Axions are one of the few particle-physics candidates for dark matter which are well motivated independently of their possible cosmological role

GEORG RAFFELT

Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München, Germany (e-mail: raffelt@mppmu.mpg.de)

(Received 7 August 2001; accepted 29 August 2001)

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 theoretical motivation for axions, their possible role in cosmology, the existing astrophysical limits, and the status of experimental searches.

1. Introduction

Despite its uncanny success, the particle-physics standard model has many loose ends, among them the CP problem of quantum chromodynamics (QCD). The non- trivial field structure of the QCD ground state (‘-vacuum’) and a phase of the quark mass matrix each induce a non-perturbative CP-violating term in the QCD Lagrangian which is proportional to the coefficient = QCD +arg detMquark, wherecould lie anywhere between 0 and 2π. The experimental upper limit to a putative neutron electric dipole moment, a CP-violating quantity, informs us that 10⁻⁹, a severe fine-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 the parameteris re-interpreted as a dynamical variable,→a(x)/fa, wherea(x)is the axion field andfaan energy scale called the Peccei-Quinn scale or axion decay constant (Peccei and Quinn, 1977a,b; Weinberg, 1977; Wilczek, 1977). The previ- ous CP-violating term automatically includes a potential for the axion field which drives it to its CP-conserving minimum (dynamical symmetry restoration). While this may sound complicated, Sikivie (1996) has constructed a beautiful mechanical analogy 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 axion properties are roughly determined by those ofπ⁰, scaled withfπ/fawherefπ = 93 MeV is the pion decay constant. For example, the axion mass is roughly given bymafa =mπfπ, and the coupling to photons or nucleons is roughly suppressed byfπ/farelative to the pion couplings.

Axions have not been found during the quarter century since they were first proposed, but the interest in this hypothesis is well alive because other proposed

Space Science Reviews 100: 153–158, 2002.

© 2002Kluwer Academic Publishers. Printed in the Netherlands.

154 G. RAFFELT

solutions 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 (Groomet 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 Limits

The main argument which proves that the Peccei-Quinn scalefamust be very large, corresponding to a very small axion massma, 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+amust not be too efficient in these stars, leading to a limit ofma 0.4 eV (Figure 1).

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 SN 1987A neutrino signal provides the most restrictive limits on the axion-nucleon coupling (Figure 1). 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 (Jankaet 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 SN 1987A signal (Turner, 1988; Burrowset 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 SN 1987A arguments (Figure 1), sometimes called the ‘hadronic axion window’. Therefore, in fine-tuned axion models where the tree-level coupling to photons nearly vanishes, eV-mass axions

Figure 1.Astrophysical and cosmological exclusion regions (hatched) for the axion massmaor the Peccei–Quinn scalef_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 thatE/N = ⁸₃as in GUT models or the DFSZ model. The SN 1987A 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 requires fine-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 onma andfa

do not extend the range covered by the previous arguments.

3. Cosmology

In the early universe, axions come into thermal equilibrium only iffa 10⁸GeV, a region excluded by the stellar-evolution limits. Forfa 10⁸GeV cosmic axions are produced nonthermally. If inflation occurred after the Peccei-Quinn symmetry breaking or if Treheat < fa, 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 ofah²≈1.9×3^±1(1µeV/m_a)^1.1752_iF (i)

156 G. RAFFELT

wherehis the Hubble constant in units of 100 km 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 functionF ()withF (0) =1 and F (π ) = ∞accounts for anharmonic corrections to the axion potential. Be- cause the initial misalignment angleican be very small or very close toπ, there is no real prediction for the mass of dark-matter axions even though one would expect²_iF (i)∼1 to avoid fine-tuning the initial conditions.

A possible fine-tuning of i is limited by inflation-induced quantum fluctu- ations which in turn lead to temperature fluctuations of the cosmic microwave background (Lyth, 1990; Turner and Wilczek, 1991; Linde, 1991). In a broad class of inflationary models one thus finds an upper limit tomawhere axions could be the dark matter. According to the most recent discussion (Shellard and Battye, 1998) it is about 10⁻³eV (Figure 1).

If inflation did not occur at all or if it occurred before the Peccei-Quinn symme- try breaking withTreheat> fa, 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 Figure 1.

4. Experimental Search

If 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 ↔ γ in the presence of external electromagnetic fields. Therefore, the galactic axions should excite a microwave resonator which is placed in a strong magnetic field, 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 ma range. In the late 1980s, this method was pioneered in two pilot experiments (Wuenschet al., 1989; Hagmannet 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;

Yamamotoet al., 2001), the latter one using a beam of Rydberg atoms as a low- noise microwave detector. The projected sensitivity shown in Figure 1 covers the lower end of the plausible mass range for dark-matter axions. If axions are indeed

the galactic dark matter, these experiments for the first 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 Bibberet 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 (Inoueet 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.

Therefore, the direct search experiments for particle candidates such as axions are among the most important efforts in the area of experimental cosmology.

Acknowledgements

This research was supported, in part, by the Deutsche Forschungsgemeinschaft under grant No. SFB-375 and by the ESF network Neutrino Astrophysics.

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