In search of WISPs

4 March 2021

Experiments such as MADMAX, IAXO and ALPS II are expanding the search for axions and other weakly interacting ‘slim’ particles that could hail from far above the TeV scale, write Axel Lindner, Béla Majorovits and Andreas Ringwald.

The ALPS II experiment at DESY

The Standard Model (SM) cannot be the complete theory of particle physics. Neutrino masses evade it. No viable dark-matter candidate is contained within it. And under its auspices the electric dipole moment of the neutron, experimentally compatible with zero, requires the cancellation of two non-vanishing SM parameters that are seemingly unrelated – the strong-CP problem. The physics explaining these mysteries may well originate from new phenomena at energy scales inaccessible to any collider in the foreseeable future. Fortunately, models involving such scales can be probed today and in the next decade by a series of experiments dedicated to searching for very weakly interacting slim particles (WISPs).

WISPs are pseudo Nambu–Goldstone bosons (pNGBs) that arise automatically in extensions of the SM from global symmetries which are broken both spontaneously and explicitly. NGBs are best known for being “eaten” by the longitudinal degrees of freedom of the W and Z bosons in electroweak gauge-symmetry breaking, which underpins the Higgs mechanism, but theorists have also postulated a bevy of pNGBs that get their tiny masses by explicit symmetry breaking and are potentially discoverable as physical particles. Typical examples arising in theoretically well-motivated grand-unified theories are axions, flavons and majorons. Axions arise from a broken “Peccei–Quinn” symmetry and could potentially explain the strong-CP problem, while flavons and majorons arise from broken flavour and lepton symmetries.

The Morpurgo magnet

Being light and very weakly interacting, WISPs would be non-thermally produced in the early universe and thus remain non-relativistic during structure formation. Such particles would inevitably contribute to the dark matter of the universe. WISPs are now the target of a growing number and type of experimental searches that are complementary to new-physics searches at colliders.

Among theorists and experimentalists alike, the axion is probably the most popular WISP. Recently, massive efforts have been undertaken to improve the calculations of model-dependent relic-axion production in the early universe. This has led to a considerable broadening of the mass range compatible with the explanation of dark matter by axions. The axion could make up all of the dark matter in the universe for a symmetry-breaking scale fa between roughly 108 and 1019 GeV (the lower limit being imposed by astrophysical arguments, the upper one by the Planck scale), corresponding to axion masses from 10–13 eV to 10 meV. For other light pNGBs, generically dubbed axion-like particles (ALPs), the parameter range is even broader. With many plausible relic-ALP-production mechanisms proposed by theorists, experimentalists need to cover as much of the unexplored parameter range as possible.

Although the strengths of the interactions between axions or ALPs and SM particles are very weak, being inversely proportional to fa, several strategies for observing them are available. Limits and projected sensitivities span several orders of magnitude in the mass-coupling plane (see “The field of play” figure).

IAXO’s design profited greatly from experience with the ATLAS toroid

Since axions or ALPs can usually decay to two photons, an external static magnetic field can substitute one of the two photons and induce axion-to-photon conversion. Originally proposed by Pierre Sikivie, this inverse Primakoff effect can classically be described by adding source terms proportional to B and E to Maxwell’s equations. Practically, this means that inside a static homogeneous magnetic field the presence of an axion or ALP field induces electric-field oscillations – an effect readily exploited by many experiments searching for WISPs. Other processes exploited in some experimental searches and suspected to lead to axion production are their interactions with electrons, leading to axion bremsstrahlung, and their interactions with nucleons or nuclei, leading to nucleon-axion bremsstrahlung or oscillations of the electric dipole moment of the nuclei or nucleons.

The potential to make fundamental discoveries from small-scale experiments is a significant appeal of experimental WISP physics, however the most solidly theoretically motivated WISP parameter regions and physics questions require setups that go well beyond “table-top” dimensions. They target WISPs that flow through the galactic halo, shine from the Sun, or spring into existence when lasers pass through strong magnetic fields in the laboratory.

Dark-matter halo

Haloscopes target the detection of dark-matter WISPs in the halo of our galaxy, where non-relativistic cold-dark-matter axions or ALPs induce electric field oscillations as they pass through a magnetic field. The frequency of the oscillations corresponds to the axion mass, and the amplitude to B/fa. When limits or projections are given for these kinds of experiments, it is assumed that the particle under scrutiny homogeneously makes up all of the dark matter in the universe, introducing significant cosmological model dependence.

Axion–photon coupling versus axion mass plane

The furthest developed currently operating haloscopes are based on resonant enhancement of the axion-induced electric-field oscillations in tunable resonant cavities. Using this method, the presently running ADMX project at the University of Washington has the sensitivity to discover dark-matter axions with masses of a few µeV. Nuclear resonance methods could be sensitive to halo dark-matter axions with mass below 1 neV and “fuzzy” dark-matter ALPs down to 10–22 eV within the next decade, for example at the CASPEr experiments being developed at the University of Mainz and Boston University. Meanwhile, experiments based on classical LC circuits, such as ABRACADABRA at MIT, are being designed to measure ALP- or axion-induced magnetic field oscillations in the centre of a toroidal magnet. These could be sensitive in a mass range between 10 neV and 1 µeV.

ALPS II is the first laser-based setup to fully exploit resonance techniques

For dark-matter axions with masses up to approximately 50 µeV, promising developments in cavity technologies such as multiple matched cavities and superconducting or diel­ectric cavities are ongoing at several locations, including at CAPP in South Korea, the University of Western Australia, INFN Legnaro and the RADES detector, which has taken data as part of the CAST experiment at CERN. Above ~40 µeV, however, the cavity concept becomes more and more challenging, as sensitivity scales with the volume of the resonant cavity, which decreases dramatically with increasing mass (as roughly 1/ma3). To reach sensitivity at higher masses, in the region of a few hundred µeV, a novel “dielectric haloscope” is being developed by the MADMAX (Magnetized Disk and Mirror Axion experiment) collaboration for potential installation at DESY. It exploits the fact that static magnetic-field boundaries between media with different dielectric constants lead to tiny power emissions that compensate the discontinuity in the axion-induced electric fields in neighbouring media. If multiple surfaces are stacked in front of each other, this should lead to constructive interference, boosting the emitted power from the expected axion dark matter in the desired mass range to detectable levels. Other novel haloscope concepts, based on meta-materials (“plasma haloscopes”, for example) and topological insulators, are also currently being developed. These could have sensitivity to even higher axion masses, up to a few meV.

Staying in tune

In principle, axion-dark-matter detection should be relatively simple, given the very high number density of particles – approximately 3 × 1013 axions/cm3 for an axion mass of 10 µeV – and the well-established technique of resonant axion-to-photon conversion. But, as the axion mass is unknown, the experiments must be painstakingly tuned to each possible mass value in turn. After about 15 years of steady progress, the ADMX experiment has reached QCD-axion dark-matter sensitivity in the mass regime of a few µeV.

ADMX uses tunable microwave resonators inside a strong solenoidal magnetic field, and modern quantum sensors for readout. Unfortunately, however, this technology is not scalable to the higher axion-mass regions as preferred, for example, by cosmological models where Peccei–Quinn symmetry breaking happened after an inflationary phase of the universe. That’s where MADMAX comes in. The collaboration is working on the dielectric-haloscope concept – initiated and led by scientists at the Max Planck Institute for Physics in Munich – to investigate the mass region around 100 µeV.

Astrophysical hints

Globular clusters

Weakly interacting slim particles (WISPs) could be produced in hot astrophysical plasmas and transport energy out of stars, including the Sun, stellar remnants and other dense sources. Observed lifetimes and energy-loss rates can therefore probe their existence. For the axion, or an axion-like particle (ALP) with sub-MeV mass that couples to nucleons, the most stringent limit, fa > ~108 GeV, stems from the duration of the neutrino signal from the progenitor neutron star of Supernova 1987A.

Tantalisingly, there are stellar hints from observations of red giants, helium-burning stars, white dwarfs and pulsars that seem to indicate energy losses with slight excesses with respect to those expected from standard energy emission by neutrinos. These hints may be explained by axions with masses below 100 meV or sub-keV-mass ALPs with a coupling to both electrons and photons.

Other observations suggest that TeV photons from distant blazars are less absorbed than expected by standard interactions with extragalactic background light – the so-called transparency hint. This could be explained by the conversion of photons into ALPs in the magnetic field of the source, and back to photons in astrophysical magnetic fields. Interestingly, these would have about the same ALP–photon coupling strength as indicated by the observed stellar anomalies, though with a mass that is incompatible with both ALPs which can explain dark matter and with QCD axions (see “The field of play” figure).

MADMAX will use a huge ~9 T superconducting dipole magnet with a bore of about 1.35 m and a stored energy of roughly 480 MJ. Such a magnet has never been built before. The MADMAX collaboration teamed up with CEA-IRFU and Bilfinger-Noell and successfully worked out a conceptual design. First steps towards qualifying the conductor are under way. The plan is for the magnet to be installed at DESY inside the old iron yoke of the former HERA experiment H1. DESY is already preparing the required infrastructure, including the liquid-helium supply necessary to cool the magnet. R&D for the dielectric booster, with up to 80 adjustable 1.25 m2 disks, is in full swing.

A first prototype, containing a more modest 20 discs of 30 cm diameter, will be tested in the “Morpurgo” magnet at CERN during future accelerator shutdowns (see “Haloscope home” figure). With a peak field strength of 1.6 T, its dipole field will allow new ALP-dark-matter parameter regions to be probed, though the main purpose of the prototype is to demonstrate the operation of the booster system in cryogenic surroundings inside a magnetic field. The MADMAX collaboration is extremely happy to have found a suitable magnet at CERN for such tests. If sufficient funds can be acquired within the next two to three years for magnet construction, and provided that the prototype efforts at CERN are successful, MADMAX could start data taking at DESY in 2028.

While direct dark-matter search experiments like ADMX and MADMAX offer by far the highest sensitivity for axion searches, this is based on the assumption that the dark matter problem is solved by axions, and if no signal is discovered any claim of an exclusion limit must rely on specific cosmological assumptions. Therefore, other less model-dependent experiments, such as helioscopes or light shining through a wall (LSW) experiments, are extremely beneficial in addition to direct dark-matter searches.

Solar axions

In contrast to dark-matter axions or ALPs, those produced in the Sun or in the laboratory should have considerable momentum. Indeed, solar axions or ALPs should have energies of a few keV, corresponding to the temperature at which they are produced. These could be detected by helioscopes, which seek to use the inverse Primakoff effect to convert solar axions or ALPs into X-rays in a magnet pointed towards the Sun, as at the CERN Axion Solar Telescope (CAST) experiment. Helioscopes could cover the mass range compatible with the simplest axion models, in the vicinity of 10 meV, and could be sensitive to ALPs with masses below 1 eV without any tuning at all.

The CAST helioscope, which reused an LHC prototype dipole magnet, has driven this field in the past decade, and provides the most sensitive exclusion limits to date. Going beyond CAST calls for a much larger magnet. For the next-generation International Axion Observatory (IAXO) helioscope, CERN members of the international collaboration worked out a conceptual design for a 20 m-long toroidal magnet with eight 60 cm-diameter bores. IAXO’s design profited greatly from experience with the ATLAS toroid.

BabyIAXO helioscope

In the past three years, the collaboration, led by the University of Zaragoza, has been concentrating its activities on the BabyIAXO prototype in order to finesse the magnet concept, the X-ray telescopes necessary to focus photons from solar axion conversion and the low-background detectors. BabyIAXO will increase the signal-to-noise ratio of CAST by two orders of magnitude; IAXO by a further two orders of magnitude.

In December 2020 the directorates of CERN and DESY signed a collaboration agreement regarding BabyIAXO: CERN will provide the detailed design of the prototype magnet including its cryostat, while DESY will design and prepare the movable platform and infrastructure (see “Prototype” figure). BabyIAXO will be located at DESY in Hamburg. The collaboration hopes to attract the remaining funds for BabyIAXO so construction can begin in 2021 and first science runs could take place in 2025. The timeline for IAXO will depend strongly on experiences during the construction and operation of BabyIAXO, with first light potentially possible in 2028.

Light shining through a wall

In contrast to haloscopes, helioscopes do not rely on the assumption that all dark matter is made up by axions. But light-shining-through-wall (LSW) experiments are even less model dependent with respect to ALP production. Here, intense laser light could be converted to axions or ALPs inside a strong magnetic field by the Primakoff effect. Behind a light-impenetrable wall they would be re-converted to photons and detected at the same wavelength as the laser light. The disadvantage of LSW experiments is that they only reach sensitivity to ALPs with a mass up to a few hundred µeV with comparably high coupling to photons. However, this is sensitive enough to test the parameter range consistent with the transparency hint and parts of the mass range consistent with the stellar hints (see “Astrophysical hints” panel).

The Any Light Particle Search (ALPS II) at DESY follows this approach. By seeking to observe light shining through a wall, any ALPs would be generated in the experiment itself, removing the need to make assumptions about their production. ALPS II is based on 24 modified superconducting dipole magnets that have been straightened by brute-force deformation, following their former existence in the proton accelerator of the HERA complex. With the help of two 124 m-long high-finesse optical resonators, encompassed by the magnets on both sides of the wall, ALPS II is also the first laser-based setup to fully exploit resonance techniques. Two readout systems capable of measuring a 1064 nm photon flux down to a rate of 2 × 10–5 s–1 have been developed by the collaboration. Compared to the present best LSW limits provided by OSQAR at CERN, the signal-to-noise ratio will rise by no less than 12 orders of magnitude at ALPS II. Nevertheless, MADMAX would surpass ALPS II in the sensitivity for the axion-photon coupling strength by more than three orders of magnitude. This is the price to pay for a model-independent experiment – however, ALPS II principally targets not dark-matter candidates but ALPs indicated by astrophysical phenomena.

Tunelling ahead

The installation of the 24 dipole magnets in a straight section of the HERA tunnel was completed in 2020. Three clean rooms at both ends and in the centre of the experiment were also installed, and optics commissioning is under way. A first science run is expected for autumn 2021.


In the overlapping mass region up to 0.1 meV, the sensitivities of ALPS II and BabyIAXO are roughly equal. In the event of a discovery, this would provide a unique opportunity to study the new WISP. Excitingly, a similar case might be realised for IAXO: combining the optics and detectors of ALPS II with simplified versions of the dipole magnets being studied for FCC-hh would provide an LSW experiment with “IAXO sensitivity” regarding the axion-photon coupling, albeit in a reduced mass range. This has been outlined as the putative JURA (Joint Undertaking on Research for Axions) experiment in the context of the CERN-led Physics Beyond Colliders study.

The past decade has delivered significant developments in axion and ALP theory and phenomenology. This has been complemented by progress in experimental methods to cover a large fraction of the interesting axion and ALP parameter range. In close collaboration with universities and institutes across the globe, CERN, DESY and the Max Planck society will together pave the road to the exciting results that are expected this decade.

Further reading

L Di Luzio et al. 2020 Phys. Rept. 870 1.

MADMAX Collaboration 2019 Eur. Phys. J. C 79 186.

IAXO Collaboration 2019 JCAP 06 047.

ALPS II Collaboration 2013 JINST 8 T09001.


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