Axion

Axion
Interactions Gravity, electromagnetic
Status Hypothetical
Symbol A0
Theorized 1977, Peccei and Quinn
Mass 10−5 to 10−3 eV/c2
Electric charge 0
Spin 0

The axion is a hypothetical elementary particle postulated by the Peccei–Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics (QCD). If axions exist and have low mass within a specific range, they are of interest as a possible component of cold dark matter.

History

Prediction

As shown by Gerard 't Hooft, strong interactions of the standard model, QCD, possess a non-trivial vacuum structure that in principle permits violation of the combined symmetries of charge conjugation and parity, collectively known as CP. Together with effects generated by weak interactions, the effective periodic strong CP-violating term, Θ, appears as a Standard Model input – its value is not predicted by the theory, but must be measured. However, large CP-violating interactions originating from QCD would induce a large electric dipole moment (EDM) for the neutron. Experimental constraints on the currently unobserved EDM implies CP violation from QCD must be extremely tiny and thus Θ must itself be extremely small. Since a priori 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 0? (Or, why should QCD find itself CP-preserving?) This question constitutes what is known as the strong CP problem.

One simple solution exists: If at least one of the quarks of the standard model is massless, Θ becomes unobservable. However, empirical evidence strongly suggests that none of the quarks is massless.

In 1977, Roberto Peccei and Helen Quinn postulated a more elegant solution to the strong CP problem, the Peccei–Quinn mechanism. The idea is to effectively promote Θ to a field. This is accomplished by adding a new global symmetry (called a Peccei–Quinn symmetry) that becomes spontaneously broken. This results in a new particle, as shown by Frank Wilczek and Steven Weinberg, that fills the role of Θ, naturally relaxing the CP-violation parameter to zero. This hypothesized new particle is called the axion. [note 1] The original Weinberg–Wilczek axion was ruled out. Current literature discusses the mechanism as the "invisible axion", which has two forms: KSVZ (Kim-Shifman-Vainshtein-Zakharov)[1][2] and DFSZ (Dine-Fischler-Srednicki-Zhitnitsky).[3][4]

Searches

It had been thought that the invisible axion solves the strong CP problem without being amenable to verification by experiment. Axion models choose coupling that does not appear in any of the prior experiments. The very weakly coupled axion is also very light because axion couplings and mass are proportional. The situation changed when it was shown that a very light axion is overproduced in the early universe and therefore excluded.[5][6][7] The critical mass is of order 10−11 times the electron mass, where axions may account for the dark matter. The axion is thus a dark-matter candidate, as well as a solution to the strong CP problem. Furthermore, in 1983, Pierre Sikivie wrote down the modification of Maxwell's equations from a light stable axion[8] and showed that axions can be detected on Earth by converting them to photons, using a strong magnetic field, the principle of the ADMX. Solar axions may be converted to x-rays, as in CAST. Many experiments are searching laser light for signs of axions.[9]

A mass value between 50 and 1,500 µeV for axion was reported in a paper published in November 2016 (Borsanyi, S. et al.).[10] The result was calculated by simulating the formation of axion during the post-inflation period on supercomputer.[11]

Maxwell's equations with axion modifications

If magnetic monopoles exist then there is a symmetry in Maxwell's equations where the electric and magnetic fields can be rotated into each other with the new fields still satisfying Maxwell's equations. Luca Visinelli showed that the duality symmetry can be carried over to the axion-electromagnetic theory as well. Assuming the existence of magnetic charges and axions, Maxwell's equations read

Name Equations
Gauss's law
Gauss's law for magnetism
Faraday's law
Ampère–Maxwell law
Axion law

Incorporating the axion has the effect of rotating the electric and magnetic fields into each other.

where the mixing angle depends on the coupling constant and the axion field strength

By plugging the new values for electromagnetic field and into Maxwell's equations we obtain the axion-modified Maxwell equations above. Incorporating the axion into the electromagnetic theory also gives a new differential equation – the axion law – which is simply the Klein-Gordon Equation (the quantum field theory equation for massive spin-zero particles) with an source term.

A term analogous to the one that would be added to Maxwell's equations to account for axions[12] also appears in recent (2008) theoretical models for topological insulators.[13] This term leads to several interesting predicted properties at the interface between topological and normal insulators.[14] In this situation the field θ describes something very different from its use in high-energy physics.[14]

Experiments

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.[15] A rotation claim[16] in 2006 was excluded by an upgraded setup.[17] An optimized search began in 2014.

Another technique is so called "light shining through walls",[18] where light passes through an intense magnetic field to convert photons into axions, that pass through metal. Experiments by BFRS and a team led by Rizzo ruled out an axion cause.[19] GammeV saw no events in a 2008 PRL. ALPS-I conducted similar runs,[20] setting new constraints in 2010; ALPS-II will run in 2014. OSQAR found no signal, limiting coupling[21] and will continue.

Several experiments search for astrophysical axions by the Primakoff effect, which converts axions to photons and vice versa in electromagnetic fields. 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. ADMX searches the galactic dark matter halo[22] for resonant axions with a cold microwave cavity and has excluded optimistic axion models in the 1.9-3.53 μeV range.[23][24][25] It is amidst a series of upgrades and is taking new data, including at 4.9-6.2 µeV. Other experiments of this type include HAYSTAC[26], CULTASK [27], and ORGAN[28]. HAYSTAC recently completed the first scanning run of a haloscope above 20 µeV[26].

Resonance effects may be evident in Josephson junctions[29] from a supposed high flux of axions from the galactic halo with mass of 0.11  meV and density 0.05 GeV⋅cm−3[30] compared to the implied dark matter density 0.3±0.1 GeV⋅cm−3, indicating said axions would only partially compose dark matter. The ORGAN experiment plans to conduct a direct test of this result via the haloscope method[28].

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.[31]

Axion-like bosons could have a signature in astrophysical settings. In particular, several recent works have proposed axion-like particles as a solution to the apparent transparency of the Universe to TeV photons.[32][33] It has also been demonstrated in a few recent works that, in the large magnetic fields threading the atmospheres of compact astrophysical objects (e.g., magnetars), photons will convert much more efficiently. This would in turn give rise to distinct absorption-like features in the spectra detectable by current telescopes.[34] A new promising means is looking for quasi-particle refraction in systems with strong magnetic gradients. In particular, the refraction will lead to beam splitting in the radio light curves of highly magnetized pulsars and allow much greater sensitivities than currently achievable.[35] The International Axion Observatory (IAXO) is a proposed fourth generation helioscope.[36]

Axions may be produced within neutron stars, by nucleon-nucleon bremsstrahlung. The subsequent decay of axions to gamma rays allows constraints on the axion mass to be placed from observations of neutron stars in gamma-rays using the Fermi LAT. From an analysis of 4 neutron stars, Berenji et al. obtained a 95% CL upper limit on the axion mass of 0.079 eV.[37]

Possible detection

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.[38][39] 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.[40]

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.[41]

In 2016 a theoretical team from MIT devised a possible way of detecting axions using a strong magnetic field. The magnetic field need be no stronger than that produced in a MRI scanning machine and it should show a slight wavering variation that is linked to the mass of the axion. The experiment is now being implemented by experimentalists at the university. Another approach being used by the University of Washington uses a strong magnetic field to detect the possible weak conversion of axions to microwaves.[42]

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 10−6 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 change to and from photons in magnetic fields.

Supersymmetry

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

The axino has been predicted to be the lightest supersymmetric particle in such a model.[43] In part due to this property, it is considered a candidate for dark matter.[44]

Cosmological implications

Theory suggests that axions were created abundantly during the Big Bang.[45] 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.

If axions have low mass, thus preventing other decay modes (since there's no lighter particles to decay into), theories predict that the universe would be filled with a very cold Bose–Einstein condensate of primordial axions. Hence, axions could plausibly explain the dark matter problem of physical cosmology.[46] Observational studies are underway, but they are not yet sufficiently sensitive to probe the mass regions if they are the solution to the dark matter problem. High mass axions of the kind searched for by Jain and Singh (2007)[47] 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.[48]

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.[49] The gravitational effects of these rings on galactic structure and rotation might then be observable.[50] 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 pronounced.

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

References

Notes

  1. ↑ Kim, J.E. (1979). "Weak-Interaction Singlet and Strong CP Invariance". Phys. Rev. Lett. 43 (2): 103–107. Bibcode:1979PhRvL..43..103K. doi:10.1103/PhysRevLett.43.103.
  2. ↑ Shifman, M.; Vainshtein, A.; Zakharov, V. (1980). "Can confinement ensure natural CP invariance of strong interactions?". Nucl. Phys. B166 (3): 493–506. Bibcode:1980NuPhB.166..493S. doi:10.1016/0550-3213(80)90209-6.
  3. ↑ Dine, M.; Fischler, W.; Srednicki, M. (1981). "A simple solution to the strong CP problem with a harmless axion". Phys. Lett. B104 (3): 199–202. Bibcode:1981PhLB..104..199D. doi:10.1016/0370-2693(81)90590-6.
  4. ↑ Zhitnitsky, A. (1980). "On possible suppression of the axion-hadron interactions". Sov. J. Nucl. Phys. 31: 260.
  5. ↑ Preskill, J.; Wise, M.; Wilczek, F. (6 January 1983). "Cosmology of the invisible axion" (PDF). Physics Letters B. 120 (1–3): 127–132. Bibcode:1983PhLB..120..127P. doi:10.1016/0370-2693(83)90637-8.
  6. ↑ Abbott, L.; Sikivie, P. (1983). "A cosmological bound on the invisible axion". Physics Letters B. 120 (1–3): 133–136. Bibcode:1983PhLB..120..133A. doi:10.1016/0370-2693(83)90638-X.
  7. ↑ Dine, M.; Fischler, W. (1983). "The not-so-harmless axion". Physics Letters B. 120 (1–3): 137–141. Bibcode:1983PhLB..120..137D. doi:10.1016/0370-2693(83)90639-1.
  8. ↑ Sikivie, P. (17 October 1983). "Experimental Tests of the "Invisible" Axion". Phys. Rev. Lett. 51 (16): 1413. Bibcode:1983PhRvL..51.1415S. doi:10.1103/physrevlett.51.1415.
  9. ↑ http://home.web.cern.ch/about/experiments/osqar
  10. ↑ Borsanyi, S.; et al. (2016). "Calculation of the axion mass based on high-temperature lattice quantum chromodynamics". Nature. 539 (69–71): 69–71. Bibcode:2016Natur.539...69B. PMID 27808190. doi:10.1038/nature20115.
  11. ↑ Castelvecchi, Davide (3 Nov 2016). "Axion alert! Exotic-particle detector may miss out on dark matter". Nature (journal).
  12. ↑ Wilczek, Frank (1987-05-04). "Two applications of axion electrodynamics". Physical Review Letters. 58 (18): 1799–1802. Bibcode:1987PhRvL..58.1799W. PMID 10034541. doi:10.1103/PhysRevLett.58.1799.
  13. ↑ Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng (2008-11-24). "Topological field theory of time-reversal invariant insulators". Physical Review B. 78 (19): 195424. Bibcode:2008PhRvB..78s5424Q. arXiv:0802.3537 Freely accessible. doi:10.1103/PhysRevB.78.195424.
  14. 1 2 Franz, Marcel (2008-11-24). "High-energy physics in a new guise". Physics. 1: 36. Bibcode:2008PhyOJ...1...36F. doi:10.1103/Physics.1.36.
  15. ↑ Maiani, L.; Petronzio, R.; Zavattini, E. (7 August 1986). "Effects of nearly massless, spin-zero particles on light propagation in a magnetic field" (PDF). Physics Letters B. 175 (3): 359–363. Bibcode:1986PhLB..175..359M. doi:10.1016/0370-2693(86)90869-5. CERN-TH.4411/86.
  16. ↑ Steve Reucroft, John Swain. Axion signature may be QED CERN Courier, 2006-10-05
  17. ↑ Zavattini, E.; Zavattini, G.; Ruoso, G.; Polacco, E.; Milotti, E.; Karuza, M.; Gastaldi, U.; Di Domenico, G.; Della Valle, F.; Cimino, R.; Carusotto, S.; Cantatore, G.; Bregant, M.; Pvlas, Collaboration (2006). "Experimental Observation of Optical Rotation Generated in Vacuum by a Magnetic Field" (PDF). Physical Review Letters. 96 (11): 110406. Bibcode:2006PhRvL..96k0406Z. PMID 16605804. arXiv:hep-ex/0507107 Freely accessible. doi:10.1103/PhysRevLett.96.110406.
  18. ↑ Ringwald, A. (16–21 October 2001). "Fundamental Physics at an X-Ray Free Electron Laser". Electromagnetic Probes of Fundamental Physics - Proceedings of the Workshop. Workshop on Electromagnetic Probes of Fundamental Physics. Erice, Italy. pp. 63–74. ISBN 978-981-238-566-6. arXiv:hep-ph/0112254 Freely accessible. doi:10.1142/9789812704214_0007.
  19. ↑ Robilliard, C.; Battesti, R.; Fouche, M.; Mauchain, J.; Sautivet, A.-M.; Amiranoff, F.; Rizzo, C. (2007). "No "Light Shining through a Wall": Results from a Photoregeneration Experiment". Physical Review Letters. 99 (19): 190403. Bibcode:2007PhRvL..99s0403R. PMID 18233050. arXiv:0707.1296 Freely accessible. doi:10.1103/PhysRevLett.99.190403.
  20. ↑ Ehret, Klaus; Frede, Maik; Ghazaryan, Samvel; Hildebrandt, Matthias; Knabbe, Ernst-Axel; Kracht, Dietmar; Lindner, Axel; List, Jenny; Meier, Tobias; Meyer, Niels; Notz, Dieter; Redondo, Javier; Ringwald, Andreas; Wiedemann, Günter; Willke, Benno (May 2010). "New ALPS results on hidden-sector lightweights". Phys. Lett. B. 689 (4–5): 149–155. Bibcode:2010PhLB..689..149E. arXiv:1004.1313 Freely accessible. doi:10.1016/j.physletb.2010.04.066.
  21. ↑ Pugnat, P.; Ballou, R.; Schott, M.; Husek, T.; Sulc, M.; Deferne, G.; Duvillaret, L.; Finger, M.; Finger, M.; Flekova, L.; Hosek, J.; Jary, V.; Jost, R.; Kral, M.; Kunc, S.; MacUchova, K.; Meissner, K. A.; Morville, J.; Romanini, D.; Siemko, A.; Slunecka, M.; Vitrant, G.; Zicha, J. (Aug 2014). "Search for weakly interacting sub-eV particles with the OSQAR laser-based experiment: results and perspectives". Eur Phys J C. 74 (8): 3027. Bibcode:2014EPJC...74.3027P. arXiv:1306.0443 Freely accessible. doi:10.1140/epjc/s10052-014-3027-8.
  22. ↑ Duffy, L. D.; Sikivie, P.; Tanner, D. B.; Bradley, R. F.; Hagmann, C.; Kinion, D.; Rosenberg, L. J.; Van Bibber, K.; Yu, D. B.; Bradley, R. F. (2006). "High resolution search for dark-matter axions". Physical Review D. 74: 12006. Bibcode:2006PhRvD..74a2006D. arXiv:astro-ph/0603108 Freely accessible. doi:10.1103/PhysRevD.74.012006.
  23. ↑ Asztalos, S. J.; Carosi, G.; Hagmann, C.; Kinion, D.; Van Bibber, K.; Hoskins, J.; Hwang, J.; Sikivie, P.; Tanner, D. B.; Hwang, J.; Sikivie, P.; Tanner, D. B.; Bradley, R.; Clarke, J.; ADMX Collaboration (2010). "SQUID-Based Microwave Cavity Search for Dark-Matter Axions". Physical Review Letters. 104 (4): 41301. Bibcode:2010PhRvL.104d1301A. PMID 20366699. arXiv:0910.5914 Freely accessible. doi:10.1103/PhysRevLett.104.041301.
  24. ↑ "ADMX | Axion Dark Matter eXperiment". Phys.washington.edu. Retrieved 2014-05-10.
  25. ↑ Phase 1 Results, dated 2006-03-04
  26. 1 2 Brubaker, B. M.; Zhong, L.; Gurevich, Y. V.; Cahn, S. B.; Lamoreaux, S. K.; Simanovskaia, M.; Root, J. R.; Lewis, S. M.; Al Kenany, S.; Backes, K. M.; Urdinaran, I.; Rapidis, N. M.; Shokair, T. M.; van Bibber, K. A.; Palken, D. A.; Malnou, M.; Kindel, W. F.; Anil, M. A.; Lehnert, K. W.; Carosi, G. (2017-02-09). "First Results from a Microwave Cavity Axion Search at 24  μeV". Physical Review Letters. American Physical Society (APS). 118 (6). ISSN 0031-9007. doi:10.1103/physrevlett.118.061302.
  27. ↑ Petrakou, Eleni (2017-02-13). "Haloscope searches for dark matter axions at the Center for Axion and Precision Physics Research". INSPIRE-HEP. Retrieved 2017-08-04.
  28. 1 2 McAllister, Ben T.; Flower, Graeme; Kruger, Justin; Ivanov, Eugene N.; Goryachev, Maxim; Bourhill, Jeremy; Tobar, Michael E. (2017-06-01). "The ORGAN Experiment: An axion haloscope above 15 GHz". arXiv.org e-Print archive. Retrieved 2017-08-04.
  29. ↑ Beck, Christian (December 2, 2013). "Possible Resonance Effect of Axionic Dark Matter in Josephson Junctions". Physical Review Letters. 111 (23): 1801. Bibcode:2013PhRvL.111w1801B. PMID 24476255. arXiv:1309.3790 Freely accessible. doi:10.1103/PhysRevLett.111.231801.
  30. ↑ Moskvitch, Katia. "Hints of cold dark matter pop up in 10-year-old circuit". New Scientist magazine (Reed Business Information). Retrieved 3 December 2013.
  31. ↑ Aprile, E.; et al. (9 September 2014). "First axion results from the XENON100 experiment". Phys. Rev. D 90, 062009. 90 (6): 062009. Bibcode:2014PhRvD..90f2009A. arXiv:1404.1455 Freely accessible. doi:10.1103/PhysRevD.90.062009.
  32. ↑ De Angelis, A.; Mansutti, O.; Roncadelli, M. (2007). "Evidence for a new light spin-zero boson from cosmological gamma-ray propagation?". Physical Review D. 76 (12): 121301. Bibcode:2007PhRvD..76l1301D. arXiv:0707.4312 Freely accessible. doi:10.1103/PhysRevD.76.121301.
  33. ↑ De Angelis, A.; Mansutti, O.; Persic, M.; Roncadelli, M. (2009). "Photon propagation and the very high energy gamma-ray spectra of blazars: How transparent is the Universe?". Monthly Notices of the Royal Astronomical Society: Letters. 394: L21–L25. Bibcode:2009MNRAS.394L..21D. arXiv:0807.4246 Freely accessible. doi:10.1111/j.1745-3933.2008.00602.x.
  34. ↑ Chelouche, Doron; Rabadan, Raul; Pavlov, Sergey S.; Castejon, Francisco (2009). "Spectral Signatures of Photon-Particle Oscillations from Celestial Objects". The Astrophysical Journal Supplement Series. 180: 1–29. Bibcode:2009ApJS..180....1C. arXiv:0806.0411 Freely accessible. doi:10.1088/0067-0049/180/1/1.
  35. ↑ Chelouche, Doron; Guendelman, Eduardo I. (2009). "COSMIC ANALOGS OF THE STERN-GERLACH EXPERIMENT AND THE DETECTION OF LIGHT BOSONS". The Astrophysical Journal. 699: L5–L8. Bibcode:2009ApJ...699L...5C. arXiv:0810.3002 Freely accessible. doi:10.1088/0004-637X/699/1/L5.
  36. ↑ "The International Axion Observatory". CERN. Retrieved March 19, 2016.
  37. ↑ Berenji, B.; Gaskins, J.; Meyer, M. (2016). "Constraints on axions and axionlike particles from Fermi Large Area Telescope observations of neutron stars". Physical Review D. 93 (14): 045019. Bibcode:2016PhRvD..93d5019B. arXiv:1602.00091 Freely accessible. doi:10.1103/PhysRevD.93.045019.
  38. ↑ Sample, Ian. "Dark matter may have been detected – streaming from sun’s core". www,theguardian.com. The Guardian. Retrieved 16 October 2014.
  39. ↑ Fraser, G. W.; Read, A. M.; Sembay, S.; Carter, J. A.; Schyns, E. (2014). "Potential solar axion signatures in X-ray observations with the XMM-Newton observatory". Monthly Notices of the Royal Astronomical Society. 445 (2): 2146–2168. ISSN 0035-8711. doi:10.1093/mnras/stu1865.
  40. ↑ Roncadelli, M.; Tavecchio, F. (2015). "No axions from the Sun". Monthly Notices of the Royal Astronomical Society: Letters. 450 (1): L26–L28. ISSN 1745-3925. doi:10.1093/mnrasl/slv040.
  41. ↑ Beck, Christian (2015). "Axion mass estimates from resonant Josephson junctions". Physics of the Dark Universe. 7–8: 6–11. Bibcode:2015PDU.....7....6B. arXiv:1403.5676 Freely accessible. doi:10.1016/j.dark.2015.03.002.
  42. ↑ "Team simulates a magnetar to seek dark matter particle". Retrieved 2016-10-09.
  43. ↑ Abe, Nobutaka; Takeo Moroi & Masahiro Yamaguchi (2002). "Anomaly-Mediated Supersymmetry Breaking with Axion". Journal of High Energy Physics. 1: 10. Bibcode:2002JHEP...01..010A. arXiv:hep-ph/0111155 Freely accessible. doi:10.1088/1126-6708/2002/01/010.
  44. ↑ Hooper, Dan; Lian-Tao Wang (2004). "Possible evidence for axino dark matter in the galactic bulge". Physical Review D. 70 (6): 063506. Bibcode:2004PhRvD..70f3506H. arXiv:hep-ph/0402220 Freely accessible. doi:10.1103/PhysRevD.70.063506.
  45. ↑ Redondo, J.; Raffelt, G.; Viaux Maira, N. (2012). "Journey at the axion meV mass frontier". Journal of Physics: Conference Series. 375 022004: 022004. doi:10.1088/1742-6596/375/1/022004.
  46. ↑ P. Sikivie,Dark matter axions,arXiv.
  47. ↑ P. L. Jain, G. Singh, Search for new particles decaying into electron pairs of mass below 100 MeV/c2, J. Phys. G: Nucl. Part. Phys., 34, 129–138, (2007); doi:10.1088/0954-3899/34/1/009, (possible early evidence of 7±1 and 19±1 MeV axions of less than 10−13 s lifetime).
  48. ↑ Salvio, Alberto; Strumia, Alessandro; Xue, Wei (2014). "Thermal axion production". JCAP. 2014 (1): 11. Bibcode:2014JCAP...01..011S. arXiv:1310.6982 Freely accessible. doi:10.1088/1475-7516/2014/01/011.
  49. ↑ P. Sikivie, "Dark matter axions and caustic rings"
  50. ↑ P. Sikivie (personal website): pictures of alleged triangular structure in Milky Way; hypothetical flow diagram which could give rise to such a structure.
  1. ↑ On a more technical note, the axion is the would-be Nambu–Goldstone boson that results from the spontaneously broken Peccei–Quinn symmetry. However, the non-trivial QCD vacuum effects (e.g., instantons) spoil the Peccei–Quinn symmetry explicitly and provide a small mass for the axion. Hence, the axion is actually a pseudo-Nambu–Goldstone boson.

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