In Particle Physics
* Motivation: Their existence is required by the Peccei-Quinn mechanism for enforcing strong PT symmetry; > s.a. neutron.
* Properties: A pseudoscalar, a negative-parity, spin-zero particle, a very light cousin of the neutral pion; Its mass and couplings are related to a parameter of the Peccei-Quinn theory; It is currently thought that its mass is likely to be less than a meV (based on SN1987A neutrino production), and more than a micro-eV (based on non-overproduction in the early universe); 2020, ADMX excludes 2.81–3.31 μeV range.
* Searches: The axion interacts directly with quarks and leptons, and indirectly with nucleons and photons; 2006, All of the current searches are based on the axion-photon interaction (the reason is related to the Primakoff effect); The PVLAS experiment reports seeing birefringence for laser photons in a magnetic field (best explained if a photon from the PVLAS laser combines with a photon in the vacuum to produce an axion); 2007, The PVLAS team failed to reproduce their results, says tiny rotation in the polarization of laser light that they reported last year does not support the existence of axions, but rather is an artefact related to how the experiment had been performed; New experiments question usefulness of other planned experiments.
@ General references: Sikivie PT(96)dec [pool-table analogy]; Raffelt JPA(07) [rev]; Alves et al BJP(17)-a1703 [maximum-entropy inferences].
@ Experimental searches: Collar et CAST he/03-conf; news pw(04)nov [CAST]; Sikivie hp/06-conf [and bounds]; news pw(06)jul [PVLAS collaboration experiment]; van Bibber & Rosenberg PT(06)aug; Bignami & Dupays pw(06)nov [PVLAS signal]; Mohapatra & Nasri PRL(07) + pw(07)feb [reconciling PVLAS and CAST's findings]; news pw(07)jul [PVLAS follow-up]; news pw(07)nov [new results question merit of experiments]; Carosi et al CP(08); Melissinos PRL(09) [proposed optical-cavity search]; Chou a1009-proc [rev]; Avignone Phy(18), news sn(20)mar [current searches and the ADMX]; news Phy(20)may [photon-photon collisions].
@ Phenomenology: Csáki et al PRL(02) [photon-axion oscillation and supernova dimming]; Andrianov et al PLB(10)-a0912 [particle propagation in pseudoscalar background]; Belikov et al PRD(11)-a1007 [no evidence of photon-axion oscillation in gamma-ray spectra]; Beck PhyC-a1008 [analogue simulation using superconducting electronic devices]; Balakin & Popov PRD(15)-a1509 [spinor-axion coupling]; Mendonça et al a1901 [production in unstable magnetized plasmas].
@ In solids: Wilczek PRL(87) [action and effects]; Qi et al PRB(08) + Franz Phy(08) [in topological insulators]; Gooth et al Nat(19)oct + news sn(19)oct [electrons in a Weyl semimetal].

Theory > s.a. physics beyond the standard model; supersymmetric theories [axionic extension of standard model].
* Idea: A theory of a 2-form B (Kalb-Ramond field), with field strength the 3-form H = dB (axion field), and equations of motion d*H = 0 and the Bianchi identity dH = 0; 2004, They are a viable dark-matter candidate.
* Action: In 4 dimensions, it is

S = (1/16) H ∧ *H = (1/16π) Habc Habc dv .

* Symmetry: B \(\mapsto\) B + dA, with A a 1-form; The axion is massless if this symmetry is exact.
* Degrees of freedom: In D-dimensional spacetime, B has (D−3)(D−2)/2 physical degrees of freedom; Thus, in D = 4, it is equivalent to a (free massless) scalar field φ, with *H = dφ.
* Axion charge: Inside a closed 2-surface S = ∂V,

q = S B = V H = V *dφ .

* Axionic black holes: They can have axionic charge if non-static; Use the same metric as without axions, H = φ = 0, but B belongs to H2(M; \(\mathbb R\)) (can tell only if something couples to B); > s.a. black-hole hair.
@ References: Turner PRP(90); Srednicki ht/02-in [rev]; Svrček & Witten JHEP(06) [in string theory]; Balakin & Ni CQG(10)-a0909 [coupling to photons]; Kim & Carosi RMP(10) [and the strong CP problem]; Quevillon & Smith EPJC(19)-a1903 [couplings to gauge bosons].
> Related topics: see Axino; dilaton [axion-dilaton gravity].

And Astrophysics / Cosmology > s.a. quintessence; star formation and evolution; types of dark matter.
* 1996: Considered as dark-matter candidates, but the window appears to be very small.
* 2002: Considered as a possible explanation for the dimming of supernovas, alternative to universal acceleration.
* 2006: Combined constraints suggest that its mass is bounded by 1 μeV < ma < 3 meV.
* 2007: Absence of X-rays from axion decays in galaxy clusters leads to estimate τ > 1023 s.
* 2010: No evidence of photon-axion oscillation in gamma-ray spectra from AGILE and Fermi data.
@ General references: Massó & Redondo JCAP(05) [evading bounds]; Raffelt JPA(07) [rev]; Wantz & Shellard PRD(10)-a0910; Roncadelli et al JPCS(12)-a1207; news sn(20)mar [as solution to dark matter, CP violation, and baryon asymmetry problems].
@ Cosmology, theory: Kim ap/98-conf, ap/98-conf, proc(00)ap; Sikivie LNP(08)ap/06 [rev]; Mack JCAP(11)-a0911 [inflation]; Corianò et al PRD(10) [gauged axion]; Marsh PRP(16)-a1510 [rev]; Vagenas KJS-a1710 [as dark energy particle].
@ Cosmology, observation: Hannestad et al a0911-proc [bounds]; Ralston AIP(10)-a1011 [and isotropy]; Cadamuro at el JCAP(11) [bounds on sub-MeV axions].
@ As cold-dark-matter candidate: Hwang & Noh PLB(09)-a0902; Duffy & van Bibber NJP(09)-a0904; Sikivie PLB(11)-a1003, a1210-conf; Ringwald a1310-conf; Noh et al PLB(13) [using second-order cosmological perturbations]; Berezhiani & Khoury PLB(16)-a1506 [with superfluid behavior in galaxies]; Ajello et Fermi-LAT PRL(16) + news upi(16)apr [axion-like particles not found]; Ringwald a1612-proc [rev].
@ Axion stars: Iwazaki PLB(00) [and X-rays], PLB(00) [and uhe cosmic rays]; Barranco & Bernal PRD(11)-a1001 [self-gravitating systems]; Eby et al MPLA(16)-a1512 [decay]; > s.a. types of black holes.
@ Searches: Hagmann et al PRL(98); Fairbairn et al PRL(07) + pn(07)may [indirect, from transparency of Sun to photons]; Grin et al PRD(07) [from 2-photon decay]; Riemer-Sørensen et al PRL(07)ap/07 [bound on lifetime from galaxy cluster X-ray emission]; Burrage et al PRL(09), Pettinari & Crittenden PRD(10) [AGNs]; Sánchez-Conde et al eConf-a1001; Budker et al PRX(14)-a1306 [Cosmic Axion Spin Precession Experiment (CASPEr)]; Beck PRL(13) [superconducting detectors]; Ringwald a1506-conf; Redondo a1601-conf [International AXion Observatory (IAXO)]; van Bibber et al PT(19)jun; Aprile et al PRL(19) [XENON1T experiment].
@ Evidence, gamma rays: Roncadelli et al AIP(08)-a0902 [propagation]; Sánchez-Conde et al PRD(09)-a0905; De Angelis et al PRD(11).
@ Related topics: Raffelt et al PRD(12) [supernovae, white dwarves, and meV-mass axions]; Erken et al PRL(12) + news pw(12)feb [proposed solution of the Li-7 problem]; Isern et al a1204-proc, Melendez et al a1210-proc [and white-dwarf evolution]; Córsico et al JCAP(12) [mass bound from white-dwarf cooling rates]; Friedland et al PRL(13) [limit on the strength of the axion-photon coupling from massive star evolution]; Arvanitaki et al PRD(17) [evidence from gap in the black-hole mass vs spin distribution in Advanced LIGO].

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