View source for Axion

{{short description|Hypothetical elementary particle}}
{{hatnote group|
{{about-distinguish|the hypothetical elementary particle|Axiom|Axon}}
{{other uses}}
}}
{{infobox particle
| name = Axion
| composition =
| status = Hypothetical
| interaction = [[Gravitational]], [[Electromagnetic interaction|electromagnetic]], [[Strong interaction|strong]], [[Weak interaction|weak]]
| theorized = 1978, [[Frank Wilczek|Wilczek]] and [[Steven Weinberg|Weinberg]]
| symbol = A<sup>0</sup>, a, θ
| mass = 10<sup>−7</sup> to 1&nbsp;[[electronvolt|eV]]/[[Speed of light|''c'']]<sup>2</sup>{{spaces|1}}<ref name="peccei2008">{{cite book|last=Peccei | first=R. D. | title=Axions: Theory, Cosmology, and Experimental Searches <!-- leave subtitle --> |year=2008 |chapter=The Strong CP Problem and Axions |editor1-last=Kuster |editor1-first=Markus |editor2-last=Raffelt |editor2-first=Georg |editor3-last=Beltrán |editor3-first=Berta |series=Lecture Notes in Physics |volume=741 |pages=3–17 |arxiv=hep-ph/0607268 |doi=10.1007/978-3-540-73518-2_1 |isbn=978-3-540-73517-5|s2cid=119482294 }}</ref>
| electric_charge = 0&nbsp;''e''
| spin = 0&nbsp;''ħ''
<!-- | Grouping = [[Goldstone Boson]] -->
}}

An '''axion''' ({{IPAc-en|ˈ|æ|k|s|i|ɒ|n}}) 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]],<ref>{{cite journal |last='t Hooft |first=Gerard |year=1976 |title=Symmetry breaking through Bell-Jackiw anomalies |journal=Physical Review Letters |volume=37 |issue=1|page=8 |doi=10.1103/PhysRevLett.37.8 |bibcode=1976PhRvL..37....8T }}{{cite journal |last='t Hooft |first=Gerard |year=1976 |title=Computation of the quantum effects due to a four-dimensional pseudo-particle |journal=Physical Review D |publisher=APS |volume=14 |issue=12 |pages=3432–3450 |bibcode=1976PhRvD..14.3432T |doi=10.1103/PhysRevD.14.3432}}</ref> [[strong interaction]]s of the Standard Model, QCD, possess a non-trivial vacuum structure{{efn|This non-trivial vacuum structure solves a problem associated to the U(1) axial symmetry of QCD.<ref>{{cite journal |last1=Katz |first1=Emanuel |last2=Schwartz |first2=Matthew D |title=An eta primer: solving the U(1) problem with AdS/QCD |journal=Journal of High Energy Physics |date=28 August 2007 |volume=2007 |issue=8 |page=077 |doi=10.1088/1126-6708/2007/08/077 |arxiv=0705.0534 |bibcode=2007JHEP...08..077K |s2cid=119594300 }}</ref><ref>{{cite web |url=https://www.classe.cornell.edu/~pt267/files/documents/A_instanton.pdf |title='t Hooft and η'ail Instantons and their applications | first=Flip | last=Tanedo | publisher=Cornell University | access-date=2023-06-20}}</ref>}} that in principle permits violation of the combined symmetries of [[C-symmetry|charge conjugation]] and [[parity (physics)|parity]], collectively known as CP. Together with effects generated by [[weak interaction]]s, the effective periodic strong CP-violating term, {{overline|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 [[Neutron electric dipole moment|electric dipole moment (EDM) for the neutron]]. Experimental constraints on the EDM implies that CP violation from QCD must be extremely tiny and thus {{overline|Θ}} must itself be extremely small. Since {{overline|Θ}} could have any value between 0 and 2{{math|π}}, 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]].{{efn|<!-- This same paragraph appears in [[strong CP problem]]. Does it need to be repeated here? --> 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.}}

=== Prediction ===
In 1977, [[Roberto Peccei]] and [[Helen Quinn]] postulated a more elegant solution to the strong CP problem, the [[Peccei–Quinn theory|Peccei–Quinn mechanism]]. The idea is to effectively promote {{overline|Θ}} to a field. This is accomplished by adding a new global symmetry (called a [[Peccei–Quinn symmetry|Peccei–Quinn (PQ) symmetry]]) that becomes spontaneously broken. This results in a new particle, as shown independently by [[Frank Wilczek]]<ref>{{cite journal |last= Wilczek |first=Frank |year=1978 |journal=Physical Review Letters |volume=40 | issue=5 |pages= 279–282 |title=Problem of Strong P and T Invariance in the Presence of Instantons |doi=10.1103/PhysRevLett.40.279 |bibcode=1978PhRvL..40..279W}}</ref> and [[Steven Weinberg]],<ref>{{cite journal |last= Weinberg |first=Steven |year=1978 |journal=Physical Review Letters |volume=40 | issue=4 |pages=223–226 |title=A New Light Boson? |doi=10.1103/PhysRevLett.40.223 |bibcode=1978PhRvL..40..223W}}</ref> that fills the role of {{overline|Θ}}, naturally relaxing the CP-violation parameter to zero. Wilczek named this new hypothesized particle the "axion" after a [[Axion (brand)|brand of laundry detergent]] because it carries the CP-violating [[axial current|"axial" current]] that "cleaned up" the problem,<ref>{{cite news |last=Overbye |first=Dennis |date=17 June 2020 |title=Seeking dark matter, they detected another mystery |newspaper=[[The New York Times]] |url=https://www.nytimes.com/2020/06/17/science/xenon-axions-neutrinos-tritium.html}}</ref><ref name="WilczekQuanta2016" /> while Weinberg called it "the higglet". Weinberg later agreed to adopt Wilczek's name for the particle.<ref name="WilczekQuanta2016">{{cite magazine |last=Wilczek |first=Frank |author-link=Frank Wilczek |date=7 January 2016 |title=Time's (almost) reversible arrow |magazine=[[Quanta Magazine]] |url=https://www.quantamagazine.org/how-axions-may-explain-times-arrow-20160107/ |access-date=17 June 2020}}</ref> Because it has a non-zero mass, the axion is a [[pseudo-Nambu–Goldstone boson]].<ref>{{cite arXiv|eprint=hep-ph/0309143v1 |last1=Miller |first1=D. J. |last2=Nevzorov |first2=R. |title=The Peccei–Quinn Axion in the Next-to-Minimal Supersymmetric Standard Model |year=2003 }}</ref>

== Axion dark matter ==
[[File:Dark matter candidates.pdf|thumb|upright=2|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.]]
QCD effects produce an effective periodic potential in which the axion field moves.<ref name="peccei2008"/> 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 {{val|60|u=keV/c2}} 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.<ref name="auto">{{cite journal |last1=Preskill |first1=J. |author1-link=John Preskill |last2=Wise |first2=M. |author2-link=Mark B. Wise |last3=Wilczek |first3=F. |author3-link=Frank Wilczek |date=6 January 1983 |journal=Physics Letters&nbsp;B |volume=120 |issue=1–3 |pages=127–132 |title=Cosmology of the invisible axion |doi=10.1016/0370-2693(83)90637-8 |bibcode=1983PhLB..120..127P |url=http://www.theory.caltech.edu/~preskill/pubs/preskill-1983-axion.pdf |citeseerx=10.1.1.147.8685 }}</ref><ref name="A cosmological bound on the invisib">{{cite journal |last1=Abbott |first1=L. |last2=Sikivie |first2=P. |year=1983 |journal=Physics Letters&nbsp;B |volume=120 |issue=1–3 |pages=133–136 |title=A cosmological bound on the invisible axion |bibcode=1983PhLB..120..133A |doi=10.1016/0370-2693(83)90638-X |citeseerx=10.1.1.362.5088}}</ref><ref name="The not-so-harmless axion">{{cite journal |last1=Dine |first1=M. |last2=Fischler |first2=W. |year=1983 |journal=Physics Letters B |volume=120 |issue=1–3 |pages=137–141 |title=The not-so-harmless axion |doi=10.1016/0370-2693(83)90639-1 |bibcode=1983PhLB..120..137D}}</ref> With a mass above 5&nbsp;[[electronvolt|μeV/''c''<sup>2</sup>]] ({{10^|−11}} 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&nbsp;peV/''c''<sup>2</sup>.<ref>{{cite journal |last1=di Luzio |first1=L. |last2=Nardi |first2=E. |last3=Giannotti |first3=M. |last4=Visinelli |first4=L. |date=25 July 2020 |journal=Physics Reports |volume=870 |pages=1–117 |title=The landscape of QCD axion models |bibcode=2020PhR...870....1D |doi=10.1016/j.physrep.2020.06.002 |arxiv=2003.01100 |s2cid=211678181 }}</ref><ref>{{cite journal |last1=Graham |first1=Peter W. |last2=Scherlis |first2=Adam |title=Stochastic axion scenario |journal=Physical Review D |date=9 August 2018 |volume=98 |issue=3 |article-number=035017 |doi=10.1103/PhysRevD.98.035017 |arxiv=1805.07362 |bibcode=2018PhRvD..98c5017G |s2cid=119432896 }}</ref><ref>{{cite journal |last1=Takahashi |first1=Fuminobu |last2=Yin |first2=Wen |last3=Guth |first3=Alan H. |title=The QCD Axion Window and Low Scale Inflation |journal=Physical Review D |date=31 July 2018 |volume=98 |issue=1 |article-number=015042 |doi=10.1103/PhysRevD.98.015042 |arxiv=1805.08763 |bibcode=2018PhRvD..98a5042T |s2cid=54584447 }}</ref>

There are two distinct scenarios in which the axion field begins its evolution, depending on the following two conditions:
{|
|- style="vertical-align:top;"
| (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.
|- style="vertical-align:top;"
| (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, [[Inflation (cosmology)|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 defect]]s are inflated away and do not contribute to the axion energy density. However, other bounds that come from [[isocurvature mode]]s severely constrain this scenario, which require a relatively low-energy scale of inflation to be viable.<ref>{{cite journal |last1= Crotty |first1=P. |last2=Garcia-Bellido |first2=J. |last3=Lesgourgues |first3=J. |last4=Riazuelo |first4=A. |year=2003 |journal=Physical Review Letters |volume=91 |article-number=171301 |title=Bounds on isocurvature perturbations from CMB and LSS data |issue=17 |doi=10.1103/PhysRevLett.91.171301 |pmid=14611330 |bibcode=2003PhRvL..91q1301C |arxiv=astro-ph/0306286 |s2cid=12140847 }}</ref><ref>{{cite journal |last1= Beltran |first1=Maria |last2=Garcia-Bellido |first2=Juan |last3=Lesgourgues |first3=Julien |last4=Liddle |first4=Andrew R. |last5=Slosar |first5= Anze |year=2005 |journal=Physical Review D |volume=71 |issue=6 |article-number= 063532 |title=Bayesian model selection and isocurvature perturbations |bibcode=2005PhRvD..71f3532B |doi=10.1103/PhysRevD.71.063532 |arxiv=astro-ph/0501477|s2cid=2220608 }}</ref><ref>{{cite journal |last1= Beltran |first1=Maria |last2=Garcia-Bellido |first2=Juan |last3=Lesgourgues |first3=Julien |year=2007 |journal=Physical Review D |volume=75 |issue=10 |article-number= 103507 |title=Isocurvature bounds on axions revisited |doi=10.1103/PhysRevD.75.103507 |bibcode=2007PhRvD..75j3507B |arxiv=hep-ph/0606107 |s2cid=119451896 }}</ref>

=== 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 [[Cosmological horizon#Hubble horizon|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" [[cosmic string|strings]] and [[domain wall]]s. An axion mass estimate between {{val|0.05|and|1.50|u=meV/''c''<sup>2</sup>}} was reported by Borsanyi et al. (2016).<ref>{{cite journal |display-authors=6 |last1=Borsanyi |first1=S. |last2=Fodor |first2=Z. |last3=Guenther |first3=J. |last4=Kampert |first4=K.-H. |last5=Katz |first5=S. D. |last6=Kawanai |first6=T. |last7=Kovacs |first7=T. G. |last8=Mages |first8=S. W. |last9=Pasztor |first9=A. |last10=Pittler |first10=F. |last11=Redondo |first11=J. |last12=Ringwald |first12=A. |last13=Szabo |first13=K. K. |title=Calculation of the axion mass based on high-temperature lattice quantum chromodynamics |journal=Nature |date=3 November 2016 |volume=539 |issue=7627 |pages=69–71 |doi=10.1038/nature20115 |pmid=27808190 |bibcode=2016Natur.539...69B |s2cid=2943966 |url=https://bib-pubdb1.desy.de/record/311362 |arxiv=1606.07494 }}</ref> The result was calculated by simulating the formation of axions during the [[Inflation (cosmology)|post-inflation]] period on a [[supercomputer]].<ref>{{cite journal |first=Davide |last=Castelvecchi |date=3 November 2016 |title=Axion alert! Exotic-particle detector may miss out on dark matter |series=news |journal=[[Nature (journal)|Nature]] |doi=10.1038/nature.2016.20925 |s2cid=125299733 |doi-access=free }}</ref>

Progress in the late 2010s in determining the present abundance of a KSVZ-type axion{{efn|At present, physics literature discusses "invisible axion" mechanisms in two forms, one of them is called KSVZ for [[Kim Jihn-eui|Kim]]–[[Mikhail Shifman|Shifman]]–[[Arkady Vainshtein|Vainshtein]]–{{nowrap|{{abbr|Zakharov|Valya Zakharov}}.<ref name=Kim-1979/><ref name=Shifman-etal-1980/>}} See discussion in the "Searches" section, [[#K-S-V-Z-vs-D-F-S-Z-anchor|below]].}} using numerical simulations lead to values between 0.02 and 0.1&nbsp;meV/''c''<sup>2</sup>,<ref>{{cite journal |last1=Klaer |first1=Vincent B. |last2=Moore |first2=Guy D. |year=2017 |journal=Journal of Cosmology and Astroparticle Physics |volume=2017 |page= 049 |title=The dark-matter axion mass |issue=11 |doi=10.1088/1475-7516/2017/11/049 |bibcode=2017JCAP...11..049K |arxiv=1708.07521 |s2cid=119227153 }}</ref><ref>{{cite journal |last1= Buschmann |first1= Malte |last2= Foster |first2=Joshua W. |last3=Safdi |first3=Benjamin R. |year=2020 |journal=Physical Review Letters |volume=124 |issue=16 |article-number=161103 |title=Early-Universe Simulations of the Cosmological Axion |doi=10.1103/PhysRevLett.124.161103 |pmid= 32383908 |bibcode=2020PhRvL.124p1103B |arxiv= 1906.00967 |s2cid= 174797749 }}</ref> although these results have been challenged by the details on the power spectrum of emitted axions from strings.<ref>{{cite journal |last1=Gorghetto |first1=Marco |last2=Hardy |first2=Edward |last3=Villadoro |first3=Giovanni |title=More axions from strings |journal=SciPost Physics |year=2021 |volume=10 |issue=2 |page=050 |doi=10.21468/SciPostPhys.10.2.050 |arxiv=2007.04990 |bibcode=2021ScPP...10...50G |s2cid=220486728 |doi-access=free }}</ref>

== Phenomenology of the axion field ==
=== Searches <span class="anchor" id="K-S-V-Z-vs-D-F-S-Z-anchor"></span> ===
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 theory|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 {{nowrap|KSVZ}} ([[Kim Jihn-eui|Kim]]–[[Mikhail Shifman|Shifman]]–[[Arkady Vainshtein|Vainshtein]]–{{nowrap|{{abbr|Zakharov|Valya Zakharov}})<ref name=Kim-1979>{{cite journal |last1=Kim |first1=J. E. |year=1979 |title=Weak-interaction singlet and strong CP invariance |journal=Physical Review Letters |volume=43 |issue=2 |pages=103–107 |bibcode=1979PhRvL..43..103K |doi=10.1103/PhysRevLett.43.103}}</ref><ref name=Shifman-etal-1980>{{cite journal |last1=Shifman |first1=M. |last2=Vainshtein |first2=A. |last3=Zakharov |first3=V. |year=1980 |journal=Nuclear Physics&nbsp;B |volume=166 |issue=3 |pages=493–506 |title=Can confinement ensure natural CP invariance of strong interactions? |doi=10.1016/0550-3213(80)90209-6 |bibcode=1980NuPhB.166..493S}}</ref>}} and {{nowrap|DFSZ}} ([[Michael Dine|Dine]]–[[Willy Fischler|Fischler]]–{{abbr|Srednicki|Mark Srednicki}}–{{nowrap|{{abbr|Zhitnitsky|Ariel R. Zhitnitsky}}).<ref>{{cite journal |last1=Dine |first1=M. |last2=Fischler |first2=W. |last3=Srednicki |first3=M. |year=1981 |journal=Physics Letters B |volume=104 |issue=3 |pages=199–202 |title=A simple solution to the strong CP problem with a harmless axion |doi=10.1016/0370-2693(81)90590-6 |bibcode=1981PhLB..104..199D}}</ref><ref>{{cite journal |last1=Zhitnitsky |first1=A. |year=1980 |journal=Soviet Journal of Nuclear Physics |language=en |volume=31 |page=260 |title=On possible suppression of the axion–hadron interactions |url= https://www.inp.nsk.su/images/preprint/1979_081.pdf}}</ref>}}

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.<ref name="auto"/><ref name="A cosmological bound on the invisib"/><ref name="The not-so-harmless axion"/>

=== Maxwell's equations with axion modifications ===
[[Pierre Sikivie]] computed how [[Maxwell's equations]] are modified in the presence of an axion in 1983.<ref>{{cite journal |last1=Sikivie |first1=P. |title=Experimental Tests of the 'Invisible' Axion |date=17 October 1983 |journal=Physical Review Letters |volume=51 |issue=16 |page=1413 |doi=10.1103/physrevlett.51.1415 |bibcode=1983PhRvL..51.1415S}}</ref> 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.<ref>{{cite web |title=OSQAR |url=http://home.cern/about/experiments/osqar |publisher=CERN |date=2017 |access-date=3 October 2017}}</ref> As of the early 2020s, there are dozens of proposed or ongoing experiments searching for axion dark matter.<ref>{{cite arXiv |title=Axion Dark Matter |date=2022 |eprint=2203.14923 |last1=Adams |first1=C. B. |last2=Aggarwal |first2=N. |last3=Agrawal |first3=A. |last4=Balafendiev |first4=R. |last5=Bartram |first5=C. |last6=Baryakhtar |first6=M. |last7=Bekker |first7=H. |last8=Belov |first8=P. |last9=Berggren |first9=K. K. |last10=Berlin |first10=A. |last11=Boutan |first11=C. |last12=Bowring |first12=D. |last13=Budker |first13=D. |last14=Caldwell |first14=A. |last15=Carenza |first15=P. |last16=Carosi |first16=G. |last17=Cervantes |first17=R. |last18=Chakrabarty |first18=S. S. |last19=Chaudhuri |first19=S. |last20=Chen |first20=T. Y. |last21=Cheong |first21=S. |last22=Chou |first22=A. |last23=Co |first23=R. T. |last24=Conrad |first24=J. |last25=Croon |first25=D. |last26=D'Agnolo |first26=R. T. |last27=Demarteau |first27=M. |last28=DePorzio |first28=N. |last29=Descalle |first29=M. |last30=Desch |first30=K. |class=hep-ex |display-authors=1 }}</ref>

Treating the reduced Planck constant <math>\hbar</math>, speed of light <math>c</math>, and permittivity of free space <math>\varepsilon_0</math> 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
| <math> \nabla \cdot \mathbf{E} = \rho - g_{a\gamma\gamma} \mathbf{B} \cdot \nabla a </math>
|-
! scope="row" | Gauss's law for magnetism
| <math> \nabla \cdot \mathbf{B}  = 0 </math>
|-
! scope="row" | Faraday's law
| <math> \nabla \times \mathbf{E} = - \dot{ \mathbf{B} } </math>
|-
! scope="row" | Ampère–Maxwell law
| <math>\quad \nabla \times \mathbf{B} = \dot{\mathbf{E}} + \mathbf{J} + g_{a\gamma\gamma} \left( \dot{a} \mathbf{B} - \mathbf{E} \times \nabla a \right) \quad</math>
|-
! scope="row" | Axion field's equation of motion
| <math> \ddot{a} - \nabla^2 a + m_a^2 a = -g_{a\gamma\gamma} \mathbf{E} \cdot \mathbf{B} </math>
|}

Above, a dot above a variable denotes its time derivative; the dot spaced between variables is the [[vector dot product]]; the factor <math> g_{a\gamma\gamma} </math> 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 monopole]]s.<ref>{{cite journal |last=Visinelli |first=L. |year=2013 |title=Axion-electromagnetic waves |journal=Modern Physics Letters&nbsp;A |volume=28 |number=35 |page=1350162 |doi=10.1142/S0217732313501629 |arxiv=1401.0709 |bibcode=2013MPLA...2850162V |s2cid=119221244 }}</ref> However, these alternative formulations are less theoretically motivated, and in many cases cannot even be derived from an [[action (physics)|action]].

=== Analogous effect for topological insulators ===
A term analogous to the one that would be added to [[Maxwell's equations]] to account for axions<ref>{{cite journal |last=Wilczek |first=Frank |title=Two applications of axion electrodynamics |journal=Physical Review Letters |date=4 May 1987 |volume=58 |issue=18 |pages=1799–1802 |doi=10.1103/PhysRevLett.58.1799 |pmid=10034541 |bibcode=1987PhRvL..58.1799W}}</ref> also appears in recent (2008) theoretical models for [[topological insulators]] giving an effective axion description of the electrodynamics of these materials.<ref>{{cite journal |last1=Qi |first1=Xiao-Liang |last2=Hughes |first2=Taylor L. |last3=Zhang |first3=Shou-Cheng |title=Topological field theory of time-reversal invariant insulators |date=24 November 2008 |journal=Physical Review&nbsp;B |volume=78 |issue=19 |article-number=195424 |doi=10.1103/PhysRevB.78.195424 |bibcode=2008PhRvB..78s5424Q |arxiv=0802.3537|s2cid=117659977 }}</ref>

This term leads to several interesting predicted properties including a quantized [[magnetoelectric effect]].<ref name="Franz 36">{{cite journal |doi=10.1103/Physics.1.36 |volume=1 |article-number=36 |last=Franz |first=Marcel |title=High-energy physics in a new guise |journal=Physics |date=24 November 2008 |bibcode=2008PhyOJ...1...36F |doi-access=free}}</ref> Evidence for this effect has been given in [[N. Peter Armitage|THz spectroscopy experiments]] performed at the [[Johns Hopkins University]] on quantum regime thin film topological insulators developed at [[Rutgers University]].<ref>{{cite journal |last1=Wu |first1=Liang |last2=Salehi |first2=M. |last3=Koirala |first3=N. |last4=Moon |first4=J. |last5=Oh |first5=S. |last6=Armitage |first6=N. P. |date=2 December 2016 |title=Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator |journal=Science |volume=354 |issue=6316 |pages=1124–1127 |arxiv=1603.04317 |bibcode=2016Sci...354.1124W |doi=10.1126/science.aaf5541 |pmid=27934759 |s2cid=25311729 }}</ref>

In 2019, a team at the [[Max Planck Institute for Chemical Physics of Solids]] published their detection of an [[Magnetic topological insulator#Axion coupling|axion insulator]] phase of a [[Weyl semimetal]] material.<ref>
{{cite journal
 |first1=J.    |last1=Gooth      |first2=B.   |last2=Bradlyn
 |first3=S.    |last3=Honnali    |first4=C.   |last4=Schindler
 |first5=N.    |last5=Kumar      |first6=J.   |last6=Noky
 |first7=Y.    |last7=Qi         |first8=C.   |last8=Shekhar
 |first9=Y.    |last9=Sun        |first10=Z.  |last10=Wang
 |first11=B. A.|last11=Bernevig  |first12=C.  |last12=Felser 
 |display-authors=6
 |date=7 October 2019
 |title=Axionic charge-density wave in the Weyl semimetal (TaSe<sub>4</sub>)<sub>2</sub>I
 |journal=Nature
 |volume=575  |issue=7782   |pages=315–319
 |doi=10.1038/s41586-019-1630-4  |pmid=31590178    |arxiv=1906.04510
 |bibcode=2019Natur.575..315G    |s2cid=184487056
}}</ref> 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.<ref>
{{cite web
 |last=Fore
 |first=Meredith
 |date=22 November 2019
 |title=Physicists have finally seen traces of a long-sought particle. Here's why that's a Big Deal.
 |website=Live Science
 |publisher=Future US, Inc.
 |url=https://www.livescience.com/axion-found-in-weyl-semimetal.html
 |access-date=25 February 2020
}}</ref>
[[File:AxionPhoton.pdf|thumb|upright=1.8|Constraints on the axion's coupling to the photon<ref name=":0">{{Cite web |last=O'Hare |first=Ciaran |title=Data, plots and code for constraints on axions, axion-like particles, and dark photons |url=https://cajohare.github.io/AxionLimits/ |access-date=2025-06-13 |website=AxionLimits}}</ref>]]
[[File:AxionElectron.pdf|thumb|upright=1.8|Constraints on the axion's dimensionless coupling to electrons<ref name=":0" />]]

== Experiments ==
Despite not having been found to date, the axion has been well studied for over 40&nbsp;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.

=== Direct conversion in a magnetic field ===
[[File:A-conceptual-schematic-of-the-ADMX-haloscope-A-resonant-cavity-is-placed-in-a-strong.png|left|thumb|upright=0.8|Haloscope concept of a resonance cavity]]
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]] is a [[Haloscope (physics)|haloscope]] that uses a strong magnetic field to detect the possible weak conversion of axions to [[microwave]]s.<ref>{{cite press release |last1=Chu |first1=Jennifer |title=Team simulates a magnetar to seek dark matter particle |url=https://phys.org/news/2016-10-team-simulates-magnetar-dark-particle.html |work=Phys.org |publisher=Massachusetts Institute of Technology }}</ref> ADMX searches the galactic [[dark matter halo]]<ref>
{{cite journal
 |last1=Duffy   |first1=L. D.   |last2=Sikivie  |first2=P.
 |last3=Tanner  |first3=D. B.   |last4=Bradley  |first4=R. F.
 |last5=Hagmann |first5=C.      |last6=Kinion   |first6=D.
 |last7=Rosenberg |first7=L. J. |last8=van&nbsp;Bibber |first8=K.
 |last9=Yu      |first9=D. B.   |last10=Bradley |first10=R. F.
 |display-authors=6
 |year=2006
 |title=High resolution search for dark-matter axions
 |journal=Physical Review D
 |volume=74  |issue=1  |article-number=12006
 |arxiv=astro-ph/0603108  |doi=10.1103/PhysRevD.74.012006
 |bibcode=2006PhRvD..74a2006D  |s2cid=35236485
}}
</ref> for axions resonant with a cold microwave cavity. ADMX has excluded optimistic axion models in the range {{val|1.9|–|3.53|u=μeV/''c''<sup>2</sup>}}.<ref>
{{cite journal |last1=Asztalos |first1=S. J. |last2=Carosi |first2=G. |last3=Hagmann |first3=C. |last4=Kinion |first4=D. |last5=van&nbsp;Bibber |first5=K. |last6=Hoskins |first6=J. |last7=Hwang |first7=J. |last8=Sikivie |first8=P. |last9=Tanner |first9=D. B. |last10=Hwang |first10=J. |last11=Sikivie |first11=P. |last12=Tanner |first12=D. B. |last13=Bradley |first13=R. |last14=Clarke |first14=J. |display-authors=6 |year=2010 |title=SQUID-based microwave cavity search for dark-matter axions |url=https://digital.library.unt.edu/ark:/67531/metadc1012348/m2/1/high_res_d/986065.pdf |journal=Physical Review Letters |volume=104 |issue=4 |article-number=41301 |arxiv=0910.5914 |bibcode=2010PhRvL.104d1301A |doi=10.1103/PhysRevLett.104.041301 |pmid=20366699 |s2cid=35365606}}
</ref><ref>
{{cite web |title=ADMX {{pipe}} Axion Dark Matter eXperiment |url=http://www.phys.washington.edu/groups/admx/home.html |access-date=2014-05-10 |website=phys.washington.edu |publisher=University of Washington |place=Seattle, Washington |department=Physics |df=dmy-all}}
</ref><ref>
{{cite web |date=2006-03-04 |title=Phase&nbsp;1 results |url=http://www.phys.washington.edu/groups/admx/results.html |website=phys.washington.edu |publisher=University of Washington |place=Seattle, Washington |df=dmy-all |department=Physics}}</ref> From 2013 to 2018 a series of upgrades<ref>{{cite tech report | doi=10.2172/1508642 | title=The "Gen 2" Axion Dark Matter Experiment (ADMX) | year=2019 | last1=Tanner | first1=David B. | last2=Sullivan | first2=Neil | osti=1508642 | s2cid=204183272 }}</ref> were done and it is taking new data, including at {{val|4.9|–|6.2|u=μeV/''c''<sup>2</sup>}}. In December 2021 it excluded the range {{val|3.3|–|4.2|u=μeV/''c''<sup>2</sup>}} for the KSVZ model.<ref>{{cite journal |display-authors=6 |last1=Bartram |first1=C. |last2=Braine |first2=T. |last3=Burns |first3=E. |last4=Cervantes |first4=R. |last5=Crisosto |first5=N. |last6=Du |first6=N. |last7=Korandla |first7=H. |last8=Leum |first8=G. |last9=Mohapatra |first9=P. |last10=Nitta |first10=T. |last11=Rosenberg |first11=L. J |last12=Rybka |first12=G. |last13=Yang |first13=J. |last14=Clarke |first14=John |last15=Siddiqi |first15=I. |last16=Agrawal |first16=A. |last17=Dixit |first17=A. V. |last18=Awida |first18=M. H. |last19=Chou |first19=A. S. |last20=Hollister |first20=M. |last21=Knirck |first21=S. |last22=Sonnenschein |first22=A. |last23=Wester |first23=W. |last24=Gleason |first24=J. R. |last25=Hipp |first25=A. T. |last26=Jois |first26=S. |last27=Sikivie |first27=P. |last28=Sullivan |first28=N. S. |last29=Tanner |first29=D. B. |last30=Lentz |first30=E. |last31=Khatiwada |first31=R. |last32=Carosi |first32=G. |last33=Robertson |first33=N. |last34=Woollett |first34=N. |last35=Duffy |first35=L. D. |last36=Boutan |first36=C. |last37=Jones |first37=M. |last38=LaRoque |first38=B. H. |last39=Oblath |first39=N. S. |last40=Taubman |first40=M. S. |last41=Daw |first41=E. J. |last42=Perry |first42=M. G. |last43=Buckley |first43=J. H. |last44=Gaikwad |first44=C. |last45=Hoffman |first45=J. |last46=Murch |first46=K. W. |last47=Goryachev |first47=M. |last48=McAllister |first48=B. T. |last49=Quiskamp |first49=A. |last50=Thomson |first50=C. |last51=Tobar |first51=M. E. |title=Search for Invisible Axion Dark Matter in the 3.3 – 4.2&nbsp;μeV Mass Range |journal=Physical Review Letters |date=23 December 2021 |volume=127 |issue=26 |article-number=261803 |doi=10.1103/PhysRevLett.127.261803 |pmid=35029490 |bibcode=2021PhRvL.127z1803B |s2cid=238634307 |doi-access=free|arxiv=2110.06096 }}</ref><ref>{{cite journal |last1=Stephens |first1=Marric |title=Tightening the Net on Two Kinds of Dark Matter |journal=Physics |date=23 December 2021 |volume=14 |article-number=s164 |doi=10.1103/Physics.14.s164 |bibcode=2021PhyOJ..14.s164S |s2cid=247277808 |doi-access=free}}</ref>

Other experiments of this type include DMRadio,<ref>{{cite journal |last1=Silva-Feaver |first1=Maximiliano |last2=Chaudhuri |first2=Saptarshi |last3=Cho |first3=Hsaio-Mei |last4=Dawson |first4=Carl |last5=Graham |first5=Peter |last6=Irwin |first6=Kent |last7=Kuenstner |first7=Stephen |last8=Li |first8=Dale |last9=Mardon |first9=Jeremy |last10=Moseley |first10=Harvey |last11=Mule |first11=Richard |last12=Phipps |first12=Arran |last13=Rajendran |first13=Surjeet |last14=Steffen |first14=Zach |last15=Young |first15=Betty |title=Design Overview of DM Radio Pathfinder Experiment |journal=IEEE Transactions on Applied Superconductivity |date=June 2017 |volume=27 |issue=4 |pages=1–4 |doi=10.1109/TASC.2016.2631425 |arxiv=1610.09344 |bibcode=2017ITAS...2731425S |s2cid=29416513 }}</ref> HAYSTAC,<ref name=HAYSTAC>{{cite journal |display-authors=6 |last1=Brubaker |first1=B. M. |last2=Zhong |first2=L. |last3=Gurevich |first3=Y. V. |last4=Cahn |first4=S. B. |last5=Lamoreaux |first5=S. K. |last6=Simanovskaia |first6=M. |last7=Root |first7=J. R. |last8=Lewis |first8=S. M. |last9=Al Kenany |first9=S. |last10=Backes |first10=K. M. |last11=Urdinaran |first11=I. |last12=Rapidis |first12=N. M. |last13=Shokair |first13=T. M. |last14=van Bibber |first14=K. A. |last15=Palken |first15=D. A. |last16=Malnou |first16=M. |last17=Kindel |first17=W. F. |last18=Anil |first18=M. A. |last19=Lehnert |first19=K. W. |last20=Carosi |first20=G. |title=First Results from a Microwave Cavity Axion Search at 24&nbsp;μeV |journal=Physical Review Letters |date=9 February 2017 |volume=118 |issue=6 |article-number=061302 |doi=10.1103/physrevlett.118.061302 |s2cid=6509874 |pmid=28234529  |arxiv=1610.02580 |bibcode=2017PhRvL.118f1302B }}
</ref> CULTASK,<ref name=CULTASK>{{cite journal |last1=Petrakou |first1=Eleni |title=Haloscope searches for dark matter axions at the Center for Axion and Precision Physics Research |journal=EPJ Web of Conferences |date=2017 |volume=164 |page=01012 |doi=10.1051/epjconf/201716401012 |s2cid=119381143 |arxiv=1702.03664 |bibcode=2017EPJWC.16401012P
 |url=https://inspirehep.net/record/1513138 }}
</ref> and ORGAN.<ref name=ORGAN>{{cite journal |last1=McAllister |first1=Ben T. |last2=Flower |first2=Graeme |last3=Ivanov |first3=Eugene N. |last4=Goryachev |first4=Maxim |last5=Bourhill |first5=Jeremy |last6=Tobar |first6=Michael E. |title=The ORGAN experiment: An axion haloscope above 15 GHz |journal=Physics of the Dark Universe |date=December 2017 |volume=18 |pages=67–72 |doi=10.1016/j.dark.2017.09.010 |bibcode=2017PDU....18...67M |arxiv=1706.00209 |s2cid=118887710 }}
</ref> HAYSTAC completed the first scanning run of a [[Haloscope (physics)|haloscope]] above 20&nbsp;μeV/''c''<sup>2</sup> in the late 2010s.<ref name=HAYSTAC/>
[[File:Conceptual-arrangement-of-an-enhanced-axion-helioscope-with-x-ray-focalization-Solar.png|thumb|upright=1.8|Principle of operation of IAXO/BabyIAXO helioscope]]
Another type of direct conversion experiments are the [[Helioscope|helioscopes]] where the magnet is pointed at the Sun. Axions produced in the Sun would have an energy range of 1–10&nbsp;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|CERN Axion Solar Telescope (CAST)]] which reached the axion–photon coupling limit of {{val|5.8e-11|ul=GeV|s=<sup>&minus;1</sup>}} at 95% CL (for <math>m_a</math> ≲ 0.02  eV) in 2024.<ref>{{cite journal |last1=CAST Collaboration |last2=Altenmüller |first2=K. |last3=Anastassopoulos |first3=V. |last4=Arguedas-Cuendis |first4=S. |last5=Aune |first5=S. |last6=Baier |first6=J. |last7=Barth |first7=K. |last8=Bräuninger |first8=H. |last9=Cantatore |first9=G. |last10=Caspers |first10=F. |last11=Castel |first11=J. F. |last12=Çetin |first12=S. A. |last13=Christensen |first13=F. |last14=Cogollos |first14=C. |last15=Dafni |first15=T. |date=2024-11-27 |title=New Upper Limit on the Axion-Photon Coupling with an Extended CAST Run with a Xe-Based Micromegas Detector |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.221005 |journal=Physical Review Letters |volume=133 |issue=22 |article-number=221005 |doi=10.1103/PhysRevLett.133.221005|pmid=39672143 |arxiv=2406.16840 |bibcode=2024PhRvL.133v1005A }}</ref> The next-generation helioscope is the [[International Axion Observatory|International AXion Observatory (IAXO)]], which is currently in development.

=== Polarized light in a magnetic field ===
The Italian [[PVLAS]] experiment searches for polarization changes of [[polarized light|light]] propagating in a magnetic field. The concept was first put forward in 1986 by [[Luciano Maiani]], Roberto Petronzio and [[Emilio Zavattini]].<ref>
{{cite journal
 |last1=Maiani    |first1=L. |author-link1=Luciano Maiani
 |last2=Petronzio |first2=R.
 |last3=Zavattini |first3=E. |author-link3=Emilio Zavattini
 |date=7 August 1986
 |title=Effects of nearly massless, spin-zero particles on light propagation in a magnetic field
 |journal=Physics Letters B
 |volume=175 |issue=3 |pages=359–363
 |doi=10.1016/0370-2693(86)90869-5 |bibcode=1986PhLB..175..359M
 |id=CERN-TH.4411/86
 |url=http://cdsweb.cern.ch/record/167556/files/198606014.pdf
}}
</ref> A rotation claim<ref>
{{cite magazine
 |first1=Steve |last1=Reucroft
 |first2=John |last2=Swain
 |date=2006-10-05
 |title=Axion signature may be QED
 |magazine=CERN Courier
 |url=http://cerncourier.com/main/article/46/8/10
 |archive-url=https://web.archive.org/web/20080820154706/http://cerncourier.com/main/article/46/8/10
 |archive-date=2008-08-20
 |df=dmy-all
}}
</ref> in 2006 was excluded by an upgraded setup.<ref name="zavattini_1">
{{cite journal
 |last1=Zavattini
 |first1=E.
 |collaboration=PVLAS Collaboration
 |display-authors=etal
 |year=2006
 |title=Experimental Observation of Optical Rotation Generated in Vacuum by a Magnetic Field
 |journal=Physical Review Letters
 |volume=96
 |issue=11
 |article-number=110406
 |doi=10.1103/PhysRevLett.96.110406
 |pmid=16605804
 |arxiv=hep-ex/0507107
 |bibcode=2006PhRvL..96k0406Z
}}</ref> An optimized search began in 2014.

=== Light shining through walls ===
Another technique is so called "light shining through walls",<ref>
{{cite conference
 |last=Ringwald |first=A.
 |date=16–21 October 2001
 |title=Fundamental Physics at an X-Ray Free Electron Laser
 |book-title=Electromagnetic Probes of Fundamental Physics – Proceedings of the Workshop
 |pages=63–74
 |conference=Workshop on Electromagnetic Probes of Fundamental Physics
 |location=[[Erice]], Italy
 |arxiv=hep-ph/0112254   |doi=10.1142/9789812704214_0007
 |isbn=978-981-238-566-6
}}</ref> 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.<ref name="rizzo_1">
{{cite journal
 |last1=Robilliard |first1=C.
 |last2=Battesti   |first2=R.
 |last3=Fouche     |first3=M.
 |last4=Mauchain   |first4=J.
 |last5=Sautivet   |first5=A.-M.
 |last6=Amiranoff  |first6=F.
 |last7=Rizzo      |first7=C.
 |year=2007
 |title=No 'light shining through a wall': Results from a photoregeneration experiment
 |journal=Physical Review Letters
 |volume=99  |issue=19  |article-number=190403
 |arxiv=0707.1296  |doi=10.1103/PhysRevLett.99.190403  |pmid=18233050
 |bibcode=2007PhRvL..99s0403R  |s2cid=23159010
}}
</ref> GammeV saw no events, reported in a 2008 Physics Review Letter. ALPS I conducted similar runs,<ref>
{{cite journal
 |last1=Ehret     |first1=Klaus    |last2=Frede      |first2=Maik
 |last3=Ghazaryan |first3=Samvel  |last4=Hildebrandt |first4=Matthias
 |last5=Knabbe    |first5=Ernst-Axel |last6=Kracht   |first6=Dietmar
 |last7=Lindner   |first7=Axel     |last8=List       |first8=Jenny
 |last9=Meier     |first9=Tobias   |last10=Meyer     |first10=Niels
 |last11=Notz     |first11=Dieter  |last12=Redondo   |first12=Javier
 |last13=Ringwald |first13=Andreas |last14=Wiedemann |first14=Günter
 |last15=Willke   |first15=Benno
 |display-authors=6
 |title=New ALPS results on hidden-sector lightweights
 |date=May 2010
 |journal= Physics Letters B
 |volume=689 |issue=4–5 |pages=149–155
 |doi=10.1016/j.physletb.2010.04.066
 |bibcode=2010PhLB..689..149E  |arxiv=1004.1313  |s2cid=58898031
 |url=http://pubman.mpdl.mpg.de/pubman/faces/viewItemOverviewPage.jsp?itemId=escidoc:417635
}}</ref> setting new constraints in 2010; ALPS&nbsp;II began collecting data in May 2023.<ref>{{cite journal |last1=Diaz Ortiz |first1=M. |last2=Gleason |first2=J. |last3=Grote |first3=H. |last4=Hallal |first4=A. |last5=Hartman |first5=M.T. |last6=Hollis |first6=H. |last7=Isleif |first7=K.-S. |last8=James |first8=A. |last9=Karan |first9=K. |last10=Kozlowski |first10=T. |last11=Lindner |first11=A. |last12=Messineo |first12=G. |last13=Mueller |first13=G. |last14=Põld |first14=J.H. |last15=Smith |first15=R.C.G. |last16=Spector |first16=A.D. |last17=Tanner |first17=D.B. |last18=Wei |first18=L.-W. |last19=Willke |first19=B. |title=Design of the ALPS II optical system |journal=Physics of the Dark Universe |date=March 2022 |volume=35 |article-number=100968 |doi=10.1016/j.dark.2022.100968 |bibcode=2022PDU....3500968D |s2cid=222067049 |doi-access=free |arxiv=2009.14294 }}</ref><ref>{{cite web |date=2023-05-23 |title='Light shining through a wall' experiment ALPS starts searching for dark matter |url=https://www.desy.de/news/news_search/index_eng.html?openDirectAnchor=2758 |access-date=2024-09-25 |website=DESY |language=en}}</ref> OSQAR found no signal, limiting coupling,<ref>
{{cite journal
 |last1=Pugnat     |first1=P.    |last2=Ballou     |first2=R.
 |last3=Schott     |first3=M.    |last4=Husek      |first4=T.
 |last5=Sulc       |first5=M.    |last6=Deferne    |first6=G.
 |last7=Duvillaret |first7=L.    |last8=Finger     |first8=M.
 |last9=Finger     |first9=M.    |last10=Flekova   |first10=L.
 |last11=Hosek     |first11=J.   |last12=Jary      |first12=V.
 |last13=Jost      |first13=R.   |last14=Kral      |first14=M.
 |last15=Kunc      |first15=S.   |last16=MacUchova |first16=K.
 |last17=Meissner  |first17=K. A.|last18=Morville  |first18=J.
 |last19=Romanini  |first19=D.   |last20=Siemko    |first20=A.
 |last21=Slunecka  |first21=M.   |last22=Vitrant   |first22=G.
 |last23=Zicha     |first23=J.
 |display-authors=6
 |date=August 2014 
 |title=Search for weakly interacting sub-eV particles with the OSQAR laser-based experiment: Results and perspectives
 |journal=The European Physical Journal C
 |volume=74 |issue=8 |page=3027
 |doi=10.1140/epjc/s10052-014-3027-8 |bibcode=2014EPJC...74.3027P
 |arxiv=1306.0443|s2cid=29889038 
}}</ref> and will continue.

=== Astrophysical axion searches ===
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 ray|very-high-energy gamma rays]]).<ref>
{{cite journal
 |last1=De Angelis |first1=A.
 |last2=Mansutti   |first2=O.
 |last3=Roncadelli |first3=M.
 |year=2007
 |title=Evidence for a new light spin-zero boson from cosmological gamma-ray propagation?
 |journal=Physical Review D
 |volume=76 |issue=12 |article-number=121301
 |bibcode=2007PhRvD..76l1301D  |s2cid=119152884
 |doi=10.1103/PhysRevD.76.121301 |arxiv=0707.4312
}}
</ref><ref>
{{cite journal
 |last1=De Angelis  |first1=A.
 |last2=Mansutti    |first2=O.
 |last3=Persic      |first3=M.
 |last4=Roncadelli  |first4=M.
 |year=2009
 |title=Photon propagation and the very high energy gamma-ray spectra of blazars: How transparent is the Universe?
 |journal=Monthly Notices of the Royal Astronomical Society: Letters
 |volume=394  |issue=1  |pages=L21–L25
 |doi=10.1111/j.1745-3933.2008.00602.x  |doi-access=free
 |arxiv=0807.4246
 |bibcode=2009MNRAS.394L..21D  |s2cid=18184567
}}
</ref> It has also been demonstrated that, in the large magnetic fields threading the atmospheres of compact astrophysical objects (e.g., [[magnetar]]s), 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.<ref>
{{cite journal
 |last1=Chelouche |first1=Doron
 |last2=Rabadan   |first2=Raul
 |last3=Pavlov    |first3=Sergey S.
 |last4 =Castejon |first4=Francisco
 |year=2009
 |title=Spectral signatures of photon–particle oscillations from celestial objects
 |journal=The Astrophysical Journal
 |series=Supplement Series
 |volume=180  |issue=1  |pages=1–29
 |arxiv=0806.0411  |doi=10.1088/0067-0049/180/1/1  |s2cid=5018245
 |bibcode=2009ApJS..180....1C
}}
</ref> 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.<ref>
{{cite journal
 |last1=Chelouche |first1=Doron
 |last2=Guendelman |first2=Eduardo I.
 |year=2009
 |title=Cosmic analogs of the Stern–Gerlach experiment and the detection of light bosons
 |journal=The Astrophysical Journal
 |volume=699  |issue=1  |pages=L5–L8
 |doi=10.1088/0004-637X/699/1/L5  |arxiv=0810.3002
 |bibcode=2009ApJ...699L...5C  |s2cid=11868951
}}
</ref> The [[International Axion Observatory]] (IAXO) is a proposed fourth generation [[helioscope]].<ref>
{{cite web
 |title=The International Axion Observatory
 |publisher=[[CERN]]
 |url=http://iaxo.web.cern.ch/content/home-international-axion-observatory
 |access-date=19 March 2016
}}
</ref>

Axions can resonantly convert into photons in the [[magnetosphere]]s of [[neutron star]]s.<ref>
{{cite journal
 |last1=Pshirkov |first1=Maxim S.
 |last2=Popov    |first2=Sergei B.
 |year=2009
 |title=Conversion of Dark matter axions to photons in magnetospheres of neutron stars
 |journal=Journal of Experimental and Theoretical Physics
 |volume= 108 |issue=3 |pages=384–388
 |doi=10.1134/S1063776109030030
 |arxiv=0711.1264
 |bibcode= 2009JETP..108..384P
 |s2cid=119269835
}}
</ref> 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 range {{val|5|–|11|u=μeV/''c''<sup>2</sup>}}, by re-analyzing existing data from the [[Green Bank Telescope]] and the [[Effelsberg 100-m Radio Telescope|Effelsberg 100&nbsp;m Radio Telescope]].<ref>
{{cite journal
 |last1=Foster     |first1=Joshua W.
 |last2=Kahn       |first2=Yonatan
 |last3=Macias     |first3=Oscar
 |last4=Sun        |first4=Zhiquan
 |last5=Eatough    |first5=Ralph P.
 |last6=Kondratiev |first6=Vladislav I.
 |last7=Peters     |first7=Wendy M.
 |last8=Weniger    |first8=Christoph
 |last9=Safdi      |first9=Benjamin R.
 |year=2020
 |title=Green Bank and Effelsberg Radio Telescope Searches for Axion Dark Matter Conversion in Neutron Star Magnetospheres
 |journal=Physical Review Letters
 |volume=125 |number=17 |article-number= 171301
 |doi=10.1103/PhysRevLett.125.171301
 |pmid=33156637
 |arxiv=2004.00011
 |bibcode= 2020PhRvL.125q1301F
 |s2cid=214743261
}}
</ref> A novel, alternative strategy consists of detecting the transient signal from the encounter between a neutron star and an axion minicluster in the [[Milky Way]].<ref>
{{cite journal
 |last1=Edwards   |first1=Thomas D. P. 
 |last2=Kavanagh  |first2=Bradley J.
 |last3=Visinelli |first3=Luca
 |last4=Weniger   |first4=Christoph
 |year=2021
 |title=Transient Radio Signatures from Neutron Star Encounters with QCD Axion Miniclusters
 |journal=Physical Review Letters
 |volume=127 |number=13 |article-number= 131103
 |doi=10.1103/PhysRevLett.127.131103
 |pmid=34623827 
 |arxiv=2011.05378
 |bibcode=2021PhRvL.127m1103E 
 |s2cid=226300099 
}}
</ref>

Axions can be produced in the Sun's core when X-rays scatter in strong electric fields. The [[CERN Axion Solar Telescope|CAST]] solar telescope is underway, and has set limits on coupling to photons and electrons. Axions may also 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 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 of {{val|0.079|u=eV/c2}}.<ref>
{{cite journal
 |last1=Berenji |first1=B. 
 |last2=Gaskins |first2=J.
 |last3=Meyer   |first3=M.
 |year=2016
 |title=Constraints on axions and axionlike particles from Fermi Large Area Telescope observations of neutron stars
 |journal=Physical Review D
 |volume=93  |issue=14  |article-number=045019
 |arxiv=1602.00091  |doi=10.1103/PhysRevD.93.045019
 |bibcode=2016PhRvD..93d5019B  |s2cid=118723146
}}
</ref> In 2021 it has been also suggested<ref>{{cite journal |last1=Buschmann |first1=Malte |last2=Co |first2=Raymond T. |last3=Dessert |first3=Christopher |last4=Safdi |first4=Benjamin R. |title=Axion Emission Can Explain a New Hard X-Ray Excess from Nearby Isolated Neutron Stars |journal=Physical Review Letters |date=12 January 2021 |volume=126 |issue=2 |article-number=021102 |doi=10.1103/PhysRevLett.126.021102 |pmid=33512228 |arxiv=1910.04164 |bibcode=2021PhRvL.126b1102B |s2cid=231764983 }}</ref><ref>{{cite web |last=O'Callaghan |first=Jonathan |date=2021-10-19 |title=A Hint of Dark Matter Sends Physicists Looking to the Skies |url=https://www.quantamagazine.org/a-hint-of-dark-matter-sends-physicists-looking-to-the-skies-20211019/ |access-date=2021-10-25 |website=Quanta Magazine |language=en }}</ref> that a reported<ref>{{cite journal |last1=Dessert |first1=Christopher |last2=Foster |first2=Joshua W. |last3=Safdi |first3=Benjamin R. |title=Hard X-Ray Excess from the Magnificent Seven Neutron Stars |journal=The Astrophysical Journal |date=November 2020 |volume=904 |issue=1 |page=42 |doi=10.3847/1538-4357/abb4ea |arxiv=1910.02956 |bibcode=2020ApJ...904...42D |s2cid=203902766 |doi-access=free }}</ref> excess of hard X-ray emission from a system of neutron stars known as the [[The Magnificent Seven (neutron stars)|magnificent seven]] could be explained as axion emission.

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 an [[Magnetic resonance imaging|MRI]] 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 {{val|4.1|e=-10|u=eV/c2}} to {{val|8.27|e=-9|u=eV/c2}}.<ref>{{cite journal |last1=Salemi |first1=Chiara P. |last2=Foster |first2=Joshua W. |last3=Ouellet |first3=Jonathan L. |last4=Gavin |first4=Andrew |last5=Pappas |first5=Kaliroë M. W. |last6=Cheng |first6=Sabrina |last7=Richardson |first7=Kate A. |last8=Henning |first8=Reyco |last9=Kahn |first9=Yonatan |last10=Nguyen |first10=Rachel |last11=Rodd |first11=Nicholas L. |last12=Safdi |first12=Benjamin R. |last13=Winslow |first13=Lindley |date=2021-08-17 |title=Search for Low-Mass Axion Dark Matter with ABRACADABRA-10 cm |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.081801 |journal=Physical Review Letters |volume=127 |issue=8 |article-number=081801 |doi=10.1103/PhysRevLett.127.081801|pmid=34477408 |arxiv=2102.06722 |bibcode=2021PhRvL.127h1801S }}</ref>

In 2022 the polarized light [[Event Horizon Telescope#Messier 87*|measurements]] of [[Messier 87|Messier 87*]] by the [[Event 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 approximate {{val|e=-21|u=eV/c2}} – {{val|e=-20|u=eV/c2}} range of mass values.<ref>{{cite journal |last1=Chen |first1=Yifan |last2=Liu |first2=Yuxin |last3=Lu |first3=Ru-Sen |last4=Mizuno |first4=Yosuke |last5=Shu |first5=Jing |last6=Xue |first6=Xiao |last7=Yuan |first7=Qiang |last8=Zhao |first8=Yue |title=Stringent axion constraints with Event Horizon Telescope polarimetric measurements of M87⋆ |journal=Nature Astronomy |date=17 March 2022 |volume=6 |issue=5 |pages=592–598 |doi=10.1038/s41550-022-01620-3 |arxiv=2105.04572 |bibcode=2022NatAs...6..592C |s2cid=247188135 }}</ref><ref>{{cite news |last1=Kruesi |first1=Liz |title=How light from black holes is narrowing the search for axions |url=https://www.sciencenews.org/article/black-hole-light-axion-particle-search-event-horizon |work=Science News |date=17 March 2022 }}</ref>

=== Searches for resonance effects ===
Resonance effects may be evident in [[Josephson junction]]s<ref>
{{cite journal
 |last=Beck |first=Christian
 |date=2 December 2013
 |title=Possible Resonance Effect of Axionic Dark Matter in Josephson Junctions
 |journal=Physical Review Letters
 |volume=111  |issue=23  |page=1801
 |article-number=231801
 |doi=10.1103/PhysRevLett.111.231801  |pmid=24476255  |s2cid=23845250
 |arxiv=1309.3790  |bibcode=2013PhRvL.111w1801B
}}
</ref> from a supposed high flux of axions from the galactic halo with mass of {{val|110|u=μeV/''c''<sup>2</sup>}} and density {{val|0.05|u=(GeV/''c''<sup>2</sup>)/cm<sup>3</sup>}}<ref>
{{cite magazine
 |last=Moskvitch |first=Katia
 |title=Hints of cold dark matter pop up in 10&nbsp;year-old circuit
 |magazine=[[New Scientist]] Magazine
 |url=https://www.newscientist.com/article/dn24689-hints-of-cold-dark-matter-pop-up-in-10yearold-circuit.html
 |access-date=3 December 2013
}}
</ref> compared to the implied dark matter density {{val|0.3|0.1|u=(GeV/''c''<sup>2</sup>)/cm<sup>3</sup>}}, 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 (physics)|haloscope method]].<ref name=ORGAN/>

=== Dark matter recoil searches ===
Dark matter cryogenic detectors have searched for electron recoils that would indicate axions. [[Cryogenic Dark Matter Search|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.<ref>
{{cite journal
 |first1=E. |last1=Aprile
 |display-authors=etal
 |date=9 September 2014
 |title=First axion results from the XENON100 experiment
 |journal=Physical Review D
 |volume=90 |issue=6 |article-number=062009
 |doi=10.1103/PhysRevD.90.062009 |s2cid=55875111
 |bibcode=2014PhRvD..90f2009A |arxiv=1404.1455
 |url=https://science.purdue.edu/xenon1t/?p=292
}}
</ref>

=== Nuclear spin precession ===
While Schiff's theorem states that a static [[nuclear electric dipole moment]] (EDM) does not produce atomic and molecular EDMs,<ref>{{cite journal |last1=Commins |first1=Eugene D. |last2=Jackson |first2=J. D. |last3=DeMille |first3=David P. |title=The electric dipole moment of the electron: An intuitive explanation for the evasion of Schiff's theorem |journal=American Journal of Physics |date=June 2007 |volume=75 |issue=6 |pages=532–536 |doi=10.1119/1.2710486 |bibcode=2007AmJPh..75..532C }}</ref> the axion induces an oscillating nuclear EDM that oscillates at the [[Larmor precession|Larmor 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.<ref>{{cite journal |last1=Flambaum |first1=V. V. |last2=Tan |first2=H. B. Tran |title=Oscillating nuclear electric dipole moment induced by axion dark matter produces atomic and molecular electric dipole moments and nuclear spin rotation |journal=Physical Review D |date=27 December 2019 |volume=100 |issue=11 |article-number=111301 |doi=10.1103/PhysRevD.100.111301 |arxiv=1904.07609 |s2cid=119303702 |bibcode=2019PhRvD.100k1301F }}</ref>

An experiment using this technique is the Cosmic Axion Spin Precession Experiment (CASPEr).<ref>{{cite journal |last1=Budker |first1=Dmitry |last2=Graham |first2=Peter W. |last3=Ledbetter |first3=Micah |last4=Rajendran |first4=Surjeet |last5=Sushkov |first5=Alexander O. |title=Proposal for a Cosmic Axion Spin Precession Experiment (CASPEr) |journal=Physical Review X |date=19 May 2014 |volume=4 |issue=2 |article-number=021030 |doi=10.1103/PhysRevX.4.021030 |arxiv=1306.6089 |bibcode=2014PhRvX...4b1030B |s2cid=118351193 }}</ref><ref>{{cite journal |display-authors=6 |last1=Garcon |first1=Antoine |last2=Aybas |first2=Deniz |last3=Blanchard |first3=John W |last4=Centers |first4=Gary |last5=Figueroa |first5=Nataniel L |last6=Graham |first6=Peter W |last7=Kimball |first7=Derek F Jackson |last8=Rajendran |first8=Surjeet |last9=Sendra |first9=Marina Gil |last10=Sushkov |first10=Alexander O |last11=Trahms |first11=Lutz |last12=Wang |first12=Tao |last13=Wickenbrock |first13=Arne |last14=Wu |first14=Teng |last15=Budker |first15=Dmitry |title=The cosmic axion spin precession experiment (CASPEr): a dark-matter search with nuclear magnetic resonance |journal=Quantum Science and Technology |date=January 2018 |volume=3 |issue=1 |page=014008 |doi=10.1088/2058-9565/aa9861 |arxiv=1707.05312 |bibcode=2018QS&T....3a4008G |s2cid=51686418 }}</ref><ref>{{cite journal |display-authors=6 |last1=Aybas |first1=Deniz |last2=Adam |first2=Janos |last3=Blumenthal |first3=Emmy |last4=Gramolin |first4=Alexander V. |last5=Johnson |first5=Dorian |last6=Kleyheeg |first6=Annalies |last7=Afach |first7=Samer |last8=Blanchard |first8=John W. |last9=Centers |first9=Gary P. |last10=Garcon |first10=Antoine |last11=Engler |first11=Martin |last12=Figueroa |first12=Nataniel L. |last13=Sendra |first13=Marina Gil |last14=Wickenbrock |first14=Arne |last15=Lawson |first15=Matthew |last16=Wang |first16=Tao |last17=Wu |first17=Teng |last18=Luo |first18=Haosu |last19=Mani |first19=Hamdi |last20=Mauskopf |first20=Philip |last21=Graham |first21=Peter W. |last22=Rajendran |first22=Surjeet |last23=Kimball |first23=Derek F. Jackson |last24=Budker |first24=Dmitry |last25=Sushkov |first25=Alexander O. |title=Search for Axionlike Dark Matter Using Solid-State Nuclear Magnetic Resonance |journal=Physical Review Letters |date=9 April 2021 |volume=126 |issue=14 |article-number=141802 |doi=10.1103/PhysRevLett.126.141802 |pmid=33891466 |arxiv=2101.01241 |bibcode=2021PhRvL.126n1802A |s2cid=230524028 }}</ref>

=== Searches at particle colliders ===
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 the [[Two-photon physics|light-by-light scattering]] process. Those searches are sensitive for rather large axion masses between {{val|100|u=MeV/c2}} and hundreds of {{val|u=GeV/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.<ref>{{cite journal |last1=Bauer |first1=Martin |last2=Neubert |first2=Matthias |last3=Thamm |first3=Andrea |date=December 2017 |title=Collider Probes of Axion-Like Particles |journal=Journal of High Energy Physics |volume=2017 |issue=12 |page=44 |doi=10.1007/JHEP12(2017)044 |arxiv=1708.00443 |bibcode=2017JHEP...12..044B |s2cid=119422560 }}</ref>

== Disputed 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.<ref name=guardian>{{cite news |last=Sample |first=Ian |title=Dark matter may have been detected – streaming from sun's core |newspaper=[[The Guardian]] |place=London, UK |url=https://www.theguardian.com/science/2014/oct/16/dark-matter-detected-sun-axions |access-date=16 October 2014 |date=2014-10-16 |df=dmy-all}}</ref><ref name="FraserRead2014">{{cite journal |last1=Fraser |first1=G. W. |last2=Read |first2=A. M. |last3=Sembay |first3=S. |last4=Carter |first4=J. A. |last5=Schyns |first5=E. |year=2014 |title=Potential solar axion signatures in X-ray observations with the XMM-Newton observatory |journal=Monthly Notices of the Royal Astronomical Society |volume=445 |issue=2 |pages=2146–2168 |arxiv=1403.2436 |doi=10.1093/mnras/stu1865 |doi-access=free |bibcode=2014MNRAS.445.2146F |s2cid=56328280 }}</ref>

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.<ref name="RoncadelliTavecchio2015">{{cite journal |last1=Roncadelli |first1=M. |last2=Tavecchio |first2=F. |title=No axions from the Sun |journal=Monthly Notices of the Royal Astronomical Society: Letters |volume=450 |issue=1 |year=2015 |pages=L26–L28 |doi=10.1093/mnrasl/slv040 |doi-access=free |arxiv=1411.3297 |bibcode=2015MNRAS.450L..26R |s2cid=119275136 }}</ref>

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 ≈&nbsp;110&nbsp;μeV, had in fact been observed in several preexisting experiments.<ref>{{cite journal |first=Christian |last=Beck |year=2015 |title=Axion mass estimates from resonant Josephson junctions |journal=Physics of the Dark Universe |volume=7–8 |pages=6–11 |doi=10.1016/j.dark.2015.03.002 |arxiv=1403.5676 |bibcode=2015PDU.....7....6B|s2cid=119239296 }}</ref>

In 2020, the [[XENON#XENON1T|XENON1T]] experiment at the [[Laboratori Nazionali del Gran Sasso|Gran Sasso National Laboratory]] in Italy reported a result suggesting the discovery of solar axions.<ref>{{cite journal |last1=Aprile |first1=E. |last2=Aalbers |first2=J. |display-authors=1 |date=2020-06-17 |title=Observation of excess electronic recoil events in XENON1T |journal=Physical Review D |volume=102 |article-number=072004 |arxiv=2006.09721 |doi=10.1103/PhysRevD.102.072004 |s2cid=222338600}}</ref> The results were not significant at the [[Standard deviation#Experiment, industrial and hypothesis testing|5-sigma level]] required for confirmation, and other explanations of the data were possible though less likely.<ref>{{cite journal |last1=Vagnozzi |first1=Sunny |last2=Visinelli |first2=Luca |last3=Brax |first3=Philippe |last4=Davis |first4=Anne-Christine |last5=Sakstein |first5=Jeremy |title=Direct detection of dark energy: The XENON1T excess and future prospects |journal=Physical Review D |date=15 September 2021 |volume=104 |issue=6 |article-number=063023 |doi=10.1103/PhysRevD.104.063023 |arxiv=2103.15834 |bibcode=2021PhRvD.104f3023V |s2cid=232417159 }}</ref> New observations made in July 2022 after the observatory upgrade to [[XENON#XENONnT|XENONnT]] discarded the excess, thus ending the possibility of new particle discovery.<ref>{{cite news |last1=Conover |first1=Emily |title=A new dark matter experiment quashed earlier hints of new particles |url=https://www.sciencenews.org/article/xenonnt-axions-dark-matter-experiment |work=Science News |date=22 July 2022 }}</ref><ref>{{cite journal |last1=Aprile |first1=E. |last2=Abe |first2=K. |last3=Agostini |first3=F. |last4=Maouloud |first4=S. Ahmed |last5=Althueser |first5=L. |last6=Andrieu |first6=B. |last7=Angelino |first7=E. |last8=Angevaare |first8=J. R. |last9=Antochi |first9=V. C. |last10=Martin |first10=D. Antón |last11=Arneodo |first11=F. |date=2022-07-22 |title=Search for New Physics in Electronic Recoil Data from XENONnT |journal=Physical Review Letters |volume=129 |issue=16 |article-number=161805 |doi=10.1103/PhysRevLett.129.161805 |pmid=36306777 |arxiv=2207.11330 |bibcode=2022PhRvL.129p1805A |s2cid=251040527 }}</ref>

== Properties ==
=== Predictions ===
One theory of axions relevant to [[cosmology]] had predicted that they would have no [[electric charge]], a very small [[mass]] in the range from {{val|1|u=μeV/''c''<sup>2</sup>}} to {{val|1|u=eV/c2}},<ref name="peccei2008"/> and very low interaction [[cross section (physics)|cross-sections]] for [[strong interaction|strong]] and [[weak interaction|weak]] forces. Because of their properties, axions would interact only minimally with ordinary matter. Axions would also change to and from [[photon]]s in magnetic fields.

=== Cosmological implications ===
The properties of the axion, such as the axion mass, decay constant, and abundance, all have implications for cosmology.<ref name="peccei2008" />

Inflation theory suggests that if they exist, axions would be created abundantly during the [[Big Bang]].<ref>{{cite journal |last1=Redondo |first1=J. |last2=Raffelt |first2=G. |last3=Viaux Maira |first3=N. |year=2012 |title=Journey at the axion meV mass frontier |journal=[[Journal of Physics: Conference Series]] |volume=375 |issue=2 |article-number=022004 |doi=10.1088/1742-6596/375/1/022004 |doi-access=free |bibcode=2012JPhCS.375b2004R}}</ref> 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.{{citation needed|date=June 2023}}

An ultralight axion (ULA) with {{nowrap|{{mvar|m}} ~ {{val|e=-22|u=eV/c2}}}} is a kind of [[scalar 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.<ref>{{cite journal |last=Marsh |first=David J.E. |date=2016 |title=Axion cosmology |journal=Physics Reports |language=en |volume=643 |pages=1–79 |doi=10.1016/j.physrep.2016.06.005 |arxiv=1510.07633|bibcode=2016PhR...643....1M |s2cid=119264863 }}</ref>

Axions would also have stopped interaction with normal matter at a different moment after the [[Big Bang]] than other more massive dark particles.{{why|date=May 2016}} The lingering effects of this difference could perhaps be calculated and observed astronomically.{{citation needed|date=June 2020}}

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 cold [[Bose–Einstein condensate]] of primordial axions. Hence, axions could plausibly explain the [[dark matter]] problem of [[physical cosmology]].<ref>{{cite journal |last=Sikivie |first=P. |year=2009 |title=Dark matter axions |journal=International Journal of Modern Physics A |volume=25 |issue=203 |pages=554–563 |arxiv=0909.0949 |doi=10.1142/S0217751X10048846 |bibcode=2010IJMPA..25..554S|s2cid=1058708 }}</ref> 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 via [[superradiance]].<ref>{{cite journal|last1=Davoudiasl |first1=Hooman |last2=Denton |first2=Peter |year=2019 |title=Ultralight Boson Dark Matter and Event Horizon Telescope Observations of M87 |journal=Physical Review Letters |volume=123 |issue=2 |article-number=021102 |doi=10.1103/PhysRevLett.123.021102 |pmid=31386502 |bibcode=2019PhRvL.123b1102D |arxiv=1904.09242 |s2cid=126147949 }}</ref> High mass axions of the kind searched for by Jain and Singh (2007)<ref>{{cite journal |last1=Jain |first1=P. L. |last2=Singh |first2=G. |year=2007 |title=Search for new particles decaying into electron pairs of mass below 100&nbsp;MeV/''c''<sup>2</sup> |journal=Journal of Physics G |volume=34 |issue=1 |pages=129–138 |bibcode=2007JPhG...34..129J |doi=10.1088/0954-3899/34/1/009 |quote=possible early evidence of 7±1 and 19±1&nbsp;MeV axions of less than 10<sup>−13</sup>&nbsp;s lifetime}}</ref> 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.<ref>{{cite journal |last1=Salvio |first1=Alberto |last2=Strumia |first2=Alessandro |last3=Xue |first3=Wei |year=2014 |title=Thermal axion production |journal=Journal of Cosmology and Astroparticle Physics |volume=2014 |issue=1 |page=11 |url=http://inspirehep.net/record/1262100 |bibcode=2014JCAP...01..011S |doi=10.1088/1475-7516/2014/01/011 |arxiv=1310.6982|s2cid=67775116 }}</ref>

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 (mathematics)|caustic]]" rings, just as the stream of water in a continuously flowing fountain is thicker at its peak.<ref>{{cite tech report |first=P. |last=Sikivie |year=1997 |title=Dark matter axions and caustic rings |doi=10.2172/484584 |osti=484584 |s2cid=13840214 }}</ref> The gravitational effects of these rings on galactic structure and rotation might then be observable.<ref>{{cite web |first=P. |last=Sikivie |url=http://www.phys.ufl.edu/~sikivie/triangle/ |title=Pictures of alleged triangular structure in Milky Way }}{{self-published inline|date=January 2024}}</ref><ref name=Duffy2010>{{cite conference |doi=10.1063/1.3489563 |title=The Milky Way's Dark Matter Distribution and Consequences for Axion Detection |series=AIP Conference Proceedings |date=2010 |last1=Duffy |first1=Leanne D. |last2=Tanner |first2=David B. |last3=Van Bibber |first3=Karl A. |conference=Axions 2010 |volume=1274 |pages=85–90 |bibcode=2010AIPC.1274...85D }}</ref> Other cold dark matter theoretical candidates, such as [[Weakly interacting massive particles|WIMP]]s and [[MACHO]]s, could also form such rings, but because such candidates are [[fermion]]ic and thus experience friction or scattering among themselves, the rings would be less sharply defined.{{citation needed|date=June 2023}}

João G. Rosa and Thomas W. Kephart suggested that axion clouds formed around unstable [[primordial black hole]]s 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 burst]]s, being a possible origin for both phenomena.<ref>{{cite journal |last1=Rosa |first1=João G. |last2=Kephart |first2=Thomas W. |year=2018 |title=Stimulated axion decay in superradiant clouds around primordial black holes |journal=Physical Review Letters |volume=120 |issue=23 |article-number=231102 |arxiv=1709.06581 |doi=10.1103/PhysRevLett.120.231102 |pmid=29932720 |bibcode=2018PhRvL.120w1102R |s2cid=49382336 }}</ref> In 2022 a similar hypothesis was used to [[#Astrophysical axion searches|constrain]] the mass of the axion from data of M87*.{{citation needed|date=June 2023}}

In 2020, it was proposed that the axion field might actually have influenced the evolution of [[Chronology of the universe|the early Universe]] by creating more imbalance between the amounts of matter and antimatter – which possibly resolves the [[baryon asymmetry]] problem.<ref>{{cite journal |last=Anonymous |date=2020-03-19 |title=Axions Could Explain Baryon Asymmetry |url=https://physics.aps.org/articles/v13/s38 |journal=Physics |language=en |volume=13 |issue=11 |pages=s38 |doi=10.1103/PhysRevLett.124.111602|pmid=32242736 |arxiv=1910.02080 }}</ref>

=== Supersymmetry ===
In [[supersymmetry|supersymmetric theories]] the axion has both a scalar and a fermionic [[superpartner]]. The [[fermion]]ic superpartner of the axion is called the [[axino]], the scalar superpartner is called the [[saxion]] or [[dilaton]]. They are all bundled in a [[chiral superfield]].

The [[axino]] has been predicted to be the [[lightest supersymmetric particle]] in such a model.<ref>
{{cite journal
 |first1=Abe | last1=Nobutaka
 |first2=Takeo | last2=Moroi
 |first3=Masahiro | last3=Yamaguchi
 |name-list-style=amp|year=2002
 |title=Anomaly-Mediated Supersymmetry Breaking with Axion
 |journal=[[Journal of High Energy Physics]]
 |volume=1 |issue=1 |page=10
 |doi=10.1088/1126-6708/2002/01/010
 |arxiv=hep-ph/0111155 |bibcode = 2002JHEP...01..010A 
 |s2cid=15280422
}}</ref> In part due to this property, it is also considered a candidate for dark matter.<ref>
{{cite journal
 |last1=Hooper | first1=Dan
 |first2=Lian-Tao | last2=Wang
 |year=2004
 |title=Possible evidence for axino dark matter in the galactic bulge
 |journal=[[Physical Review D]]
 |volume=70 |issue=6 |article-number=063506
 |doi=10.1103/PhysRevD.70.063506
 |arxiv = hep-ph/0402220 |bibcode = 2004PhRvD..70f3506H 
 |s2cid=118153564
}}</ref>

== See also ==
{{Portal|Physics}}
* [[Dark photon]]
* [[List of particles#Hypothetical particles|List of hypothetical particles]] 
* [[WISP (particle physics)|Weakly interacting slender particle]]

== Footnotes ==
{{notelist}}

== References ==
{{reflist|colwidth=25em}}

== Sources ==
* {{cite journal |year=1977 |title=''CP'' conservation in the presence of pseudoparticles |journal=Physical Review Letters |volume=38 |issue=25 |pages=1440–1443 |doi=10.1103/PhysRevLett.38.1440 |bibcode=1977PhRvL..38.1440P |last1=Peccei |first1=R. D. |author-link1=Roberto Peccei |last2 = Quinn |first2=H. R. |s2cid=9518918 |author-link2=Helen Quinn}}
* {{cite journal |last1=Peccei |first1=R. D. |last2=Quinn |first2=H. R. |year=1977 |title=Constraints imposed by ''CP'' conservation in the presence of pseudoparticles |journal=Physical Review D |volume=16 |issue=6 |pages=1791–1797 |doi=10.1103/PhysRevD.16.1791 |bibcode=1977PhRvD..16.1791P }}
* {{cite journal |last=Weinberg |first=Steven |s2cid=610538 |author-link=Steven Weinberg |year=1978 |title=A new light boson? |journal=Physical Review Letters |volume=40 |issue=4 |pages=223–226 |doi=10.1103/PhysRevLett.40.223 |bibcode=1978PhRvL..40..223W}}
* {{cite journal |last=Wilczek |first=Frank |author-link=Frank Wilczek |year=1978 |title=Problem of strong ''P'' and ''T'' invariance in the presence of instantons |journal=Physical Review Letters |volume=40 |issue=5 |pages=279–282 |doi=10.1103/PhysRevLett.40.279 |bibcode=1978PhRvL..40..279W}}

== External links ==
{{commons category}}
{{wikiquote}}

* {{cite web |url=https://ncatlab.org/nlab/show/axion |title=Axion in nLab}}
* {{cite web |title=Plots of current experimental constraints on axion couplings |url=https://cajohare.github.io/AxionLimits/ |language=en-US}}

=== Experiments ===
* {{cite web |url=http://cern.ch/cast |title=CAST Experiment |publisher=[[CERN]] |place=Switzerland |access-date=2007-09-23 |archive-date=2013-01-16 |archive-url=https://archive.today/20130116024654/http://cern.ch/cast }}
* {{cite web |url=http://gifna.unizar.es/cast/ |title=CAST |publisher=UNIZAR |place=Spain |access-date=2015-08-12 |archive-date=2016-04-15 |archive-url=https://web.archive.org/web/20160415082435/http://gifna.unizar.es/cast/ }}
* {{cite web |url=http://astropp.physik.tu-darmstadt.de/cast/ |archive-date=2009-03-18 |archive-url=https://web.archive.org/web/20090318035648/http://astropp.physik.tu-darmstadt.de/cast/ |title=CAST |publisher=University of Technology |place=Darmstadt, Germany}}
* {{cite web |url=http://www.phys.washington.edu/groups/admx/home.html |title=ADMX |publisher=University of Washington |place=Seattle, Washington |access-date=2008-03-21 |archive-date=2015-02-14 |archive-url=https://web.archive.org/web/20150214120316/http://www.phys.washington.edu/groups/admx/home.html }}

=== Popular science coverage ===
* {{cite journal |url=https://physics.aps.org/articles/v1/36 |df=dmy-all |date=November 24, 2008 |title=High-energy physics in a new guise |journal=APS Physics |volume=1 |last1=Franz |first1=Marcel |article-number=36 |doi=10.1103/Physics.1.36 |bibcode=2008PhyOJ...1...36F }}
* {{cite web |url=https://www.newscientist.com/article/dn11041-last-gasp-test-could-reveal-dark-matter/ |url-access=registration |df=dmy-all |last=Merali |first=Zeeya |date=January 28, 2007 |title=Last-gasp test could reveal dark matter |magazine=New Scientist}}
* {{cite web |url=http://www.physorg.com/news84633896.html |archive-url=https://web.archive.org/web/20061207214335/http://www.physorg.com/news84633896.html |archive-date=7 December 2006 |df=dmy-all |date=6 December 2006 |title=Long the fixation of physicists worldwide, a tiny particle is found |website=physorg.com}}
* {{cite news |last1=Collins |first1=Graham P. |title=A Hint of Axions |url=https://www.scientificamerican.com/article/a-hint-of-axions/ |work=Scientific American |date=17 July 2006 }}
* {{cite web |url=http://physicsweb.org/articles/news/10/3/19/1 |df=dmy-all |last=Chalmers |first=Matthew |date=March 27, 2006 |title=Optical rotation sheds light on vacuum |website=PhysicsWeb.org |access-date=April 6, 2006 |archive-date=April 11, 2006 |archive-url=https://web.archive.org/web/20060411063407/http://physicsweb.org/articles/news/10/3/19/1}}
* {{cite web |url=http://physicsweb.org/articles/news/8/11/13/1 |df=dmy-all |last=Dumé |first=Belle |date=November 24, 2004 |title=Axion experiment makes its debut |website=PhysicsWeb.org |access-date=November 28, 2004 |archive-date=March 10, 2007 |archive-url=https://web.archive.org/web/20070310173022/http://physicsweb.org/articles/news/8/11/13/1}}

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[[Category:Astroparticle physics]]
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[[Category:Dark matter]]
[[Category:Hypothetical elementary particles]]
[[Category:Subatomic particles with spin 0]]
[[Category:Physics beyond the Standard Model]]
[[Category:Quantum chromodynamics]]