#### Invisible ${{\mathit A}^{0}}$ (Axion) Limits from Photon Coupling

Limits are for the modulus of the axion-two-photon coupling $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ defined by $\mathit L~=~−\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }\phi _{\mathit A}\mathbf {E}\mathbf {\cdot{}}\mathbf {B}$. For scalars ${{\mathit S}^{0}}$ the limit is on the coupling constant in $\mathit L~=~\mathit G_{ {{\mathit S}} {{\mathit \gamma}} {{\mathit \gamma}} }\phi _{S}(\mathbf {E}{}^{2}−\mathbf {B}{}^{2}$). The relation between $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ and ${\mathit m}_{{{\mathit A}^{0}}}$ is not used unless stated otherwise, i.e., many of these bounds apply to low-mass axion-like particles (ALPs), not to QCD axions.
VALUE (GeV${}^{-1}$) CL% DOCUMENT ID TECN  COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
$<9.2 \times 10^{-11}$ 95 1
 2021
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $3.6 \times 10^{-21}$ eV
$<1.8 \times 10^{-10}$ 95 2
 2021
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $2 - 6 \times 10^{-7}$ eV
$<1.6 \times 10^{-10}$ 95 3
 2021 A
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1 - 570$ keV
$<5 \times 10^{-11}$ 95 4
 2021
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $8 - 23$ neV
$<1.2 \times 10^{-4}$ 95 5
 2021
LASR ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.4 - 600$ meV
$<1.2 \times 10^{-11}$ 95 6
 2021 B
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.5 - 500$ neV
7
 2021
ASTR Magnetars
$<1 \times 10^{-13}$ 95 8
 2021
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $2.7 - 5.3$ eV
$<1.8 \times 10^{-11}$ 95 9
 2021
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $3.5 \times 10^{-11}$eV
$<7 \times 10^{-4}$ 95 10
 2020
BEL2 ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.2 - 1$ GeV
$<2 \times 10^{-4}$ 90 11
 2020 A
NA64 ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 55 MeV
$<1.0 \times 10^{-11}$ 95 12
 2020
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 3 neV
$<5 \times 10^{-10}$ 13
 2020
ASTR ${\mathit m}_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $10^{-11}$ eV
14
 2020
ASTR Globular clusters
$2 - 4 \times 10^{-10}$ 95 15
 2020 A
ASTR Solar axions
16
 2020
COSM Axion-like particles
$<3.6 \times 10^{-12}$ 95 17
 2020 A
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $5 \times 10^{-11}$ eV
18
 2020
ANIT Axion-like particles
$4 - 6 \times 10^{-10}$ 90 19
 2020
ASTR Solar axions
$<2.8 \times 10^{-11}$ 95 20
 2020
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = 25 eV
$\text{none } 6.0 \times 10^{-9} - 1.3 \times 10^{-5}$ 21
 2020 A
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 270 MeV
$<2.6 \times 10^{-11}$ 95 22
 2020
FLAT ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $3 \times 10^{-10}$ eV
$<8.4 \times 10^{-8}$ 99 23
 2020
COSM ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $4 \times 10^{-6}$ eV
$<1 \times 10^{-3}$ 95 24
 2019
PRMX ${\mathit m}_{{{\mathit A}^{0}}}$ = 0.16 GeV
$<1.4 \times 10^{-14}$ 95 25
 2019
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $5 \times 10^{-24}$ eV
$<9.6 \times 10^{-14}$ 95 26
 2019
CMB ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-22}$ eV
$<7 \times 10^{-13}$ 95 27
 2019
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $5 \times 10^{-23}$ eV
$<4 \times 10^{-11}$ 95 28
 2019
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $1.2 \times 10^{-7}$ eV
29
 2018
ASTR Axion-like particles
$<5.0 \times 10^{-3}$ 90 30
 2018
LSW ${\mathit m}_{{{\mathit A}^{0}}}$ = $46 - 1020$ eV
$<1 \times 10^{-11}$ 99.9 31
 2018
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.6 - 4$ neV
32
 2017
CMB Axion-like particles
$<6.6 \times 10^{-11}$ 95 33
 2017
CAST ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 0.02 eV
34
 2017
RVUE Axion-like particles
$<2.51 \times 10^{-4}$ 95 35
 2017
LSW ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 0.1 eV
$>1.5 \times 10^{-11}$ 95 36
 2017
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.7 - 50$ neV
$<2.6 \times 10^{-12}$ 95 37
 2017
ASTR ${\mathit m}_{{{\mathit A}^{0}}}{}\leq{}$ $10^{-13}$ eV
$<6 \times 10^{-13}$ 38
 2017
COSM ${\mathit m}_{{{\mathit A}^{0}}}{}\leq{}$ $10^{-15}$ eV
$<5 \times 10^{-12}$ 95 39
 2016
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.5 - 5$ neV
$<1.2 \times 10^{-7}$ 95 40
 2016
LASR ${\mathit m}_{{{\mathit A}^{0}}}$ = 1.3 meV
$<7.2 \times 10^{-8}$ 95 41
 2016
LASR ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 0.5 meV
$<8 \times 10^{-4}$ 42
 2016
ALPS ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.1 - 100$ GeV
$<6 \times 10^{-21}$ 43
 2016
${\mathit m}_{{{\mathit S}^{0}}}$ $<$ $10^{-18}$ eV
44
 2015
CAST Chameleons
$<1.47 \times 10^{-10}$ 95 45
 2015
CAST ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.39 - 0.42$ eV
$<3.5 \times 10^{-8}$ 95 46
 2015
LSW ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $2 \times 10^{-4}$ eV
47
 2015
ASTR ${\mathit m}_{{{\mathit S}^{0}}}$ $<$ $4 \times 10^{-12}$ eV
$<5.42 \times 10^{-4}$ 95 48
 2015
LASR ${\mathit m}_{{{\mathit A}^{0}}}$ = 0.15 eV
49
 2015
COSM Axion-like particles
50
 2015
Dilaton-like dark matter
$<4.1 \times 10^{-10}$ 99.7 51
 2015
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.6 - 185$ eV
$<3.3 \times 10^{-10}$ 95 52
 2014
CAST ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.64 - 1.17$ eV
$<6.6 \times 10^{-11}$ 95 53
 2014
ASTR Globular clusters
$<1.4 \times 10^{-7}$ 95 54
 2014
LASR ${\mathit m}_{{{\mathit A}^{0}}}$ = 1 meV
55
 2014
COSM ${\mathit m}_{{{\mathit A}^{0}}}$ = $2.66 - 48.8$ $\mu$eV
$<8 \times 10^{-8}$ 95 56
 2014
LSW ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 0.3 meV
$<1 \times 10^{-11}$ 57
 2014
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $1 \times 10^{-10}$ eV
$<2.1 \times 10^{-11}$ 95 58
 2013 A
IACT ${\mathit m}_{{{\mathit A}^{0}}}$ = $15 - 60$ neV
$<2.15 \times 10^{-9}$ 95 59
 2013
EDEL ${\mathit m}_{{{\mathit A}^{0}}}<$ 200 eV
$<4.5 \times 10^{-8}$ 95 60
 2013
LSW ${\mathit m}_{{{\mathit A}^{0}}}$ = $7.2 \times 10^{-6}$ eV
$<8 \times 10^{-11}$ 61
 2013
ASTR Red giants
$>2 \times 10^{-11}$ 62
 2013
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $1 \times 10^{-7}$ eV
$<8.3 \times 10^{-12}$ 95 63
 2013
ASTR ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $7 \times 10^{-12}$ eV
64
 2012
COSM Axion-like particles
$<2.5 \times 10^{-13}$ 95 65
 2012
ASTR ${\mathit m}_{{{\mathit A}^{0}}}<4.2 \times 10^{-14}$ eV
$<2.3 \times 10^{-10}$ 95 66
 2011
CAST ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.39 - 0.64$ eV
$<6.5 \times 10^{-8}$ 95 67
 2010
ALPS ${\mathit m}_{{{\mathit A}^{0}}}<$ 0.7 meV
$<2.4 \times 10^{-9}$ 95 68
 2009 A
CDMS ${\mathit m}_{{{\mathit A}^{0}}}<$ 100 eV
$<1.2 - 2.8 \times 10^{-10}$ 95 69
 2009
CAST ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.02 - 0.39$ eV
70
 2009
Chameleons
$<7 \times 10^{-10}$ 71
 2009
ASTR ${\mathit m}_{{{\mathit A}^{0}}}<$ few keV
$<1.3 \times 10^{-6}$ 95 72
 2008
${\mathit m}_{{{\mathit S}^{0}}}<$ 1 meV
$<3.5 \times 10^{-7}$ 99.7 73
 2008
${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 0.5 meV
$<1.1 \times 10^{-6}$ 99.7 74
 2008
${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 1 meV
$<5.6 - 13.4 \times 10^{-10}$ 95 75
 2008
${\mathit m}_{{{\mathit A}^{0}}}$ = $0.84 - 1.00$ eV
$<5 \times 10^{-7}$ 76
 2008
${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 1 meV
$<8.8 \times 10^{-11}$ 95 77
 2007
CAST ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 0.02 eV
$<1.25 \times 10^{-6}$ 95 78
 2007
${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 1 meV
$2 - 5 \times 10^{-6}$ 79
 2006
${\mathit m}_{{{\mathit A}^{0}}}$ = $1 - 1.5$ meV
$<1.1 \times 10^{-9}$ 95 80
 2002
${\mathit m}_{{{\mathit A}^{0}}}$= $0.05 - 0.27$ eV
$<2.78 \times 10^{-9}$ 95 81
 2002 B
${\mathit m}_{{{\mathit A}^{0}}}<$1 keV
$<1.7 \times 10^{-9}$ 90 82
 2001 B
${\mathit m}_{{{\mathit A}^{0}}}<$100 eV
$<1.5 \times 10^{-4}$ 90 83
 2000 B
NOMD ${\mathit m}_{{{\mathit A}^{0}}}<$40 eV
84
 2000
THEO induced ${{\mathit \gamma}}$ coupling
$<2.7 \times 10^{-9}$ 95 85
 1998
SLAX ${\mathit m}_{{{\mathit A}^{0}}}<1$ keV
$<6.0 \times 10^{-10}$ 95 86
 1998
${\mathit m}_{{{\mathit A}^{0}}}<0.03$ eV
$<3.6 \times 10^{-7}$ 95 87
 1993
${\mathit m}_{{{\mathit A}^{0}}}<10^{-3}$ eV, optical rotation
$<6.7 \times 10^{-7}$ 95 88
 1993
${\mathit m}_{{{\mathit A}^{0}}}<10^{-3}$ eV, photon regeneration
$<3.6 \times 10^{-9}$ 99.7 89
 1992
${\mathit m}_{{{\mathit A}^{0}}}<0.03$ eV
$<7.7 \times 10^{-9}$ 99.7 89
 1992
${\mathit m}_{{{\mathit A}^{0}}}$= eV
$<7.7 \times 10^{-7}$ 99 90
 1992
${\mathit m}_{{{\mathit A}^{0}}}<10^{-3}$ eV
$<2.5 \times 10^{-6}$ 91
 1990
${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $7 \times 10^{-4}$ eV
 1 BASU 2021 searched for birefringence induced by axion dark matter using multiple images of the polarized source in the strongly gravitationally lensed system CLASS B1152+199. They assume the axion makes up all dark matter, and used the axion density in the emitting region, ${{\mathit \rho}_{{A}}}$ = 20 GeV/cm${}^{3}$. Limits between $9.2 \times 10^{-11} - 7.7 \times 10^{-8}$ GeV${}^{-1}$ are obtained for ${\mathit m}_{{{\mathit A}^{0}}}$ = $3.6 \times 10^{-21} - 4.6 \times 10^{-18}$eV. See their Fig. 2 for mass-dependent limits.
 2 BI 2021 look for the gamma-ray spectral distortions induced by axion-photon oscillations in the presence of the Galactic magnetic field, using the measurements of sub-PeV gamma-rays from the Crab Nebula by the Tibet AS${{\mathit \gamma}}$ and HAWC experiments, together with MAGIC and HEGRA gamma-ray data. See their Fig. 3 for mass-dependent limits.
 3 DOLAN 2021A study the effect of axion production on the evolution of asymptotic giant branch stars, and use the white-dwarf initial-final mass relation to set the limits. See their Fig. 1 for mass-dependent limits.
 4 GUO 2021 is analogous to AJELLO 2016 , and use the Fermi-LAT and H.E.S.S. II measurements of PG 1553+113 and PKS 2155-304. See their Fig. 6 for mass-dependent limits.
 5 HOMMA 2021 look for the production of axion resonance states and their subsequent stimulated decays by combining linearly polarized creation laser pulses and circularly polarized inducing laser pulses. The quoted limit is at ${\mathit m}_{{{\mathit A}^{0}}}$ $\simeq{}$ 0.178 eV. See their Fig. 14 for mass-dependent limits.
 6 LI 2021B is analogous to AJELLO 2016 , and use the spectra of the blazar Mrk 421 measured by ARGO-YBJ and Fermi-LAT. They consider ALP-photon mixing in the magnetic fields of both the blazar jet and the Galaxy. The quoted limit applies to ${\mathit m}_{{{\mathit A}^{0}}}$ $\simeq{}$ $1 \times 10^{-9}$ eV. See their Fig. 5 for mass-dependent limits.
 7 LLOYD 2021 is analogous to FORTIN 2018 , and set limits on the product of the axion couplings to photons and nucleons as $\mathit g_{ {{\mathit A}} {{\mathit N}} {{\mathit N}} }$ $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }{ {}\lesssim{} }$ $4.6 \times 10^{-19}$ GeV${}^{-1}$ for ${\mathit m}_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $10^{-5}$ eV by using the quiescent soft gamma-ray flux upper limits in five magnetars. We use $\mathit g_{ {{\mathit A}} {{\mathit N}} {{\mathit N}} }$ = $\mathit G_{ {{\mathit A}} {{\mathit N}} }$ 2${\mathit m}_{{{\mathit N}}}$ to translate their limits. See their Table II and Fig. 3 for the limits.
 8 REGIS 2021 look for monochromatic photons from axion decay, using the MUSE spectroscopic data on the Leo T dwarf spheroidal galaxy. They assume that axions make up all of dark matter and use the integrated dark matter density along the line of sight determined by observations.
 9 XIAO 2021 use X-ray data from Betelgeuse to look for signals from axions produced in the stellar core that were converted to X-rays by the Galactic magnetic field. See their Fig. 1 for the mass-dependent limit.
 10 ABUDINEN 2020 look for the process ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit A}^{0}}$ ( ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ ) and set upper limits of around $10^{-3}$ over the mass range. The quoted limit is at ${\mathit m}_{{{\mathit A}^{0}}}$ = 0.3 GeV. See their Fig. 5 for mass dependent limits.
 11 BANERJEE 2020A look for axions produced from high-energy bremsstrahlung photons through the Primakoff effect with the electric field of the target nuclei. They exclude $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$= $2 \times 10^{-4} - 0.05$ GeV${}^{-1}$ for ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 55 MeV. See their Fig. 5 for mass-dependent limits.
 12 BUEHLER 2020 look for the ${{\mathit \gamma}}$ -ray transparency due to axion-photon oscillations using high-energy photon events from 79 sources in the Second Fermi-LAT Catalog of High-Energy Sources. The quoted limit is for the intergalactic magnetic field strength and coherence length of $\mathit B$ = 1 nG and $\mathit s$ = 1 Mpc. See their Figs. 4 and 5 for mass-dependent limits and for different magnetic-field parameters.
 13 CALORE 2020 use the isotropic diffuse ${{\mathit \gamma}}$ -ray background measured by the Fermi-LAT to constrain the ${{\mathit \gamma}}$ -ray flux converted in the Galactic magnetic field from axions produced from past core-collapse supernovae. They also derive a limit on a heavier axion with ${\mathit m}_{{{\mathit A}^{0}}}{ {}\gtrsim{} }$ keV decaying into two photons of $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }{ {}\lesssim{} }$ $5 \times 10^{-11}$ GeV${}^{-1}$ for ${\mathit m}_{{{\mathit A}^{0}}}$ = 5 keV. See their Figs. 5 and 7 for the limits as well as limits in the presence of axion-nucleon couplings.
 14 CARENZA 2020 extend the globular cluster bound of AYALA 2014 to heavier masses (${\mathit m}_{{{\mathit A}^{0}}}{}\leq{}$ a few 100 keV) by taking account of the coalescence process ${{\mathit \gamma}}$ ${+}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit A}^{0}}$ as well as the decay of the ALP inside the stellar core. See their Fig.4 for mass-dependent limits.
 15 DENT 2020A is analogous to GAO 2020 . The quoted limit is from their arXiv:2006.15118v3 (v2 is their published version), using the relativistic Hartree-Fock form factor. The limit is up to two times weaker than the published one. See Fig. 4 in their arXiv version 3 for the correlation between $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ and $\mathit g_{ {{\mathit A}} {{\mathit e}} {{\mathit e}} }$ corresponding to the excess reported in APRILE 2020 .
 16 DEPTA 2020 correct the underestimated ${}^{}\mathrm {D}$ abundance in MILLEA 2015 , and derive robust cosmological bounds by allowing the reheating temperature, $\mathit N_{{\mathrm {eff}}}$, and neutrino chemical potential to vary. See their Fig. 6 for mass-dependent limits.
 17 DESSERT 2020A use the NuSTAR data of the Quintuplet and Westerlund 1 super star clusters to look for X-rays converted in the Galactic magnetic field from the axions produced in stellar cores. See their Fig. 3 for the mass-dependent limits.
 18 ESTEBAN 2020 show that the two anomalous ANITA events can be explained by the reflected radio pulses that are resonantly produced in the ionosphere via axion-photon conversion for ${\mathit m}_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $1 \times 10^{-7}$ eV , if an axion clump passes the Earth about once a month. See their Fig.5 for the region consistent with this interpretation for different values of the axion density inside the clumps.
 19 GAO 2020 correct the limit of APRILE 2020 by including inverse Primakoff scattering in the XENON1T detector. The quoted limit is from their arXiv:2006.14598v4 (v3 is their published version), taking account of the atomic form factor of ${}^{}\mathrm {Xe}$ as pointed out in ABE 2020J. The limit is weaker by a factor of $1.5 - 2$ than the published one. See Fig. 3 in their arXiv version 4 for correlation between $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ and $\mathit g_{ {{\mathit A}} {{\mathit e}} {{\mathit e}} }$ corresponding to the excess reported in APRILE 2020 .
 20 KOROCHKIN 2020 assume the axion makes up all dark matter, and look for a dip in the observed gamma-ray spectrum of the blazer 1ES 1218+304 by Fermi/LAT and VERITAS due to the extragalactic background light produced by the axion decay. Their analysis favors nonzero axion-induced absorption with $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ = $3 \times 10^{-11} - 2 \times 10^{-10}$ GeV${}^{-1}$ over a range of ${\mathit m}_{{{\mathit A}^{0}}}$ = $2 - 18$ eV. See their Fig. 1 for mass-dependent limits between 0.25 $<$ ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 25 eV.
 21 LUCENTE 2020A study the SN 1987A energy-loss argument on the axion-like particle production. In addition to the Primakoff process, they take account of photon coalescence as well as gravitational trapping that become relevant at ${\mathit m}_{{{\mathit A}^{0}}}$ $>$ 100 MeV. See their Fig. 12 for the mass-dependent limit.
 22 MEYER 2020 look for prompt $\gamma$-rays converted in the Galactic magnetic fields from axions produced via the Primakoff process in a sample of 20 extragalactic core-collapse supernovae. The limits assume a progenitor mass of 10 times the solar mass and certain models for the optical emission and the galactic magnetic field. See their Figs. 2 and 6 in the erratum for mass- and model-dependent limits.
 23 YAMAMOTO 2020 look for X-ray photons converted by the Earth's magnetic field from the axions produced by the two-body decay of dark matter, and set the limits by using the Suzaku data. The quoted limit is for the monochromatic X-ray line from the galactic dark matter with lifetime $\tau$ = $4.32 \times 10^{17}$ sec. They also derive limits on the continuum spectrum from the extragalactic component. See their Fig. 7 for the limits.
 24 ALONI 2019 used the data collected by the PRIMEX experiment to derive a limit based on a data-driven method. See their Fig. 2 for mass-dependent limits.
 25 CAPUTO 2019 look for an oscillating variation of the polarization angle of the pulsar J0437-4715, where they assume the local axion energy density ${{\mathit \rho}_{{A}}}$ = 0.3 GeV/cm${}^{3}$. See their Fig. 2 for mass-dependent limits for $5 \times 10^{-24}$ eV ${}\leq{}{\mathit m}_{{{\mathit A}^{0}}}{}\leq{}$ $2 \times 10^{-19}$ eV.
 26 FEDDERKE 2019 look for a uniform reduction of the CMB polarization at large scales, which is induced by the oscillating axion background during CMB decoupling. The quoted limit is based on the assumption that axions make up all of the dark matter. See their Fig. 3 for mass-dependent limits for ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-22} - 10^{-19}$ eV.
 27 IVANOV 2019 look for the axion-induced periodic changes in the polarization angle of parsec-scale jets in active galactic nuclei observed by the MOJAVE program, where they use the axion energy density ${{\mathit \rho}_{{A}}}$ = 20 GeV/cm${}^{3}$. See their Fig. 6 for mass-dependent limits for $5 \times 10^{-23}$ eV ${}\leq{}{\mathit m}_{{{\mathit A}^{0}}}{}\leq{}$ $1.2 \times 10^{-21}$ eV.
 28 LIANG 2019 look for spectral irregularities in the spectrum of 10 bright H.E.S.S. sources in the Galactic plane, assuming photon-ALP mixing in the Galactic magnetic fields. See their Fig. 2 for mass-dependent limits with different Galactic magnetic field models.
 29 FORTIN 2018 studied the conversion of axion-like particles produced in the core of a magnetar to hard X-rays in the magnetosphere. See their Fig. 5 for mass-dependent limits with different values of the magnetar core temperature.
 30 YAMAJI 2018 search for axions with an x-ray LSW at Spring-8, using the Laue-case conversion in a silicon crystal. They also obtain $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ $<$ $4.2 \times 10^{-3}$ GeV${}^{-1}$ for ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 10 eV. See their Fig. 5 for mass-dependent limits.
 31 ZHANG 2018 look for spectral irregularities in the spectrum of PKS 2155-304 measured by Fermi LAT, assuming photon-ALP mixing in the intercluster and Galactic magnetic fields. See their Figs. 2 and 3 for mass-dependent limits with different values of the intercluster magnetic field parameters.
 32 ADE 2017 look for cosmic birefringence from axion-like particles using CMB polarization data taken by the BICEP2 and Keck Array experiments. They set a limit $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }\mathit H_{I}$ $<$ $0.072$ at 95 $\%$CL for ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $10^{-28}$ eV, where $\mathit H_{I}$ is the Hubble parameter during inflation.
 33 ANASTASSOPOULOS 2017 looked for solar axions by the CAST axion helioscope in the vacuum phase, and supersedes ANDRIAMONJE 2007 .
 34 DOLAN 2017 update existing limits on $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ for axion-like particles. The limits from the proton beam dump experiments in their Fig. 2 contained an error, and the corrected version is shown in Fig. 1 of DOLAN 2021 .
 35 INADA 2017 search for axions with an x-ray LSW at Spring-8. See their Fig. 4 for mass-dependent limits.
 36 KOHRI 2017 attributed to axion-photon oscillations the excess of cosmic infrared background observed by the CIBER experiment. See their Fig. 5 for the region preferred by their scenario.
 37 MARSH 2017 is similar to WOUTERS 2013 , using Chandra observations of M87. See their Fig. 6 for mass-dependent limits.
 38 TIWARI 2017 use observed limits of the cosmic distance-duality relation to constrain the photon-ALP mixing based on 3D simulations of the magnetic field configuration. The quoted value is for the averaged magnetic field of 1nG with a coherent length of 1 Mpc. See their Fig. 5 for mass-dependent limits.
 39 AJELLO 2016 look for irregularities in the energy spectrum of the NGC1275 measured by Fermi LAT, assuming photon-ALP mixing in the intra-cluster and Galactic magnetic fields. See their Fig. 2 for mass-dependent limits.
 40 DELLA-VALLE 2016 look for the birefringence induced by axion-like particles. See their Fig. 14 for mass-dependent limits.
 41 DELLA-VALLE 2016 look for the dichroism induced by axion-like particles. See their Fig. 14 for mass-dependent limits.
 42 JAECKEL 2016 use the LEP data of ${{\mathit Z}}$ $\rightarrow$ 2 ${{\mathit \gamma}}$ and ${{\mathit Z}}$ $\rightarrow$ 3 ${{\mathit \gamma}}$ to constrain the ALP production via ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit A}^{0}}$ ${{\mathit \gamma}}$ ( ${{\mathit A}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ ), assuming the ALP coupling with two hypercharge bosons. See their Fig. 4 for mass-dependent limits.
 43 LEEFER 2016 derived limits by using radio-frequency spectroscopy of dysprosium and atomic clock measurements. See their Fig. 1 for mass-dependent limits as well as limits on Yukawa-type couplings of the scalar to the electron and nucleons.
 44 ANASTASSOPOULOS 2015 search for solar chameleons with CAST and derived limits on the chameleon coupling to photons and matter. See their Fig. 12 for the exclusion region.
 45 ARIK 2015 is analogous to ARIK 2009 , and search for solar axions for ${\mathit m}_{{{\mathit A}^{0}}}$ around 0.2 and 0.4 eV. See their Figs. 1 and 3 for the mass-dependent limits.
 46 Based on OSQAR photon regeneration experiment. See their Fig. 6 for mass-dependent limits on scalar and pseudoscalar bosons.
 47 BRAX 2015 derived limits on conformal and disformal couplings of a scalar to photons by searching for a chaotic absorption pattern in the X-ray and UV bands of the Hydra A galaxy cluster and a BL lac object, respectively. See their Fig. 8.
 48 HASEBE 2015 look for an axion via a four-wave mixing process at quasi-parallel colliding laser beams. They also derived limits on a scalar coupling to photons $\mathit G_{ {{\mathit S}} {{\mathit \gamma}} {{\mathit \gamma}} }$ $<$ $2.62 \times 10^{-4}$ GeV${}^{-1}$ at ${\mathit m}_{{{\mathit S}^{0}}}$ = 0.15 eV. See their Figs. 11 and 12 for mass-dependent limits.
 49 MILLEA 2015 is similar to CADAMURO 2012 , including the Planck data and the latest inferences of primordial deuterium abundance. See their Fig. 3 for mass-dependent limits.
 50 VANTILBURG 2015 look for harmonic variations in the dyprosium transition frequency data, induced by coherent oscillations of the fine-structure constant due to dilaton-like dark matter, and set the limits, $\mathit G_{ {{\mathit S}} {{\mathit \gamma}} {{\mathit \gamma}} }$ $<$ $6 \times 10^{-27}$ GeV${}^{-1}$ at ${\mathit m}_{{{\mathit S}^{0}}}$ = $6 \times 10^{-23}$ eV. See their Fig. 4 for mass-dependent limits between $1 \times 10^{-24}<$ ${\mathit m}_{{{\mathit S}^{0}}}<$ $1 \times 10^{-15}$ eV.
 51 VINYOLES 2015 performed a global fit analysis based on helioseismology and solar neutrino observations. See their Fig. 9.
 52 ARIK 2014 is similar to ARIK 2011 . See their Fig. 2 for mass-dependent limits.
 53 AYALA 2014 derived the limit from the helium-burning lifetime of horizontal-branch stars based on number counts in globular clusters.
 54 DELLA-VALLE 2014 use the new PVLAS apparatus to set a limit on vacuum magnetic birefringence induced by axion-like particles. See their Fig. 6 for the mass-dependent limits.
 55 EJLLI 2014 set limits on a product of primordial magnetic field and the axion mass using CMB distortion induced by resonant axion production from CMB photons. See their Fig.$~$1 for limits applying specifically to the DFSZ and KSVZ axion models.
 56 PUGNAT 2014 is analogous to EHRET 2010 . See their Fig. 5 for mass-dependent limits on scalar and pseudoscalar bosons.
 57 REESMAN 2014 derive limits by requiring effects of axion-photon interconversion on gamma-ray spectra from distant blazars to be no larger than errors in the best-fit optical depth based on a certain extragalactic background light model. See their Fig. 5 for mass-dependent limits.
 58 ABRAMOWSKI 2013A look for irregularities in the energy spectrum of the BL Lac object PKS 2155--304 measured by H.E.S.S. The limits depend on assumed magnetic field around the source. See their Fig. 7 for mass-dependent limits.
 59 ARMENGAUD 2013 is analogous to AVIGNONE 1998 . See Fig. 6 for the limit.
 60 BETZ 2013 performed a microwave-based light shining through the wall experiment. See their Fig. 13 for mass-dependent limits.
 61 FRIEDLAND 2013 derived the limit by considering blue-loop suppression of the evolution of red giants with $7 - 12$ solar masses.
 62 MEYER 2013 attributed to axion-photon oscillations the observed excess of very high-energy ${{\mathit \gamma}}$ -rays with respect to predictions based on extragalactic background light models. See their Fig.4 for mass-dependent lower limits for various magnetic field configurations.
 63 WOUTERS 2013 look for irregularities in the X-ray spectrum of the Hydra cluster observed by Chandra. See their Fig. 4 for mass-dependent limits.
 64 CADAMURO 2012 derived cosmological limits on $\mathit G_{{{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ for axion-like particles. See their Fig. 1 for mass-dependent limits.
 65 PAYEZ 2012 derive limits from polarization measurements of quasar light (see their Fig.$~$3). The limits depend on assumed magnetic field strength in galaxy clusters. The limits depend on assumed magnetic field and electron density in the local galaxy supercluster.
 66 ARIK 2011 search for solar axions using ${}^{3}\mathrm {He}$ buffer gas in CAST, continuing from the ${}^{4}\mathrm {He}$ version of ARIK 2009 . See Fig.$~$2 for the exact mass-dependent limits.
 67 ALPS is a photon regeneration experiment. See their Fig.$~$4 for mass-dependent limits on scalar and pseudoscalar bosons.
 68 AHMED 2009A is analogous to AVIGNONE 1998 .
 69 ARIK 2009 is the ${}^{4}\mathrm {He}$ filling version of the CAST axion helioscope in analogy to INOUE 2002 and INOUE 2008 . See their Fig.$~$7 for mass-dependent limits.
 70 CHOU 2009 use the GammeV apparatus in the afterglow mode to search for chameleons, (pseudo)scalar bosons with a mass depending on the environment. For pseudoscalars they exclude at 3$\sigma$ the range $2.6 \times 10^{-7}$ GeV${}^{-1}<$ ${{\mathit G}}$ $_{A{{\mathit \gamma}} {{\mathit \gamma}} }<$ $4.2 \times 10^{-6}$ GeV${}^{-1}$ for vacuum ${\mathit m}_{{{\mathit A}^{0}}}$ roughly below 6 meV for density scaling index exceeding 0.8.
 71 GONDOLO 2009 use the all-flavor measured solar neutrino flux to constrain solar interior temperature and thus energy losses.
 72 LIPSS photon regeneration experiment, assuming scalar particle ${{\mathit S}^{0}}$ . See Fig.$~$4 for mass-dependent limits.
 73 CHOU 2008 perform a variable-baseline photon regeneration experiment. See their Fig.$~$3 for mass-dependent limits. Excludes the PVLAS result of ZAVATTINI 2006 .
 74 FOUCHE 2008 is an update of ROBILLIARD 2007 . See their Fig. 12 for mass-dependent limits.
 75 INOUE 2008 is an extension of INOUE 2002 to larger axion masses, using the Tokyo axion helioscope. See their Fig. 4 for mass-dependent limits.
 76 ZAVATTINI 2008 is an upgrade of ZAVATTINI 2006 , see their Fig.$~$8 for mass-dependent limits. They now exclude the parameter range where ZAVATTINI 2006 had seen a positive signature.
 77 ANDRIAMONJE 2007 looked for Primakoff conversion of solar axions in 9T superconducting magnet into X-rays. Supersedes ZIOUTAS 2005 .
 78 ROBILLIARD 2007 perform a photon regeneration experiment with a pulsed laser and pulsed magnetic field. See their Fig. 4 for mass-dependent limits. Excludes the PVLAS result of ZAVATTINI 2006 with a CL exceeding 99.9$\%$.
 79 ZAVATTINI 2006 propagate a laser beam in a magnetic field and observe dichroism and birefringence effects that could be attributed to an axion-like particle. This result is now excluded by ROBILLIARD 2007 , ZAVATTINI 2008 , and CHOU 2008 .
 80 INOUE 2002 looked for Primakoff conversion of solar axions in 4T superconducting magnet into X$~$ray.
 81 MORALES 2002B looked for the coherent conversion of solar axions to photons via the Primakoff effect in Germanium detector.
 82 BERNABEI 2001B looked for Primakoff coherent conversion of solar axions into photons via Bragg scattering in NaI crystal in DAMA dark matter detector.
 83 ASTIER 2000B looked for production of axions from the interaction of high-energy photons with the horn magnetic field and their subsequent re-conversion to photons via the interaction with the NOMAD dipole magnetic field.
 84 MASSO 2000 studied limits on axion-proton coupling using the induced axion-photon coupling through the proton loop and CAMERON 1993 bound on the axion-photon coupling using optical rotation. They obtained the bound $\mathit g{}^{2}_{{{\mathit p}} }/4{{\mathit \pi}}$ $<1.7 \times 10^{-9}$ for the coupling $\mathit g_{{{\mathit p}} }{{\overline{\mathit p}}}$ $\gamma _{5}{{\mathit p}}$ $\phi _{\mathit A}$.
 85 AVIGNONE 1998 result is based on the coherent conversion of solar axions to photons via the Primakoff effect in a single crystal germanium detector.
 86 Based on the conversion of solar axions to $\mathit X$-rays in a strong laboratory magnetic field.
 87 Experiment based on proposal by MAIANI 1986 .
 88 Experiment based on proposal by VANBIBBER 1987 .
 89 LAZARUS 1992 experiment is based on proposal found in VANBIBBER 1989 .
 90 RUOSO 1992 experiment is based on the proposal by VANBIBBER 1987 .
 91 SEMERTZIDIS 1990 experiment is based on the proposal of MAIANI 1986 . The limit is obtained by taking the noise amplitude as the upper limit. Limits extend to ${\mathit m}_{{{\mathit A}^{0}}}$ = $4 \times 10^{-3}$ where $\mathit G_{ {{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}} }$ $<$ $1 \times 10^{-4}$ GeV${}^{-1}$.
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