The axion (/ˈæksiɒn/) is a hypothetical elementary particle postulated by the Peccei–Quinn theory in 1977 to resolve 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.

Strong CP problem

As shown by Gerard 't Hooft,[4] 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, Θ, 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 currently unobserved EDM implies CP violation from QCD must be extremely tiny and thus Θ must itself be extremely small. Since Θ could have any value between 0 and 2π, 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.[a]

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 Θ to a field. This is accomplished by adding a new global symmetry (called a Peccei–Quinn 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 Θ, naturally relaxing the CP-violation parameter to zero. Wilczek named this new hypothesized particle the "axion" after a brand of laundry detergent,[5] while Weinberg called it "Higglet." Weinberg later agreed to adopt Wilczek's name for the particle.[6] Because it has a non-zero mass, the axion is a pseudo-Nambu–Goldstone boson.[7]

Axion models carefully choose coupling strengths that are too weak to have been detected in prior experiments. It had been thought that these “invisible axions” solved the strong CP problem while still being too small to have been observed before. Current literature discusses “invisible axion” mechanisms in two forms, called K S V Z (Kim–Shifman–Vainshtein–Zakharov)[8][9] and D F S Z (Dine–Fischler–Srednicki–Zhitnitsky).[10][11]

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. The critical mass is of order 10−11 times the electron mass.[12][13][14]

With a mass above 10−11 times the electron mass, axions could account for dark matter, thus be both a dark-matter candidate and a solution to the strong CP problem. A mass value between 0.05 and 1.50 meV for the axion was reported in a paper published by Borsanyi et al.. (2016).[15] The result was calculated by simulating the formation of axions during the post-inflation period on a supercomputer.[16]

Maxwell's equations with axion modifications

Pierre Sikivie published a modification of Maxwell's equations that arise from a light, stable axion in 1983.[17] He showed that these axions could be detected on Earth by converting them to photons, using a strong magnetic field, hence leading to several experiments: the ADMX; Solar axions may be converted to X-rays, as in CERN Axion Solar Telescope (CAST); Other experiments are searching laser light for signs of axions.[18]

There is a symmetry in Maxwell's equations where the electric and magnetic fields can be rotated into each other with the new fields still satisfying Maxwell's equations. Luca Visinelli showed that the duality symmetry can be carried over to the axion-electromagnetic theory as well.[19] Assuming the existence of both magnetic monopoles and axions, the complete set of Maxwell equations reads:
Name Equations
Gauss's law \( {\displaystyle \nabla \cdot (\mathbf {E} -\kappa \theta c\mathbf {B} )={\frac {\rho _{e}}{\varepsilon _{0}}}} \)
Gauss's law for magnetism \( {\displaystyle \nabla \cdot (c\mathbf {B} +\kappa \theta \mathbf {E} )=c\mu _{0}\rho _{m}} \)
Faraday's law \( {\displaystyle \nabla \times (-\mathbf {E} +\kappa \theta c\mathbf {B} )=\partial _{ct}(c\mathbf {B} +\kappa \theta \mathbf {E} )+\mu _{0}\mathbf {J} _{m}} \)
Ampère–Maxwell law \( {\displaystyle \nabla \times (c\mathbf {B} +\kappa \theta \mathbf {E} )=\partial _{ct}(\mathbf {E} -\kappa \theta c\mathbf {B} )+c\mu _{0}\mathbf {J} _{e}} \)
Axion law \( {\displaystyle (\Box +m_{a}^{2})\theta =-\kappa \mathbf {E} \cdot \mathbf {B} } \)

If magnetic monopoles do not exist, then the same equations hold, with the monopole density \( \rho_m \) and monopole current \( {\displaystyle \mathbf {J} _{m}} \) replaced by zero. With or without monopoles, incorporating the axion into Maxwell's equations has the effect of rotating the electric and magnetic fields into each other.
\( {\displaystyle {\begin{bmatrix}\mathbf {E'} \\c\mathbf {B'} \\\end{bmatrix}}={\frac {1}{\cos \xi }}{\begin{bmatrix}\cos \xi &\sin \xi \\-\sin \xi &\cos \xi \\\end{bmatrix}}{\begin{bmatrix}\mathbf {E} \\c\mathbf {B} \\\end{bmatrix}}} \)

where the mixing angle \( \xi \) depends on the coupling constant \( \kappa \) and the axion field strength \( \theta \)
\( {\displaystyle \tan \xi =-\kappa \theta } \)

By plugging the new values for electromagnetic field \( {\displaystyle \mathbf {E'} } \) and \( \mathbf{B'} \) into Maxwell's equations we obtain the axion-modified Maxwell equations above. Incorporating the axion into the electromagnetic theory also gives a new differential equation—the axion law—which is simply the Klein–Gordon equation (the quantum field theory equation for massive spin-zero particles) with an \( {\displaystyle \mathbf {E} \cdot \mathbf {B} } \) source term.
Analogous effect for topological insulators

A term analogous to the one that would be added to Maxwell's equations to account for axions[20] also appears in recent (2008) theoretical models for topological insulators giving an effective axion description of the electrodynamics of these materials.[21]

This term leads to several interesting predicted properties including a quantized magnetoelectric effect.[22] Evidence for this effect has recently been given in THz spectroscopy experiments performed at the Johns Hopkins University on quantum regime thin film topological insulators developed at Rutgers University.[23]

In 2019, a team at the Max Planck Institute for Chemical Physics of Solids published their detection of axion insulators within a Weyl semimetal.[24] An axion insulator is a quasiparticle – an excitation of electrons that behave together as an axion – and its discovery is consistent with the existence of the axion as an elementary particle.[25]

Despite not yet having been found, axion models have 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 candidates for dark matter particles, and might be discovered in some dark matter experiments.
Direct conversion in a magnetic field

Several experiments search for astrophysical axions by the Primakoff effect, which converts axions to photons and vice versa in electromagnetic fields.

The Axion Dark Matter Experiment (ADMX) at the University of Washington uses a strong magnetic field to detect the possible weak conversion of axions to microwaves.[26] ADMX searches the galactic dark matter halo[27] for axions resonant with a cold microwave cavity. ADMX has excluded optimistic axion models in the 1.9–3.53 μeV range.[28][29][30] In 2013-2018 a series of upgrades were done and it is taking new data, including at 4.9–6.2 µeV.

Other experiments of this type include HAYSTAC,[31] CULTASK,[32] and ORGAN.[33] HAYSTAC recently completed the first scanning run of a haloscope above 20 µeV.[31]
Polarized light in a magnetic field

The Italian PVLAS experiment searches for polarization changes of light propagating in a magnetic field. The concept was first put forward in 1986 by Luciano Maiani, Roberto Petronzio and Emilio Zavattini.[34] A rotation claim[35] in 2006 was excluded by an upgraded setup.[36] An optimized search began in 2014.

Light shining through walls

Another technique is so called "light shining through walls",[37] 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.[38] GammeV saw no events, reported in a 2008 Physics Review Letter. ALPS-I conducted similar runs,[39] setting new constraints in 2010; ALPS-II will run in 2019.[needs update] OSQAR found no signal, limiting coupling[40] and will continue.

Astrophysical axion searches

Axion-like bosons could have a signature in astrophysical settings. In particular, several recent works have proposed axion-like particles as a solution to the apparent transparency of the Universe to TeV photons.[41][42] It has also been demonstrated in a few recent works that, in the large magnetic fields threading the atmospheres of compact astrophysical objects (e.g., magnetars), photons will convert much more efficiently. This would in turn give rise to distinct absorption-like features in the spectra detectable by current telescopes.[43] A new promising means is looking for quasi-particle refraction in systems with strong magnetic gradients. In particular, the refraction will lead to beam splitting in the radio light curves of highly magnetized pulsars and allow much greater sensitivities than currently achievable.[44] The International Axion Observatory (IAXO) is a proposed fourth generation helioscope.[45]

Axions can be produced in the Sun's core when X-rays scatter in strong electric fields. The CAST solar telescope is underway, and has set limits on coupling to photons and electrons. Axions may be produced within neutron stars, by nucleon-nucleon bremsstrahlung. The subsequent decay of axions to gamma rays allows constraints on the axion mass to be placed from observations of neutron stars in gamma-rays using the Fermi LAT. From an analysis of four neutron stars, Berenji et al. obtained a 95% confidence interval upper limit on the axion mass of 0.079 eV.[46]

In 2016, a theoretical team from Massachusetts Institute of Technology devised a possible way of detecting axions using a strong magnetic field that need be no stronger than that produced in a MRI scanning machine. It would show variation, a slight wavering, that is linked to the mass of the axion. The experiment is now being implemented by experimentalists at the university.[47]
Searches for resonance effects

Resonance effects may be evident in Josephson junctions[48] from a supposed high flux of axions from the galactic halo with mass of 0.11 meV and density 0.05 GeV⋅cm−3[49] compared to the implied dark matter density 0.3±0.1 GeV⋅cm−3, indicating said axions would not have enough mass to be the sole component of dark matter. The ORGAN experiment plans to conduct a direct test of this result via the haloscope method.[33]

Dark matter recoil searches

Dark matter cryogenic detectors have searched for electron recoils that would indicate axions. CDMS published in 2009 and EDELWEISS set coupling and mass limits in 2013. UORE and XMASS also set limits on solar axions in 2013. XENON100 used a 225 day run to set the best coupling limits to date and exclude some parameters.[50]
Possible detections

It was reported in 2014 that evidence for axions may have been detected as a seasonal variation in observed X-ray emission that would be expected from conversion in the Earth's magnetic field of axions streaming from the Sun. Studying 15 years of data by the European Space Agency's XMM-Newton observatory, a research group at Leicester University noticed a seasonal variation for which no conventional explanation could be found. One potential explanation for the variation, described as "plausible" by the senior author of the paper, is the known seasonal variation in visibility to XMM-Newton of the sunward magnetosphere in which X-rays may be produced by axions from the Sun's core.[51][52]

This interpretation of the seasonal variation is disputed by two Italian researchers, who identify flaws in the arguments of the Leicester group that are said to rule out an interpretation in terms of axions. Most importantly, the scattering in angle assumed by the Leicester group to be caused by magnetic field gradients during the photon production, necessary to allow the X-rays to enter the detector that cannot point directly at the sun, would dissipate the flux so much that the probability of detection would be negligible.[53]

In 2013, Christian Beck suggested that axions might be detectable in Josephson junctions; and in 2014, he argued that a signature, consistent with a mass ≈110 μeV, had in fact been observed in several preexisting experiments.[54]

In 2020, the XENON1T experiment at the Gran Sasso National Laboratory in Italy reported a result suggesting the discovery of solar axions.[55] The results are not yet significant at the 5-sigma level required for confirmation, and other explanations of the data are possible though less likely. Further observations are planned after the observatory upgrade to XENONnT is completed.


One theory of axions relevant to cosmology had predicted that they would have no electric charge, a very small mass in the range from 1 µeV/c² to 1 eV/c2, and very low interaction cross-sections for strong and weak forces. Because of their properties, axions would interact only minimally with ordinary matter. Axions would also change to and from photons in magnetic fields.
Cosmological implications

Inflation suggests that if they exist, axions would be created abundantly during the Big Bang.[56] Because of a unique coupling to the instanton field of the primordial universe (the "misalignment mechanism"), an effective dynamical friction is created during the acquisition of mass, following cosmic inflation. This robs all such primordial axions of their kinetic energy.

Ultralight axion (ULA) with m ~ 10−22 eV is a kind of scalar field dark matter which seems to solve the small scale problems of CDM. A single ULA with a GUT scale decay constant provides the correct relic density without fine-tuning.[57]

Axions would also have stopped interaction with normal matter at a different moment after the Big Bang than other more massive dark particles. The lingering effects of this difference could perhaps be calculated and observed astronomically.

If axions have low mass, thus preventing other decay modes (since there are no lighter particles to decay into), theories[which?] predict that the universe would be filled with a very cold Bose–Einstein condensate of primordial axions. Hence, axions could plausibly explain the dark matter problem of physical cosmology.[58] Observational studies are underway, but they are not yet sufficiently sensitive to probe the mass regions if they are the solution to the dark matter problem. High mass axions of the kind searched for by Jain and Singh (2007)[59] would not persist in the modern universe. Moreover, if axions exist, scatterings with other particles in the thermal bath of the early universe unavoidably produce a population of hot axions.[60]

Low mass axions could have additional structure at the galactic scale. If they continuously fall into galaxies from the intergalactic medium, they would be denser in "caustic" rings, just as the stream of water in a continuously-flowing fountain is thicker at its peak.[61] The gravitational effects of these rings on galactic structure and rotation might then be observable.[62][3] Other cold dark matter theoretical candidates, such as WIMPs and MACHOs, could also form such rings, but because such candidates are fermionic and thus experience friction or scattering among themselves, the rings would be less sharply defined.

João G. Rosa and Thomas W. Kephart suggested that axion clouds formed around unstable primordial black holes might initiate a chain of reactions that radiate electromagnetic waves, allowing their detection. When adjusting the mass of the axions to explain dark matter, the pair discovered that the value would also explain the luminosity and wavelength of fast radio bursts, being a possible origin for both phenomena.[63]


In supersymmetric theories the axion has both a scalar and a fermionic superpartner. The fermionic superpartner of the axion is called the axino, the scalar superpartner is called the saxion or dilaton. They are all bundled up in a chiral superfield.

The axino has been predicted to be the lightest supersymmetric particle in such a model.[64] In part due to this property, it is considered a candidate for dark matter.[65]

One simple solution to the strong CP problem exists: If at least one of the quarks of the standard model is massless, CP-violation becomes unobservable. However, empirical evidence strongly suggests that none of the quarks are massless. Consequently, particle theorists sought other resolutions to the problem of inexplicably conserved CP.


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External links

"article". APS Physics. 24 November 2008.
"news article". 28 January 2007.
"news article". 6 December 2006. Archived from the original on 7 December 2006.
"news article" . Scientific American. 17 July 2006.
"news article". 27 March 2006.
"news article". 24 November 2004.
"CAST Experiment". Switzerland: CERN.
"CAST". Spain: UNIZAR.
"CAST". Darmstadt, DE: University of Technology. Archived from the original on 2009-03-18.
"ADMX". Seattle, WA: University of Washington.
"Axion in nLab".


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