An axion () is a hypothetical elementary particle originally theorized in 1978 independently by Frank Wilczek and Steven Weinberg as the Goldstone boson of Peccei–Quinn theory, which had been proposed in 1977 to solve the strong CP problem in quantum chromodynamics (QCD). If axions exist and have low mass within a specific range, they are of interest as a possible component of cold dark matter.
History Strong CP problem As shown by Gerard 't Hooft, strong interactions of the Standard Model, QCD, possess a non-trivial vacuum structure that in principle permits violation of the combined symmetries of charge conjugation and parity, collectively known as CP. Together with effects generated by weak interactions, the effective periodic strong CP-violating term, , appears as a Standard Model input – its value is not predicted by the theory, but must be measured. However, large CP-violating interactions originating from QCD would induce a large electric dipole moment (EDM) for the neutron. Experimental constraints on the EDM implies that CP violation from QCD must be extremely tiny and thus must itself be extremely small. Since could have any value between 0 and 2, this presents a "naturalness" problem for the Standard Model. Why should this parameter find itself so close to zero? (Or, why should QCD find itself CP-preserving?) This question constitutes what is known as the strong CP problem.
Prediction In 1977, Roberto Peccei and Helen Quinn postulated a more elegant solution to the strong CP problem, the Peccei–Quinn mechanism. The idea is to effectively promote to a field. This is accomplished by adding a new global symmetry (called a Peccei–Quinn (PQ) symmetry) that becomes spontaneously broken. This results in a new particle, as shown independently by Frank Wilczek and Steven Weinberg, that fills the role of , naturally relaxing the CP-violation parameter to zero. Wilczek named this new hypothesized particle the "axion" after a brand of laundry detergent because it carries the CP-violating "axial" current that "cleaned up" the problem, while Weinberg called it "the higglet". Weinberg later agreed to adopt Wilczek's name for the particle. Because it has a non-zero mass, the axion is a pseudo-Nambu–Goldstone boson.
Axion dark matter
QCD effects produce an effective periodic potential in which the axion field moves. Expanding the potential about one of its minima, one finds that the product of the axion mass with the axion decay constant is determined by the topological susceptibility of the QCD vacuum. An axion with mass much less than is long-lived and weakly interacting, a perfect dark matter candidate.
The oscillations of the axion field about the minimum of the effective potential, the so-called misalignment mechanism, generate a cosmological population of cold axions with an abundance depending on the mass of the axion. With a mass above 5 μeV/c2 ( times the electron mass) axions could account for dark matter, and thus be both a dark-matter candidate and a solution to the strong CP problem. If inflation occurs at a low scale and lasts sufficiently long, the axion mass can be as low as 1 peV/c2.
There are two distinct scenarios in which the axion field begins its evolution, depending on the following two conditions: (a) The PQ symmetry is spontaneously broken during inflation. This condition is realized whenever the axion energy scale is larger than the Hubble rate at the end of inflation. (b) The PQ symmetry is never restored after its spontaneous breaking occurs. This condition is realized whenever the axion energy scale is larger than the maximum temperature reached in the post-inflationary Universe.
Broadly speaking, one of the two possible scenarios outlined in the two following subsections occurs:
Pre-inflationary scenario If both (a) and (b) are satisfied, cosmic inflation selects one patch of the Universe within which the spontaneous breaking of the PQ symmetry leads to a homogeneous value of the initial value of the axion field. In this "pre-inflationary" scenario, topological defects are inflated away and do not contribute to the axion energy density. However, other bounds that come from isocurvature modes severely constrain this scenario, which require a relatively low-energy scale of inflation to be viable.
Post-inflationary scenario If at least one of the conditions (a) or (b) is violated, the axion field takes different values within patches that are initially out of causal contact, but that today populate the volume enclosed by our Hubble horizon. In this scenario, isocurvature fluctuations in the PQ field randomise the axion field, with no preferred value in the power spectrum.
The proper treatment in this scenario is to solve numerically the equation of motion of the PQ field in an expanding Universe, in order to capture all features coming from the misalignment mechanism, including the contribution from topological defects like "axionic" strings and domain walls. An axion mass estimate between was reported by Borsanyi et al. (2016). The result was calculated by simulating the formation of axions during the post-inflation period on a supercomputer.
Progress in the late 2010s in determining the present abundance of a KSVZ-type axion using numerical simulations lead to values between 0.02 and 0.1 meV/c2, although these results have been challenged by the details on the power spectrum of emitted axions from strings.
Phenomenology of the axion field Searches The axion models originally proposed by Wilczek and by Weinberg chose axion coupling strengths that were so strong that they would have already been detected in prior experiments. It had been thought that the Peccei–Quinn mechanism for solving the strong CP problem required such large couplings. However, it was soon realized that "invisible axions" with much smaller couplings also work. Two such classes of models are known in the literature as (Kim–Shifman–Vainshtein– and (Dine–Fischler––
The very weakly coupled axion is also very light, because axion couplings and mass are proportional. Satisfaction with "invisible axions" changed when it was shown that any very light axion would have been overproduced in the early universe and therefore must be excluded.
Maxwell's equations with axion modifications Pierre Sikivie computed how Maxwell's equations are modified in the presence of an axion in 1983. He showed that these axions could be detected on Earth by converting them to photons, using a strong magnetic field, motivating a number of experiments. For example, the Axion Dark Matter Experiment attempts to convert axion dark matter to microwave photons, the CERN Axion Solar Telescope attempt to convert axions that are produced in the Sun's core to X-rays, and other experiments search for axions produced in laser light. As of the early 2020s, there are dozens of proposed or ongoing experiments searching for axion dark matter.
Treating the reduced Planck constant , speed of light , and permittivity of free space all equivalent to 1, the electrodynamic equations are: {| class="wikitable" style="text-align: center;" |- ! scope="col" style="width: 15em;" | Name ! scope="col" | Equations |- ! scope="row" | Gauss's law
! scope="row" | Gauss's law for magnetism
! scope="row" | Faraday's law
! scope="row" | Ampère–Maxwell law
! scope="row" | Axion field's equation of motion
Above, a dot above a variable denotes its time derivative; the dot spaced between variables is the vector dot product; the factor is the axion-to-photon coupling constant.
Alternative forms of these equations have been proposed, which imply completely different physical signatures. For example, Visinelli wrote a set of equations that imposed duality symmetry, assuming the existence of magnetic monopoles. However, these alternative formulations are less theoretically motivated, and in many cases cannot even be derived from an action.
Analogous effect for topological insulators A term analogous to the one that would be added to Maxwell's equations to account for axions also appears in recent (2008) theoretical models for topological insulators giving an effective axion description of the electrodynamics of these materials.
This term leads to several interesting predicted properties including a quantized magnetoelectric effect. Evidence for this effect has been given in THz spectroscopy experiments performed at the Johns Hopkins University on quantum regime thin film topological insulators developed at Rutgers University.
In 2019, a team at the Max Planck Institute for Chemical Physics of Solids published their detection of an axion insulator phase of a Weyl semimetal material. In the axion insulator phase, the material has an axion-like quasiparticle – an excitation of electrons that behave together as an axion – and its discovery demonstrates the consistency of axion electrodynamics as a description of the interaction of axion-like particles with electromagnetic fields. In this way, the discovery of axion-like quasiparticles in axion insulators provides motivation to use axion electrodynamics to search for the axion itself.
Experiments Despite not having been found to date, the axion has been well studied for over 40 years, giving time for physicists to develop insight into axion effects that might be detected. Several experimental searches for axions are presently underway; most exploit axions' expected slight interaction with photons in strong magnetic fields. Axions are also one of the few remaining plausible candidates for dark matter particles, and might be discovered in some dark matter experiments.
Most searches for the axions probe the axion-photon coupling via the Primakoff effect, the conversion between axions and photons in the presence of magnetic fields.
Laboratory experiments
Helioscopes
Axion helioscopes search for axions produced by the Sun. A large magnet is used to convert solar axions into x-ray photons. Axions produced in the Sun might have an energy range of 1–10 keV and can therefore be converted into x-rays of the same energy in the magnet. The current state-of-the-art experiment is the CERN Axion Solar Telescope (CAST) which reached the axion–photon coupling limit of at 95% CL (for ≲ 0.02 eV) in 2024. The next-generation helioscope is the International AXion Observatory (IAXO), which is currently in development.
Light-shining-through-walls Another technique is so called "light shining through walls", where light passes through an intense magnetic field to convert photons into axions, which then pass through metal and are reconstituted as photons by another magnetic field on the other side of the barrier. Experiments by BFRS and a team led by Rizzo ruled out an axion cause. GammeV saw no events, reported in a 2008 Physics Review Letter. ALPS I conducted similar runs, setting new constraints in 2010; ALPS II began collecting data in May 2023. OSQAR found no signal, limiting coupling, and will continue.
Haloscopes Unlike the previous two approaches, axion haloscopes directly search for dark matter axions in the Milky Way dark matter halo. The Axion Dark Matter Experiment (ADMX) at the University of Washington is a haloscope that uses a strong magnetic field to weakly convert axions to microwaves. These microwave photons are then detected in a resonant cavity. ADMX has excluded optimistic axion models in the range . From 2013 to 2018 a series of upgrades were done and it is taking new data, including at . In December 2021 it excluded the range for the KSVZ model.
Many other experiments use a wide variety of techniques to detect halo axions, including DMRadio, HAYSTAC, CULTASK, and ORGAN. HAYSTAC completed the first scanning run of a haloscope above 20 μeV/c2 in the late 2010s. ORGAN plans to search for axions through resonance effects in Josephson junctions.
Polarized light in a magnetic field