As shown byGerard 't Hooft,[2]strong interactions of the Standard Model, QCD, possess a non-trivial vacuum structure[a] that in principle permits violation of the combined symmetries ofcharge conjugation andparity, collectively known as CP. Together with effects generated byweak interactions, the effective periodic strong CP-violating term,Θ, appears as aStandard 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 largeelectric dipole moment (EDM) for the neutron. Experimental constraints on the unobserved EDM implies CP violation from QCD must be extremely tiny and thusΘ must itself be extremely small. SinceΘ 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 thestrong CP problem.[b]
In 1977,Roberto Peccei andHelen Quinn postulated a more elegant solution to the strong CP problem, thePeccei–Quinn mechanism. The idea is to effectively promoteΘ to a field. This is accomplished by adding a new global symmetry (called aPeccei–Quinn (PQ) symmetry) that becomes spontaneously broken. This results in a new particle, as shown independently byFrank Wilczek[5] andSteven Weinberg,[6] that fills the role ofΘ, naturally relaxing the CP-violation parameter to zero. Wilczek named this new hypothesized particle the "axion" after abrand of laundry detergent because it carries the CP-violating"axial" current that "cleaned up" the problem,[7][8] while Weinberg called it "the higglet". Weinberg later agreed to adopt Wilczek's name for the particle.[8] Because it has a non-zero mass, the axion is apseudo-Nambu–Goldstone boson.[9]
QCD effects produce an effective periodic potential in which the axion field moves.[1] 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 than60 keV/c2 is long-lived and weakly interacting, a perfect dark matter candidate.
The number-line is broken into the two major classifications of dark matter particle hypotheses, particle-like dark matter (e.g. WIMPs) and wave-like dark matter (e.g. axions). The Compton wavelength and Compton frequency of the particles are shown for comparison, along with a few major reference points. Created in 2024 by Ciaran O'Hare.
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.[10][11][12] With a mass above 5 μeV/c2 (10−11 times theelectron mass) axions could account fordark 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.[13][14][15]
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:
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 fromisocurvature modes severely constrain this scenario, which require a relatively low-energy scale of inflation to be viable.[16][17][18]
If at least one of the conditions (a) or (b) is violated, the axion field takes different values within patches that are initially out ofcausal contact, but that today populate the volume enclosed by ourHubble 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 anddomain walls. An axion mass estimate between 0.05 and 1.50 meV was reported by Borsanyi et al. (2016).[19] The result was calculated by simulating the formation of axions during thepost-inflation period on asupercomputer.[20]
Progress in the late 2010s in determining the present abundance of a KSVZ-type axion[c] using numerical simulations lead to values between 0.02 and 0.1 meV,[23][24] although these results have been challenged by the details on the power spectrum of emitted axions from strings.[25]
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 thePeccei–Quinn mechanism for solving thestrong 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 asKSVZ (Kim–Shifman–Vainshtein–Zakharov)[21][22] andDFSZ (Dine–Fischler–Srednicki–Zhitnitsky).[26][27]
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.[10][11][12]
Pierre Sikivie computed howMaxwell's equations are modified in the presence of an axion in 1983.[28] 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, theAxion Dark Matter Experiment attempts to convert axion dark matter to microwave photons, theCERN 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.[29] As of the early 2020s, there are dozens of proposed or ongoing experiments searching for axion dark matter.[30]
Treating the reduced Planck constant, speed of light, and permittivity of free space all equivalent to 1, the electrodynamic equations are:
Name
Equations
Gauss's law
Gauss's law for magnetism
Faraday's law
Ampère–Maxwell law
Axion field's equation of motion
Above, a dot above a variable denotes its time derivative; the dot spaced between variables is thevector 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 ofmagnetic monopoles.[31] However, these alternative formulations are less theoretically motivated, and in many cases cannot even be derived from anaction.
A term analogous to the one that would be added toMaxwell's equations to account for axions[32] also appears in recent (2008) theoretical models fortopological insulators giving an effective axion description of the electrodynamics of these materials.[33]
In 2019, a team at theMax Planck Institute for Chemical Physics of Solids published their detection of anaxion insulator phase of aWeyl semimetal material.[36] In the axion insulator phase, the material has an axion-likequasiparticle – 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.[37]
Constraints on the axion's coupling to the photon[38]Constraints on the axion's dimensionless coupling to electrons[38]
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.
Several experiments search for astrophysical axions by thePrimakoff effect, which converts axions to photons and vice versa in electromagnetic fields.
TheAxion Dark Matter Experiment (ADMX) at theUniversity of Washington is ahaloscope that uses a strong magnetic field to detect the possible weak conversion of axions tomicrowaves.[39] ADMX searches the galacticdark matter halo[40] for axions resonant with a cold microwave cavity. ADMX has excluded optimistic axion models in the range1.9–3.53 μeV.[41][42][43] From 2013 to 2018 a series of upgrades[44] were done and it is taking new data, including at4.9–6.2 μeV. In December 2021 it excluded the range3.3–4.2 μeV for the KSVZ model.[45][46]
Other experiments of this type include DMRadio,[47] HAYSTAC,[48] CULTASK,[49] and ORGAN.[50] HAYSTAC completed the first scanning run of ahaloscope above 20 μeV in the late 2010s.[48]
Principle of operation of IAXO/BabyIAXO helioscope
Another type of direct conversion experiments are thehelioscopes where the magnet is pointed at the Sun. Axions produced in the Sun would 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 theCERN Axion Solar Telescope (CAST) which reached the axion-photon coupling limit of5.8×10−11GeV−1 at 95% CL (for ≲ 0.02 eV) in 2024.[51] The next-generation helioscope is theInternational AXion Observatory (IAXO), which is currently in development.
The ItalianPVLAS experiment searches for polarization changes oflight propagating in a magnetic field. The concept was first put forward in 1986 byLuciano Maiani, Roberto Petronzio andEmilio Zavattini.[52] A rotation claim[53] in 2006 was excluded by an upgraded setup.[54] An optimized search began in 2014.
Another technique is so called "light shining through walls",[55] 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.[56] GammeV saw no events, reported in a 2008 Physics Review Letter. ALPS I conducted similar runs,[57] setting new constraints in 2010; ALPS II began collecting data in May 2023.[58][59] OSQAR found no signal, limiting coupling,[60] and will continue.
Axion-like bosons could have a signature in astrophysical settings. In particular, several works have proposed axion-like particles as a solution to the apparent transparency of the Universe to TeV photons (very-high-energy gamma rays).[61][62] It has also been demonstrated 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 early 21st century telescopes.[63] A new (2009) 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.[64] TheInternational Axion Observatory (IAXO) is a proposed fourth generationhelioscope.[65]
Axions can resonantly convert into photons in themagnetospheres ofneutron stars.[66] The emerging photons lie in the GHz frequency range and can be potentially picked up in radio detectors, leading to a sensitive probe of the axion parameter space. This strategy has been used to constrain the axion–photon coupling in the mass range5–11 μeV/c2, by re-analyzing existing data from theGreen Bank Telescope and theEffelsberg 100 m Radio Telescope.[67] A novel, alternative strategy consists of detecting the transient signal from the encounter between a neutron star and an axion minicluster in theMilky Way.[68]
Axions can be produced in the Sun's core when X-rays scatter in strong electric fields. TheCAST solar telescope is underway, and has set limits on coupling to photons and electrons. Axions may also be produced within neutron stars by nucleon–nucleonbremsstrahlung. 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 theFermi Gamma-ray Space Telescope. From an analysis of four neutron stars, Berenji et al. (2016) obtained a 95%confidence interval upper limit on the axion mass of0.079 eV/c2.[69] In 2021 it has been also suggested[70][71] that a reported[72] excess of hard X-ray emission from a system of neutron stars known as themagnificent seven could be explained as axion emission.
In 2016, a theoretical team fromMassachusetts Institute of Technology devised a possible way of detecting axions using a strong magnetic field that need be no stronger than that produced in anMRI scanning machine. It would show variation, a slight wavering, that is linked to the mass of the axion. Results from the ensuing experiment published in 2021 reported no evidence of axions in the mass range from 4.1x10−10 to 8.27x10−9 eV.[73]
In 2022 the polarized lightmeasurements ofMessier 87* by theEvent Horizon Telescope were used to constrain the mass of the axion assuming that hypothetical clouds of axions could form around a black hole, rejecting the approximate10−21 eV/c2 –10−20 eV/c2 range of mass values.[74][75]
Resonance effects may be evident inJosephson junctions[76] from a supposed high flux of axions from the galactic halo with mass of110 μeV/c2 and density0.05 (GeV/c2)/cm3[77] compared to the implied dark matter density0.3±0.1 (GeV/c2)/cm3, 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 thehaloscope method.[50]
Dark matter cryogenic detectors have searched for electron recoils that would indicate axions.CDMS published in 2009 andEDELWEISS set coupling and mass limits in 2013.UORE andXMASS 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.[78]
While Schiff's theorem states that a staticnuclear electric dipole moment (EDM) does not produce atomic and molecular EDMs,[79] the axion induces an oscillating nuclear EDM that oscillates at theLarmor frequency. If this nuclear EDM oscillation frequency is in resonance with an external electric field, a precession in the nuclear spin rotation occurs. This precession can be measured using precession magnetometry and if detected, would be evidence for axions.[80]
An experiment using this technique is the Cosmic Axion Spin Precession Experiment (CASPEr).[81][82][83]
Axions may also be produced at colliders, in particular in electron-positron collisions as well as in ultra-peripheral heavy ion collisions at the Large Hadron Collider at CERN, reinterpreting thelight-by-light scattering process. Those searches are sensitive for rather large axion masses between100 MeV/c2 and hundreds ofGeV/c2. Assuming a coupling of axions to the Higgs boson, searches for anomalous Higgs boson decays into two axions can theoretically provide even stronger limits.[84]
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 theEuropean Space Agency'sXMM-Newton observatory, a research group atLeicester 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.[85][86]
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.[87]
In 2013, Christian Beck suggested that axions might be detectable inJosephson junctions; and in 2014, he argued that a signature, consistent with a mass ≈110 μeV, had in fact been observed in several preexisting experiments.[88]
In 2020, theXENON1T experiment at theGran Sasso National Laboratory in Italy reported a result suggesting the discovery of solar axions.[89] The results were not significant at the5-sigma level required for confirmation, and other explanations of the data were possible though less likely.[90] New observations made in July 2022 after the observatory upgrade toXENONnT discarded the excess, thus ending the possibility of new particle discovery.[91][92]
One theory of axions relevant tocosmology had predicted that they would have noelectric charge, a very smallmass in the range from1 μeV/c2 to1 eV/c2,[1] and very low interactioncross-sections forstrong andweak forces. Because of their properties, axions would interact only minimally with ordinary matter. Axions would also change to and fromphotons in magnetic fields.
An ultralight axion (ULA) withm ~10−22 eV/c2 is a kind ofscalar field dark matter that 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.[94]
Axions would also have stopped interaction with normal matter at a different moment after theBig Bang than other more massive dark particles.[why?] The lingering effects of this difference could perhaps be calculated and observed astronomically.[citation needed]
If axions have low mass, thus preventing other decay modes (since there are no lighter particles to decay into), the low coupling constant thus predicts that the axion is not scattered out of its state despite its small mass so that the universe would be filled with a very coldBose–Einstein condensate of primordial axions. Hence, axions could plausibly explain thedark matter problem ofphysical cosmology.[95] 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 with the fuzzy dark matter region starting to be probed viasuperradiance.[96] High mass axions of the kind searched for by Jain and Singh (2007)[97] 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.[98]
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.[99] The gravitational effects of these rings on galactic structure and rotation might then be observable.[100][101] Other cold dark matter theoretical candidates, such asWIMPs andMACHOs, could also form such rings, but because such candidates arefermionic and thus experience friction or scattering among themselves, the rings would be less sharply defined.[citation needed]
João G. Rosa and Thomas W. Kephart suggested that axion clouds formed around unstableprimordial 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 offast radio bursts, being a possible origin for both phenomena.[102] In 2022 a similar hypothesis was used toconstrain the mass of the axion from data of M87*.[citation needed]
In 2020, it was proposed that the axion field might actually have influenced the evolution ofthe early Universe by creating more imbalance between the amounts of matter and antimatter – which possibly resolves thebaryon asymmetry problem.[103]
^This non-trivial vacuum structure solves a problem associated to the U(1) axial symmetry of QCD[3][4]
^ One simple solution to thestrong CP problem exists: If at least one of thequarks 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.
^At present, physics literature discusses "invisible axion" mechanisms in two forms, one of them is called KSVZ forKim–Shifman–Vainshtein–Zakharov.[21][22] See discussion in the "Searches" section,below.
^Ringwald, A. (16–21 October 2001). "Fundamental Physics at an X-Ray Free Electron Laser".Electromagnetic Probes of Fundamental Physics – Proceedings of the Workshop. Workshop on Electromagnetic Probes of Fundamental Physics.Erice, Italy. pp. 63–74.arXiv:hep-ph/0112254.doi:10.1142/9789812704214_0007.ISBN978-981-238-566-6.
^Foster, Joshua W.; Kahn, Yonatan; Macias, Oscar; Sun, Zhiquan; Eatough, Ralph P.; Kondratiev, Vladislav I.; Peters, Wendy M.; Weniger, Christoph; Safdi, Benjamin R. (2020). "Green Bank and Effelsberg Radio Telescope Searches for Axion Dark Matter Conversion in Neutron Star Magnetospheres".Physical Review Letters.125 (17) 171301.arXiv:2004.00011.Bibcode:2020PhRvL.125q1301F.doi:10.1103/PhysRevLett.125.171301.PMID33156637.S2CID214743261.
^Commins, Eugene D.; Jackson, J. D.; DeMille, David P. (June 2007). "The electric dipole moment of the electron: An intuitive explanation for the evasion of Schiff's theorem".American Journal of Physics.75 (6):532–536.Bibcode:2007AmJPh..75..532C.doi:10.1119/1.2710486.
^Garcon, Antoine; Aybas, Deniz; Blanchard, John W; Centers, Gary; Figueroa, Nataniel L; Graham, Peter W; et al. (January 2018). "The cosmic axion spin precession experiment (CASPEr): a dark-matter search with nuclear magnetic resonance".Quantum Science and Technology.3 (1): 014008.arXiv:1707.05312.Bibcode:2018QS&T....3a4008G.doi:10.1088/2058-9565/aa9861.S2CID51686418.
^Jain, P. L.; Singh, G. (2007). "Search for new particles decaying into electron pairs of mass below 100 MeV/c2".Journal of Physics G.34 (1):129–138.Bibcode:2007JPhG...34..129J.doi:10.1088/0954-3899/34/1/009.possible early evidence of 7±1 and 19±1 MeV axions of less than 10−13 s lifetime
^Duffy, Leanne D.; Tanner, David B.; Van Bibber, Karl A. (2010).The Milky Way's Dark Matter Distribution and Consequences for Axion Detection. Axions 2010. AIP Conference Proceedings. Vol. 1274. pp. 85–90.Bibcode:2010AIPC.1274...85D.doi:10.1063/1.3489563.
