion coupling constant. In particu-lar, a new idea of integration of optical cavities into laseraxion searches will produce several orders of magnitudeimprovement in sensitivity. Hints of axion-like particlesare seen in astroparticle data, and will be checked withlaboratory probes. Ideas about the role of axions in cos-mology are being refined and checked against new data.

As a side benefit, data from axion search experimentsis also being used to constrain many types of models ofother low-mass particles such as chameleons or parapho-tons. The discussion of this fascinating work is beyondthe scope of this paper but can be found elsewhere.

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