Wikipedia

Axion

Not to be confused with axiom or axon. For other uses, see Axion (disambiguation).

An axion (/ˈæksiɒn/) is a hypothetical elementary particle proposed independently by Frank Wilczek and Steven Weinberg in 1978 on the basis of the Peccei–Quinn theory for resolving the strong CP problem posed by the apparent success of quantum chromodynamics (QCD) as a theory of the strong nuclear force. If axions exist and were made in the Big Bang with sufficient number density, they would form the dark matter in the universe provided the axion mass falls within a narrow range set by the ratio of the present cold dark matter mass density to the present axion number density.

Axion
InteractionsGravitational, electromagnetic, strong nuclear, weak nuclear
StatusHypothetical
SymbolA0, a, θ
Theorized1978, Wilczek and Weinberg
Mass 10−5 to 1 eV/c2 [1]
Electric charge0
Spin0

History

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Strong CP problem

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As shown by Gerard '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 of charge conjugation and parity, collectively known as CP. Together with effects generated by weak interactions, the effective periodic strong CP-violating term, Θ, appears as a Standard Model input – its value is not predicted by the theory, but must be measured. However, large CP-violating interactions originating from QCD would induce a large electric dipole moment (EDM) for the neutron. Experimental constraints on the unobserved EDM implies CP violation from QCD must be extremely tiny and thus Θ must itself be extremely small. Since Θ could have any value between 0 and 2π, this presents a "naturalness" problem for the standard model. Why should this parameter find itself so close to zero? (Or, why should QCD find itself CP-preserving?) This question constitutes what is known as the strong CP problem.[b]

Prediction

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In 1977, Roberto Peccei and Helen Quinn postulated a more elegant solution to the strong CP problem, the Peccei–Quinn mechanism. The idea is to effectively promote Θ to a field. This is accomplished by adding a new global symmetry (called a Peccei–Quinn (PQ) symmetry) that becomes spontaneously broken. This results in a new particle, as shown independently by Frank Wilczek[5] and Steven Weinberg,[6] that fills the role of Θ, naturally relaxing the CP-violation parameter to zero. Wilczek named this new hypothesized particle the "axion" after a brand of laundry detergent because it "cleaned up" a 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 a pseudo-Nambu–Goldstone boson.[9]

Early searches and the emergence of axions as dark matter candidate

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Searches for the axion began in 1978 soon after its existence was first theorized. Quickly, the rest-mass energy that theorists had first proposed--around 60 keV--was ruled out by analyzing existing experimental results from particle detectors at high-energy particle accelerators.[1] However, it was soon realized by KSVZ (Kim–Shifman–Vainshtein–Zakharov) [10][11] and DFSZ (Dine–Fischler–Srednicki–Zhitnitsky)[12][13] that the mass of the axion is a free parameter in the Peccei-Quinn theory for solving the strong CP problem, and so the axion mass is subject only to the constraint from quantum chromodynamics that the topological susceptibility of the vacuum--roughly the product of the pion mass with the pion decay constant--be given by the product of the axion mass with the axion decay constant.[1] This realization added a cosmological dimension to the searches for axions since axions with mass much less than 60 keV would couple only weakly to photons and other particles of the standard model of particle physics and these "invisible axions" could then form the dark matter in the universe if the Big Bang makes them in large enough numbers. [14][15][16]

Axion Electrodynamics

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Axions couple to the vector dot product of an electric field with a magnetic field.[1] In 1983, just after it was realized that axions might form the dark matter in the universe, Pierre Sikivie proposed searching for axions in the local dark matter halo of the Milky Way galaxy using this coupling. Maxwell's equations of electrodynamics change in the presence of the axion field and the resulting axion electrodynamic equations can be used to design "haloscopes" that search for halo axions using the coupling of the axion to the vector dot product of the electric and magnetic fields. [17]

Axion haloscopes

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Given a sufficiently precise prediction for the mass of the axion, axion electrodynamics suggests a straightforward way to search for axions from the local dark matter halo. Simply set up a strong static magnetic field within a large high quality factor electromagnetic cavity resonator such that the resonance frequency is tuned to the ratio of the axion energy with the Planck constant: "Halo" axion will spontaneously excite the cavity by creating a resonant electric field polarized along the static magnetic field. A long-running search of this kind, the Axion Dark Matter Experiment, in 2010 reached the level of sensitivity needed to see the microwave electric fields that should be generated by halo axions with mass in the range 1 μeV to 4 μeV; however, the lack of significant microwave power generated within the ADMX resonant cavity during the search rule ou almost all of this mass range.

Axion helioscopes

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The same axion electrodynamic equations also suggest a natural design for a "helioscope" that can see axions coming from the core of the Sun. A long running search of this kind, the CAST experiment, used a large static magnetic field to convert axions coming from the Sun with kinetic energy between roughly 1 keV and 10 keV into X-rays. Although the experiment demonstrated impressive sensitivity to axions with mass less than 0.02 eV, in fact the best yet demonstrated by any such "helioscope," the expected signal in that mass range requires still greater sensitivity, and, conversely, in the mass range above 0.02 eV, where the expected signal strength rises, the experimental sensitivity dropped off significantly.

Making axions in the lab

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A third class of axion electrodynamic experiments simply makes axions from scratch by sending a bright laser beam through a strong static magnetic field. According to axion electrodynamics, only the light polarized with its electric field pointing along the static magnetic field gets absorbed, so the creation of axions from photons in a magnetic field shows up as a kind of birefringence somewhat similar to what is seen when light passes through minerals such as calcite but with the quantum electrodynamic vacuum serving as the birefringent medium. Another CERN experiment, OSQAR,[18] looked for vacuum birefringence caused by axions with mass around 0.001 eV, but the results of a preliminary search reported in 2008 did not reach the sensitivity that is expected to be needed to see axions with this mass.

Other axion electrodynamic searches for axions

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As of the early 2020s, there are dozens of proposed or ongoing experiments searching for axions and many use axion electrodynamics to design their searches.[19]

Equations of axion electrodynamics

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The equations of axion electrodynamics follow in a straightforward way from the coupling of the axion field to the vector dot product of the electric field and the magnetic field. [20] In "natural units", where the reduced Planck constant  , speed of light  , and permittivity of free space   all reduce to 1, the axion electrodynamic equations take the simple form:

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 the vector dot product; the factor   is the axion-to-photon coupling constant rendered in "natural units".

Axion electrodynamics in topological materials

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A term analogous to the one that would be added to Maxwell's equations to account for axions[21] also appears in recent (2008) theoretical models for topological insulators giving an effective axion description of the electrodynamics of these materials.[22]

This term leads to several interesting predicted properties including a quantized magnetoelectric effect.[23] Evidence for this effect has been given in THz spectroscopy experiments performed at the Johns Hopkins University on quantum regime thin film topological insulators developed at Rutgers University.[24]

In 2019, a team at the Max Planck Institute for Chemical Physics of Solids used axion electrodynamics to understand the way that the steady-state electrical current flowing through a Weyl semimetal material changes when you apply a static magnetic field.[25] According to their analysis, frequency modulations of charge density waves within the material act like the axion and couple to the vector dot product of the static external electric field driving the steady-state electrical current and the static external magnetic field applied to the sample. Using the axion electrodynamic equations but with the axion mass and the axion-photon coupling strength appropriate for the axion-like frequency modulations within the material, the team was able to explain their otherwise puzzling observations of a positive differential magnetoconductance that grows with the square of the magnetic field strength. [26]

Axion dark matter

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Axions are one of the leading candidates for the dark matter in the universe.[1] The coupling of axions to photons and other particles of the standard model of particle physics is weak for axions with mass much less than 60 keV. For example, an axion with mass around 0.5 eV takes longer than the present age of the universe to decay to a pair of photons and this is its fastest mode of decay. Yet, to match observations of the present mass density of cold dark matter in the universe, dark matter in the form of axions with a rest mass around 0.5 eV must have a present number density that is around six times larger than the number density of the photons in the cosmic microwave background.

Misalignment Mechanism for Making Axions in the Big Bang

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QCD effects produce an effective periodic potential in which the axion field moves. 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.[14][15][16] With a mass above 5 μeV/c2 (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 peV/c2.[27][28][29]

There are two distinct scenarios in which the axion field begins its evolution, depending on the following two conditions:

(a) The PQ symmetry is spontaneously broken during inflation. This condition is realized whenever the axion energy scale is larger than the Hubble rate at the end of inflation
(b) The PQ symmetry is never restored after its spontaneous breaking occurs. This condition is realized whenever the axion energy scale is larger than the maximum temperature reached in the post-inflationary Universe.

Broadly speaking, one of the two possible scenarios outlined in the two following subsections occurs:

Pre-inflationary scenario

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If both (a) and (b) are satisfied, cosmic inflation selects one patch of the Universe within which the spontaneous breaking of the PQ symmetry leads to a homogeneous value of the initial value of the axion field. In this "pre-inflationary" scenario, topological defects are inflated away and do not contribute to the axion energy density. However, other bounds that come from isocurvature modes severely constrain this scenario, which require a relatively low-energy scale of inflation to be viable.[30][31][32]

Post-inflationary scenario

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If at least one of the conditions (a) or (b) is violated, the axion field takes different values within patches that are initially out of causal contact, but that today populate the volume enclosed by our Hubble horizon. In this scenario, isocurvature fluctuations in the PQ field randomise the axion field, with no preferred value in the power spectrum.

The proper treatment in this scenario is to solve numerically the equation of motion of the PQ field in an expanding Universe, in order to capture all features coming from the misalignment mechanism, including the contribution from topological defects like "axionic" strings and domain walls. An axion mass estimate between 0.05 and 1.50 meV was reported by Borsanyi et al. (2016).[33] The result was calculated by simulating the formation of axions during the post-inflation period on a supercomputer.[34]

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,[35][36] although these results have been challenged by the details on the power spectrum of emitted axions from strings.[37]

Experiments and Observations

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Analysis of the results of existing high-energy particle physics experiments and astronomical observations for signs of axions began immediately after theorists proposed that axions exist in 1978. After this initial analysis ruled out axions with mass around 60 keV, theorists suggested that the axion mass could vary over a wide range.

This theoretical re-appraisal prompted the design of new experiments and astrophysical analyses to search for the axion--or rule it out--across a wide spectrum of possible values for the axion mass. A correspondingly wide range of experimental techniques and astronomical phenomena were brought to bear during the 40 years from 1978 to 2018 ranging from particle colliders to supernovae. This experimental and observational effort resulted in several parts of the suggested range of axion masses being ruled out.

 
Constraints on the axion's coupling to the photon
 
Constraints on the axion's dimensionless coupling to electrons

Despite this narrowing of the range of possible values for the axion mass, experiments and observations continue. The continued effort is motivated in part by the key role that the axion plays in the Peccei-Quinn mechanism for solving the Strong CP Problem of the standard model of particle physics. Another motivation is that axions with mass much less than 60 keV could form the dark matter in the universe. A third motivation is the recognition that axion-like excitation modes exist within magnetic topological insulators and related materials.

Direct conversion in a magnetic field

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

The Axion Dark Matter Experiment (ADMX) at the University of Washington uses a strong magnetic field to detect the possible weak conversion of axions from the local dark matter halo of the galaxy into microwaves.[38] ADMX searches the galactic dark matter halo[39] for axions resonant with a cold microwave cavity. ADMX has excluded optimistic axion models in the 1.9–3.53 μeV range.[40][41][42] From 2013 to 2018 a series of upgrades[43] were done and it is taking new data, including at 4.9–6.2 μeV. In December 2021 it excluded the 3.3–4.2 μeV range for the KSVZ model.[44][45]

Other experiments of this type include DMRadio,[46] HAYSTAC,[47] CULTASK,[48] and ORGAN.[49] HAYSTAC completed the first scanning run of a haloscope above 20 μeV in the late 2010s.[47]

Polarized light in a magnetic field

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The Italian PVLAS experiment searches for polarization changes of light propagating in a magnetic field. The concept was first put forward in 1986 by Luciano Maiani, Roberto Petronzio and Emilio Zavattini.[50] A rotation claim[51] in 2006 was excluded by an upgraded setup.[52] An optimized search began in 2014.

Light shining through walls

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Another technique is so called "light shining through walls",[53] 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.[54] GammeV saw no events, reported in a 2008 Physics Review Letter. ALPS I conducted similar runs,[55] setting new constraints in 2010; ALPS II is being built in 2022.[56] OSQAR found no signal, limiting coupling[57] and will continue.

Astrophysical axion searches

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The main astrophysical search for axions uses stars on the horizontal branch of the Hertzsprung-Russell diagram of globular clusters.[1] These stars formed shortly after the Big Bang and now fuse helium nuclei at high temperature and pressure in the core of the star to make gamma rays in the triple-alpha process. As these gamma rays make their way out of the core, they encounter the large electric fields created by the helium nuclei.

The coupling of the gamma ray magnetic field with the helium nucleus' electric field makes axions that leave the core with a rate that depends on the axion-photon coupling strength. The loss of gamma rays cools the core, shortens the life of the star, and cuts down the number of horizontal branch stars relative to the number on the red giant branch. By combining observations of the ratio of the number of horizontal branch stars to the number of stars on the red giant branch in several dozen globular clusters with models of stellar evolution that include the effect of axions, astrophysicists were able in 2014 to establish an empirical relation between the strength of the axion-photon coupling and the amount of helium in the core of these old stars when they formed shortly after the Big Bang.[58]

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.[59][60] 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.[61] 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.[62] The International Axion Observatory (IAXO) is a proposed fourth generation helioscope.[63]

Axions can resonantly convert into photons in the magnetospheres of neutron stars.[64] 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 5–11 μeV mass range, by re-analyzing existing data from the Green Bank Telescope and the Effelsberg 100 m Telescope.[65] A novel, alternative strategy consists in detecting the transient signal from the encounter between a neutron star and an axion minicluster in the Milky Way.[66]

Axions can be produced in the Sun's core when X-rays scatter in strong electric fields. The CAST solar telescope is underway, and has set limits on coupling to photons and electrons. Axions may be produced within neutron stars, by nucleon–nucleon bremsstrahlung. The subsequent decay of axions to gamma rays allows constraints on the axion mass to be placed from observations of pulsars in gamma-rays assuming that pulsars are neutron stars.

Using Fermi Gamma-ray Space Telesope observations of four pulsars, Berenji et al. (2016) obtained a 95% confidence interval upper limit on the axion mass of 0.079 eV by assuming the pulsars are neutron stars.[67] In 2021 it has been also suggested[68][69] that a reported[70] excess of hard X-ray emission from a system of pulsars known as the magnificent seven could be explained as axion emission if the pulsars are neutron stars.

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 MRI scanning machine. It would show variation, a slight wavering, that is linked to the mass of the axion. As of 2019, the experiment is being implemented by experimentalists at the university.[71]

In 2022 the polarized light measurements of Messier 87* by the EHT were used to constrain the mass of the axion assuming that hypothetical clouds of axions could form around a black hole, rejecting the approximate 10−21 eV/c2 – 10−20 eV/c2 range of mass values.[72][73]

Searches for resonance effects

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Resonance effects may be evident in Josephson junctions[74] from a supposed high flux of axions from the galactic halo with mass of 110 μeV and density 0.05 GeV/cm3[75] compared to the implied dark matter density 0.3±0.1 GeV/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 the haloscope method.[49]

Dark matter recoil searches

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Dark matter cryogenic detectors have searched for electron recoils that would indicate axions. CDMS published in 2009 and EDELWEISS set coupling and mass limits in 2013. UORE and XMASS also set limits on solar axions in 2013. XENON100 used a 225-day run to set the best coupling limits to date and exclude some parameters.[76]

Nuclear spin precession

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While Schiff's theorem states that a static nuclear electric dipole moment (EDM) does not produce atomic and molecular EDMs,[77] the axion induces an oscillating nuclear EDM that oscillates at the 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.[78]

An experiment using this technique is the Cosmic Axion Spin Precession Experiment (CASPEr).[79][80][81]

Searches at particle colliders

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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 light-by-light scattering process. Those searches are sensitive for rather large axion masses between 100 MeV/c2 and hundreds of 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.[82]

Disputed detections

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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.[83][84]

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.[85]

In 2013, Christian Beck suggested that axions might be detectable in Josephson junctions; and in 2014, he argued that a signature, consistent with a mass ≈110 μeV, had in fact been observed in several preexisting experiments.[86]

In 2020, the XENON1T experiment at the Gran Sasso National Laboratory in Italy reported a result suggesting the discovery of solar axions.[87] The results are not yet significant at the 5-sigma level required for confirmation, and other explanations of the data are possible though less likely.[88] New observations made in July 2022, after the observatory upgrade to XENONnT, discarded the excess thus ending the possibility of new particle discovery.[89][90]

Properties

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Predictions

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

Another theory relevant to cosmology predicts the mass of the axion  , the strength of the axion-photon coupling  , and the present cosmological number density of axions  . Because of their properties, axions would interact with optical phonons within a wide range of materials, including quartz, halite, and polystyrene, to create axion resonances in the mid-infrared electrodynamic response of the materials. Axions from the local dark matter halo of the galaxy would also change the effective values of the fundamental coupling constants seen in experiments, such as the electromagnetic fine-structure coupling constant in the muon g-2 spin precession experiment and the strong interaction coupling constant in measurements of the charged weak W vector boson mass, by coupling to the virtual gauge vector boson that carries the fundamental force, such that the size of effect scales "haloscopically" as the square-root of the product of the local axion energy density   with the luminous volume of space-time probed in the experiment.

Cosmological Implications of the Axion

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The main cosmological implication of the axion is that axions might form the dark matter in the universe.[1] Axions with rest-mass much less than 60 keV interact weakly with photons and the other particles of the standard model of particle physics: For example, an axion with mass around 0.5 eV would take much longer than the present age of the universe to spontaneously decay into a pair of photons which is the dominant decay mode of the axion. So, axions made in the Big Bang would persist into the present universe where they would appear as cold dark matter in the form of a cold fluid made of long-lived, weakly-interacting particles.

Inflationary cosmology and axions

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Inflation suggests that if they exist, axions would be created abundantly during the Big Bang.[91] 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]

"Small-scale" cosmological problems and the axion

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Ultralight axion (ULA) with m ~ 10−22 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.[92]

Cosmological condensate of axions

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In 2009 Sikivie argued that cold dark matter in the form of a superfluid made of axions that condenses in the Big Bang could help explain several cosmological phenomena that are hard to explain with the standard cold dark matter model in which the dark matter is not superfluid [93] If the coherence length of the superfluid is long enough, then "fuzzy" behavior of the dark matter such as superradiance might be observable using the event horizon of super-massive black holes.[94]

Cosmological upper bounds on the mass of the axion

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High mass axions of the kind searched for by Jain and Singh (2007)[95] would not persist in the modern universe. Moreover, if such axions exist, scatterings with other particles in the thermal bath of the early universe unavoidably produce a population of hot axions.[96]

Galaxy structure and axions

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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.[97] The gravitational effects of these rings on galactic structure and rotation might then be observable.[98][99] Other cold dark matter theoretical candidates, such as WIMPs and MACHOs, could also form such rings, but because such candidates are fermionic and thus experience friction or scattering among themselves, the rings would be less sharply defined.[citation needed]

Primordial black holes and axions

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João G. Rosa and Thomas W. Kephart suggested that axion clouds formed around unstable primordial black holes might initiate a chain of reactions that radiate electromagnetic waves, allowing their detection. When adjusting the mass of the axions to explain dark matter, the pair discovered that the value would also explain the luminosity and wavelength of fast radio bursts, being a possible origin for both phenomena.[100] In 2022 a similar hypothesis was used to constrain the mass of the axion from data of M87*.[citation needed]

Cosmological matter-antimatter asymmetry and axions

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In 2020, it was proposed that the axion field might actually have influenced the evolution of early Universe by creating more imbalance between the amounts of matter and antimatter – which possibly resolves the baryon asymmetry problem.[101]

Supersymmetry

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

The axino has been predicted to be the lightest supersymmetric particle in such a model.[102] In part due to this property, it is considered a candidate for dark matter.[103]

See also

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Footnotes

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  1. ^ This non-trivial vacuum structure solves a problem associated to the U(1) axial symmetry of QCD[3][4]
  2. ^ 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.
  3. ^ At present, physics literature discusses "invisible axion" mechanisms in two forms, one of them is called KSVZ for Kim–Shifman–Vainshtein–Zakharov.[10][11] See discussion in the "Searches" section, below.

References

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  1. ^ a b c d e f g Peccei, R. D. (2008). "The Strong CP Problem and Axions". In Kuster, Markus; Raffelt, Georg; Beltrán, Berta (eds.). Axions: Theory, Cosmology, and Experimental Searches. Lecture Notes in Physics. Vol. 741. pp. 3–17. arXiv:hep-ph/0607268. doi:10.1007/978-3-540-73518-2_1. ISBN 978-3-540-73517-5. S2CID 119482294.
  2. ^ 't Hooft, Gerard (1976). "Symmetry breaking through Bell-Jackiw anomalies". Physical Review Letters. 37 (1).'t Hooft, Gerard (1976). "Computation of the quantum effects due to a four-dimensional pseudo-particle". Physical Review D. 14 (12). APS: 3432–3450. Bibcode:1976PhRvD..14.3432T. doi:10.1103/PhysRevD.14.3432.
  3. ^ Katz, Emanuel; Schwartz, Matthew D (28 August 2007). "An eta primer: solving the U(1) problem with AdS/QCD". Journal of High Energy Physics. 2007 (8): 077. arXiv:0705.0534. Bibcode:2007JHEP...08..077K. doi:10.1088/1126-6708/2007/08/077. S2CID 119594300.
  4. ^ Tanedo, Flip. "'t Hooft and η'ail Instantons and their applications" (PDF). Cornell University. Retrieved 2023-06-20.
  5. ^ Wilczek, Frank (1978). "Problem of Strong P and T Invariance in the Presence of Instantons". Physical Review Letters. 40 (5): 279–282. Bibcode:1978PhRvL..40..279W. doi:10.1103/PhysRevLett.40.279.
  6. ^ Weinberg, Steven (1978). "A New Light Boson?". Physical Review Letters. 40 (4): 223–226. Bibcode:1978PhRvL..40..223W. doi:10.1103/PhysRevLett.40.223.
  7. ^ Overbye, Dennis (17 June 2020). "Seeking dark matter, they detected another mystery". The New York Times.
  8. ^ a b Wilczek, Frank (7 January 2016). "Time's (almost) reversible arrow". Quanta Magazine. Retrieved 17 June 2020.
  9. ^ Miller, D. J.; Nevzorov, R. (2003). "The Peccei-Quinn Axion in the Next-to-Minimal Supersymmetric Standard Model". arXiv:hep-ph/0309143v1.
  10. ^ a b Kim, J. E. (1979). "Weak-interaction singlet and strong CP invariance". Physical Review Letters. 43 (2): 103–107. Bibcode:1979PhRvL..43..103K. doi:10.1103/PhysRevLett.43.103.
  11. ^ a b Shifman, M.; Vainshtein, A.; Zakharov, V. (1980). "Can confinement ensure natural CP invariance of strong interactions?". Nuclear Physics B. 166 (3): 493–506. Bibcode:1980NuPhB.166..493S. doi:10.1016/0550-3213(80)90209-6.
  12. ^ Dine, M.; Fischler, W.; Srednicki, M. (1981). "A simple solution to the strong CP problem with a harmless axion". Physics Letters B. 104 (3): 199–202. Bibcode:1981PhLB..104..199D. doi:10.1016/0370-2693(81)90590-6.
  13. ^ Zhitnitsky, A. (1980). "On possible suppression of the axion–hadron interactions". Soviet Journal of Nuclear Physics. 31: 260.
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  101. ^ Anonymous (2020-03-19). "Axions Could Explain Baryon Asymmetry". Physics. 13 (11): s38. arXiv:1910.02080. doi:10.1103/PhysRevLett.124.111602. PMID 32242736.
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