AXIONSGEORG RAFFELTMax-Planck-Institut für Physik(Werner-Heisenberg-Institut),Föhringer Ring6,80805München,Germany(e-mail:*****************.de)(Received7August2001;accepted29August2001)Abstract.Axions are one of the few particle-physics candidates for dark matter which are well motivated independently of their possible cosmological role.A brief review is given of the theoreticalmotivation for axions,their possible role in cosmology,the existing astrophysical limits,and thestatus of experimental searches.1.IntroductionDespite its uncanny success,the particle-physics standard model has many looseends,among them the CP problem of quantum chromodynamics(QCD).The non-trivialfield structure of the QCD ground state(‘ -vacuum’)and a phase of thequark mass matrix each induce a non-perturbative CP-violating term in the QCDLagrangian which is proportional to the coefficient = QCD+arg det M quark, where could lie anywhere between0and2π.The experimental upper limit to aputative neutron electric dipole moment,a CP-violating quantity,informs us that 10−9,a severefine-tuning problem given that is a sum of two unrelated terms which would be expected to be of order unity each.One particularly elegant solution was proposed by Peccei and Quinn,where theparameter is re-interpreted as a dynamical variable, →a(x)/f a,where a(x)isthe axionfield and f a an energy scale called the Peccei-Quinn scale or axion decayconstant(Peccei and Quinn,1977a,b;Weinberg,1977;Wilczek,1977).The previ-ous CP-violating term automatically includes a potential for the axionfield whichdrives it to its CP-conserving minimum(dynamical symmetry restoration).Whilethis may sound complicated,Sikivie(1996)has constructed a beautiful mechanicalanalogy which nicely explains the main features of axion physics.While axions would be very weakly interacting,they are still a QCD phenom-enon.They share their quantum numbers with neutral pions;all generic axionproperties are roughly determined by those ofπ0,scaled with fπ/f a where fπ= 93MeV is the pion decay constant.For example,the axion mass is roughly given by m a f a=mπfπ,and the coupling to photons or nucleons is roughly suppressed by fπ/f a relative to the pion couplings.Axions have not been found during the quarter century since they werefirstproposed,but the interest in this hypothesis is well alive because other proposed Space Science Reviews100:153–158,2002.©2002Kluwer Academic Publishers.Printed in the Netherlands.154G.RAFFELTsolutions of the strong CP problem are not clearly superior,and mainly because axions are one of the few well-motivated particle candidates for the cold dark matter which apparently dominates the dynamics of the universe.The current status of axions physics and astrophysics was reviewed at a recent conference(Sikivie,1999).Particle-physics aspects,the status of astrophysical limits,and that of current search experiments are summarized in three separate mini-reviews in the Review of Particle Physics(Groom et al.,2000).Chapters on axions are also found in some textbooks(Kolb and Turner,1990;Raffelt,1996).For theoretical reviews see Kim(1987)and Cheng(1988),for a review of experimental searches see Rosenberg and van Bibber(2000).2.Stellar-Evolution LimitsThe main argument which proves that the Peccei-Quinn scale f a must be very large, corresponding to a very small axion mass m a,is related to stellar evolution.Axions would be produced by various processes in the hot and dense interior of stars and would thus carry away energy directly,much in analogy to the standard thermal neutrino losses.The strength of the axion interaction with photons,electrons,and nucleons can be constrained from the requirement that stellar-evolution time scales are not modified beyond observational limits(Raffelt,1996).For example,the helium-burning lifetime of horizontal-branch stars inferred from number counts in globular clusters reveals that the Primakoff processγ+Ze→Ze+a must not be too efficient in these stars,leading to a limit of m a 0.4eV(Figure1).Very restrictive limits arise from the observed neutrino signal of the supernova (SN)1987A.After collapse,the SN core is so hot and dense that neutrinos are trapped and escape only by diffusion so that it takes several seconds to cool a roughly solar-mass object the size of a few ten kilometers.The emission of axions would remove energy from the deep inner core which should show up in late-time neutrinos.Therefore,the observed duration of the SN1987A neutrino signal provides the most restrictive limits on the axion-nucleon coupling(Figure1).In the early papers on this topic,the difficulty of calculating the axion emission from a dense and hot nuclear medium had been underestimated;the most recent discussions attempt an inclusion of dense-medium effects(Janka et al.,1996).If axions are too‘strongly’interacting,they are trapped in a SN core,inval-idating the energy-loss argument and implying a mass above which axions are not excluded by the SN1987A signal(Turner,1988;Burrows et al.,1990).They would still carry away some of the energy and would cause excess counts in the water Cherenkov detectors which registered the neutrinos,allowing one to exclude another interval of axion masses(Engel et al.,1990).Probably there is a small crack of allowed axion masses between these two SN1987A arguments(Figure1), sometimes called the‘hadronic axion window’.Therefore,infine-tuned axion models where the tree-level coupling to photons nearly vanishes,eV-mass axionsAXIONS155Figure1.Astrophysical and cosmological exclusion regions(hatched)for the axion mass m a or the Peccei–Quinn scale f a.An‘open end’of an exclusion bar means that it represents a rough estimate. The globular cluster limit depends on the axion-photon coupling;it was assumed that E/N=83as in GUT models or the DFSZ model.The SN1987A limits depend on the axion-nucleon couplings; the shown case corresponds to the KSVZ model and approximately to the DFSZ model.The dot-ted‘inclusion regions’indicate where axions could plausibly be the cosmic dark matter.Most of the allowed range in the inflation scenario requiresfine-tuned initial conditions.Also shown is the projected sensitivity range of the search experiments for galactic dark-matter axions.may be allowed and could thus play the role of a cosmological hot dark matter component(Moroi and Murayama,1998).The axion coupling to electrons can be constrained from the properties of glob-ular-cluster stars and the white-dwarf luminosity function.However,the tree-level existence of such a coupling is not generic,and the resulting limits on m a and f a do not extend the range covered by the previous arguments.3.CosmologyIn the early universe,axions come into thermal equilibrium only if f a 108GeV, a region excluded by the stellar-evolution limits.For f a 108GeV cosmic axions are produced nonthermally.If inflation occurred after the Peccei-Quinn symmetry breaking or if T reheat<f a,the‘misalignment mechanism’(Preskill et al.,1983; Abbott and Sikivie,1983;Dine and Fischler,1983;Turner,1986)leads to a contri-bution to the cosmic critical density of a h2≈1.9×3±1(1µeV/m a)1.175 2i F( i)156G.RAFFELTwhere h is the Hubble constant in units of100km s−1Mpc−1.The stated range re-flects recognized uncertainties of the cosmic conditions at the QCD phase transition and of the temperature-dependent axion mass.The function F( )with F(0)=1 and F(π)=∞accounts for anharmonic corrections to the axion potential.Be-cause the initial misalignment angle i can be very small or very close toπ,there is no real prediction for the mass of dark-matter axions even though one wouldexpect 2i F( i)∼1to avoidfine-tuning the initial conditions.A possiblefine-tuning of i is limited by inflation-induced quantumfluctu-ations which in turn lead to temperaturefluctuations of the cosmic microwave background(Lyth,1990;Turner and Wilczek,1991;Linde,1991).In a broad class of inflationary models one thusfinds an upper limit to m a where axions could be the dark matter.According to the most recent discussion(Shellard and Battye,1998) it is about10−3eV(Figure1).If inflation did not occur at all or if it occurred before the Peccei-Quinn symme-try breaking with T reheat>f a,cosmic axion strings form by the Kibble mechanism (Davis,1986).Their motion is damped primarily by axion emission rather than gravitational waves.After axions acquire a mass at the QCD phase transition they quickly become nonrelativistic and thus form a cold dark matter component.The axion density is similar to that from the misalignment mechanism,but in detail the calculations are difficult and somewhat controversial between one group of authors(Davis,1986;Davis and Shellard,1989;Battye and Shellard,1994a,b)and another(Harari and Sikivie,1987;Hagmann and Sikivie,1991;Hagmann et al., 2001).Taking into account the uncertainty in various cosmological parameters one arrives at a plausible range for dark-matter axions as indicated in Figure1.4.Experimental SearchIf axions are indeed the dark matter of our galaxy one can search for them by the ‘haloscope’method(Sikivie,1983).The generic two-photon vertex which axions posess in analogy to neutral pions allows for the Primakoff conversion a↔γin the presence of external electromagneticfields.Therefore,the galactic axions should excite a microwave resonator which is placed in a strong magneticfield, i.e.,one expects a narrow line above the thermal noise of the cavity.While this line would not be difficult to identify once it has been found,searching for it requires to step a tunable cavity through many resonance intervals in order to cover a given m a range.In the late1980s,this method was pioneered in two pilot experiments (Wuensch et al.,1989;Hagmann et al.,1990).At the present time two full-scale ‘second generation’axion haloscopes are in operation,one in Livermore,Califor-nia(Hagmann et al.,1998,2000)and one in Kyoto,Japan(Ogawa et al.,1996; Yamamoto et al.,2001),the latter one using a beam of Rydberg atoms as a low-noise microwave detector.The projected sensitivity shown in Figure1covers the lower end of the plausible mass range for dark-matter axions.If axions are indeedAXIONS157 the galactic dark matter,these experiments for thefirst time are in a position to actually detect them.Axions or axion-like particles are currently also searched by the‘helioscope’method(Sikivie,1983;van Bibber et al.,1989).Axions would be produced in the Sun by the Primakoff effect,and could be back-converted into X-rays in a long dipole magnet oriented toward the Sun.A dedicated experiment of this sort in Tokyo has recently reported new limits(Inoue et al.,2000)while a much larger ef-fort using a decommissioned LHC test magnet,the CAST experiment,is currently under construction at CERN(Zioutas et al.,1999).It should be noted,however, that these searches are unrelated to axion dark matter,i.e.,if axions were to show up at CAST they almost certainly could not provide the cosmic dark matter.The evidence for the reality of dark matter has mounted for several decades,and most recently culminated with the determination of the cosmological parameters by cosmic-microwave precision experiments and other arguments.On the other hand, the physical nature of dark matter remains as mysterious as it was two decades ago. 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