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LELLA 2024 update constraints on the axion-proton coupling from supernova 1987A based on the SN cooling argument (including a treatment of the trapping regime) as well as the non-observation of any coincident axion-induced events in the Kamiokande II neutrino detector. They exclude QCD axion models above 0.01 eV, and axion-like particles in a window that extends up to 300 MeV. See their Fig. 3 for mass-dependent limits.

²	SU 2024 search for an axion-mediated dipole-dipole force between two separated spin-polarized samples of ${}^{129}\mathrm {Xe}$ gas. They set limits on the axion-neutron coupling for axion masses between 3.2 and 24.3 $\mu $eV. See their Fig. 4(b) for mass-dependent limits.

KARANTH 2023 utilized an in-plane polarized deuteron beam in a storage ring to constrain the axion-induced oscillating EDM of the deuteron for ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.496 - 0.502$ neV. Assuming axions account for all dark matter with ${{\mathit \rho}_{{{A}}}}$ $\simeq{}$ 0.55 GeV/cm${}^{3}$, they derived constraints on axion couplings to the deuteron EDM operator, gluons, and the deuteron spin. For detailed limits, see their Figs. $19 - 21$.

⁴

LEE 2023 analyzed data from a ${}^{}\mathrm {K}−{}^{3}\mathrm {He}$ comagnetometer, accounting for stochastic effects, to limit the axion-neutron coupling $\mathit g_{{{\mathit A}} {{\mathit n}} {{\mathit n}}}$ $<$ $2.4 \times 10^{-10}$ GeV${}^{-1}$ at 95$\%$ CL for ${\mathit m}_{{{\mathit A}^{0}}}$ = $0.4 - 4$ feV. They assumed axions form all dark matter with a density of 0.3 GeV/cm${}^{3}$. See their Fig. 5 for the limits.

⁵

BUSCHMANN 2022 studied the axion emission from five neutron stars with ages $\sim{}$ $10^{5} - 10^{6}$ years, comparing the simulation with axions to age and luminosity measurements. The mass bound assumes the KSVZ axion model with C$_{p}$ = $-0.47$ and C$_{n}$ = $-0.02$. See their Fig. 3 for the limits on the DFSZ axion model.

⁶	GAVRILYUK 2022 look for solar axions from the ABC interactions with the experimental setup similar to GAVRILYUK 2015. The mass bound assumes the KSVZ axion model, $\mathit S$ = 0.5, and ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ = 0.56.

⁷	SCHULTHESS 2022 look for a time-oscillating neutron EDM caused by the coupling between axion dark matter and gluons, using a Ramsey-type apparatus for a cold neutron beam. See their Fig. 4 for limits in the range of ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-19} - 4 \times 10^{-12}$ eV.

⁸

AYBAS 2021 limits the axion couplings to the nucleon EDM and the nucleons as $\mathit g_{{{\mathit A}} {{\mathit N}} {{\mathit \gamma}}}$ $<$ $9.5 \times 10^{-4}$ GeV${}^{-2}$ and $\mathit g_{{{\mathit A}} {{\mathit N}} {{\mathit N}}}/2{\mathit m}_{{{\mathit N}}}$ $<$ 0.28 GeV${}^{-1}$ (95 $\%$ CL) for ${\mathit m}_{{{\mathit A}^{0}}}$ = $162 - 166$ neV, based on a measurement of ${}^{207}\mathrm {Pb}$ solid-state NMR in a polarized ferroelecrtric crystal. Here ${\mathit m}_{{{\mathit N}}}$ is the nucleon mass and $\mathit g_{{{\mathit A}} {{\mathit N}} {{\mathit N}}}$ is the dimensionless axion-nucleon coupling. They assume that axions make up all the dark matter with ${{\mathit \rho}_{{{A}}}}$ $\simeq{}$ 0.46 GeV/cm${}^{3}$. See their Fig. 3 for the limits.

⁹

BHUSAL 2021 looked for 5.5 MeV solar axions produced by ${{\mathit p}}$ ${{\mathit d}}$ $\rightarrow{}^{3}\mathrm {He}~{{\mathit A}^{0}}$ through the axion-induced dissociation of deuterons by using SNO data, and set a limit on the isovector axion-nucleon coupling, $\vert \mathit g{}^{3}_{aN}\vert $ $<$ $2 \times 10^{-5}$ GeV${}^{-1}$, which is equivalent to $\vert \mathit g_{A n n}$ $−$ $\mathit g_{A p p}\vert $ $<$ $4 \times 10^{-5}$ in terms of the dimensionless axion-nucleon couplings.

¹⁰

JIANG 2021 use the spin-amplifier based on hyperpolarized ${}^{129}\mathrm {Xe}$ gas to set limits on the axion couplings to nucleons as $\mathit g_{{{\mathit A}} {{\mathit N}} {{\mathit N}}}/2{\mathit m}_{{{\mathit N}}}$ $<$ $3.2 \times 10^{-9}$ GeV${}^{-1}$ (95 $\%$ CL) at ${\mathit m}_{{{\mathit A}^{0}}}$ = 52.94 feV, and comparable limits in the mass range of $8.3 - 744$ feV. Here ${\mathit m}_{{{\mathit N}}}$ is the nucleon mass and $\mathit g_{{{\mathit A}} {{\mathit N}} {{\mathit N}}}$ is the dimensionless axion-nucleon coupling. They assume that axions make up all the dark matter with ${{\mathit \rho}_{{{A}}}}$ $\simeq{}$ 0.4 GeV/cm${}^{3}$. See their Fig. 4b for the limits.

¹¹	ROUSSY 2021 look for a time-oscillating EDM of molecular ions ${}^{}\mathrm {HfF}{}^{+}$ induced by axion dark matter couplings to gluons. See their Fig. 3 for limits in the range of ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-22} - 10^{-15}$ eV.

¹²

ZHANG 2021B use the gravitational waves from the binary neutron star inspiral GW170817 to look for a type of axion whose mass is suppressed due to cancellation with additional contributions. They exclude $1.6 \times 10^{16}$ $<$ $\mathit f_{A}$ $<$ $10^{18}$ GeV at 3 $\sigma $ for ${\mathit m}_{{{\mathit A}^{0}}}{ {}\lesssim{} }$ $10^{-13}$ eV. See their Fig. 1 for mass-dependent limits.

¹³

ABDELHAMEED 2020 look for the resonant excitation of ${}^{169}\mathrm {Tm}$ (8.41 keV) by solar axions produced via the Primakoff effect. The mass bound assumes the KSVZ axion model, $\mathit S$ = 0.5, and ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ = 0.56. They set a limit on the product of axion couplings to photons and nucleons as $\mathit G_{{{\mathit A}} {{\mathit \gamma}} {{\mathit \gamma}}}$ $\cdot{}$ $\mathit g_{{{\mathit A}} {{\mathit p}} {{\mathit p}}}$ $<$ $1.44 \times 10^{-14}$ GeV${}^{-1}$ (90 $\%$ CL).

¹⁴

ABDELHAMEED 2020 look for the resonant excitation of ${}^{169}\mathrm {Tm}$ (8.41 keV) by solar axions produced via the axion-electron coupling. They set a limit on the product of axion couplings to electrons and nucleons as $\mathit g_{{{\mathit A}} {{\mathit e}} {{\mathit e}} }$ $\cdot{}$ $\mathit g_{{{\mathit A}} {{\mathit p}} {{\mathit p}}}$ $<$ $2.81 \times 10^{-16}$ (90 $\%$ CL).

¹⁵	APRILE 2020 look for solar axions from the ABC interactions, the Primakoff conversion, and the 14.4 keV M1 transition of ${}^{57}\mathrm {Fe}$. An excess is observed at low energies between 2 and 3 keV. See their Fig.8 for correlation between the couplings.

¹⁶

KLIMCHITSKAYA 2020 use the measurement of the Casimir force between a ${}^{}\mathrm {Au}$-coated microsphere and a ${}^{}\mathrm {Si}{}^{}\mathrm {C}$ plate to constrain the force due to two-axion exchange for 17.8 $<$ ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 100 eV. See their Fig. 2 for mass-dependent limits.

¹⁷	WANG 2020A is an update of LIU 2017A. The limit assumes the DFSZ axion. See their Fig. 7 for the limit on product of axion couplings to electrons and nucleons.

¹⁸	LEINSON 2019 is analogous to BEZNOGOV 2018, but estimating the axion luminosity based on the Tolman's analytic solution to the Einstein equations of spherical fluids in hydrostatic equilibrium. The dimensionless axion-neutron coupling is constrained as $\mathit g_{Ann}$ $<$ $1.0 \times 10^{-10}$.

¹⁹	LLOYD 2019 is analogous to BERENJI 2016. They highlight that the limit obtained with this technique strongly depends on the assumed NS core temperature.

²⁰

SMORRA 2019 look for spin-precession effects from ultra-light axion dark matter in the ${{\overline{\mathit p}}}$ spin-flip resonance data. Assuming ${{\mathit \rho}_{{{A}}}}$ = 0.4 GeV/cm${}^{3}$, they constrain the dimensionless axion-antiproton coupling as $\mathit g_{{{\mathit A}} {{\overline{\mathit p}}} {{\overline{\mathit p}}}}$ $<$ $2 - 9$ at 95$\%$ CL for ${\mathit m}_{{{\mathit A}^{0}}}$ = $2 \times 10^{-23} - 4 \times 10^{-17}$ eV. See the right panel of their Fig. 3.

²¹

WU 2019 look for axion-induced time-oscillating features of the NMR spectrum of acetonitrile-2-${}^{13}\mathrm {C}$. Assuming C$_{p}$ = C$_{n}$ and ${{\mathit \rho}_{{{A}}}}$ = 0.4 GeV/cm${}^{3}$, they constrain the dimensionless axion-nucleon coupling as ${{\mathit g}_{{{ANN}}}}$ $<$ $6 \times 10^{-5}$ for ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-21} - 1.3 \times 10^{-17}$ eV. Note that the limits for ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $10^{-21}$ eV in their Fig. 3(a) should be weaker than those for heavier masses. See ADELBERGER 2019 and WU 2019C on this issue.

²²	AKHMATOV 2018 is an update of GAVRILYUK 2015.

²³	ARMENGAUD 2018 is analogous to ALESSANDRIA 2013. The quoted limit assumes the DFSZ axion model. See their Fig. 4 for the limit on product of axion couplings to electrons and nucleons.

²⁴

BEZNOGOV 2018 constrain the axion-neutron coupling by assuming that thermal evolution of the hot neutron star HESS J1731-347 is dominated by the lowest possible neutrino emission. The quoted limit assumes the KSVZ axion with the effective Peccei-Quinn charge of the neutron C$_{n}$ = $-0.02$. The dimensionless axion-neutron couling is constrained as $\mathit g_{Ann}$ $<$ $2.8 \times 10^{-10}$.

²⁵	GAVRILYUK 2018 look for the resonant excitation of ${}^{83}\mathrm {Kr}$ (9.4 keV) by solar axions produced via the Primakoff effect. The mass bound assumes ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ = 0.56 and $\mathit S$ = 0.5.

²⁶

HAMAGUCHI 2018 studied the axion emission from the neutron star in Cassiopeia A based on the minimal cooling scenario which explains the observed rapid cooling rate. The quoted limit corresponds to $\mathit f_{A}$ $>$ $5 \times 10^{8}$ GeV obtained for the KSVZ axion with C$_{p}$ = $-0.47$ and C$_{n}$ = $-0.02$.

²⁷	ABEL 2017 look for a time-oscillating neutron EDM and an axion-wind spin-precession effect respectively induced by axion dark matter couplings to gluons and nucleons. See their Fig. 4 for limits in the range of ${\mathit m}_{{{\mathit A}^{0}}}$ = $10^{-24} - 10^{-17}$ eV.

²⁸	ABGRALL 2017 limit assumes the hadronic axion model used in ALESSANDRIA 2013. See their Fig. 4 for the limit on product of axion couplings to electrons and nucleons.

²⁹	FU 2017A look for the 14.4 keV ${}^{57}\mathrm {Fe}$ solar axions. The limit assumes the DFSZ axion model. See their Fig. 3 for mass-dependent limits on the axion-electron coupling. Notice that in this figure the DFSZ and KSVZ lines should be interchanged.

³⁰

KLIMCHITSKAYA 2017A use the differential measurement of the Casimir force between a ${}^{}\mathrm {Ni}$-coated sphere and ${}^{}\mathrm {Au}$ and ${}^{}\mathrm {Ni}$ sectors of the structured disc to constrain the axion coupling to nucleons for $2.61$ meV $<$ ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 0.9 eV. See their Figs. 1 and 2 for mass dependent limits.

³¹	LIU 2017 is analogous to ALESSANDRIA 2013. The limit assumes the hadronic axion model. See their Fig. 6(b) for the limit on product of axion couplings to electrons and nucleons.

³²	BERENJI 2016 used the Fermi LAT observations of neutron stars to look for photons from axion decay. They assume the effective Peccei-Quinn charge of the neutron C$_{n}$ = $0.1$ and a neutron-star core temperature of 20 MeV.

³³	GAVRILYUK 2015 look for solar axions emitted by the M1 transition of ${}^{83}\mathrm {Kr}$ (9.4 keV). The mass bound assumes ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ = 0.56 and $\mathit S$ = 0.5.

³⁴

KLIMCHITSKAYA 2015 use the measurement of differential forces between a test mass and rotating source masses of ${}^{}\mathrm {Au}$ and ${}^{}\mathrm {Si}$ to constrain the force due to two-axion exchange for $1.7 \times 10^{-3}$ $<$ ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 0.9 eV. See their Figs. 1 and 2 for mass dependent limits.

³⁵

BEZERRA 2014 use the measurement of the thermal Casimir-Polder force between a Bose-Einstein condensate of ${}^{87}\mathrm {Rb}$ atoms and a ${}^{}\mathrm {SiO}_{2}$ plate to constrain the force mediated by exchange of two pseudoscalars for 0.1 meV $<$ ${\mathit m}_{{{\mathit A}^{0}}}<$ 0.3 eV. See their Fig. 2 for the mass-dependent limit on pseudoscalar coupling to nucleons.

³⁶

BEZERRA 2014A is analogous to BEZERRA 2014. They use the measurement of the Casimir pressure between two ${}^{}\mathrm {Au}$-coated plates to constrain pseudoscalar coupling to nucleons for $1 \times 10^{-3}$ eV $<$ ${\mathit m}_{{{\mathit A}^{0}}}<$ 15 eV. See their Figs. 1 and 2 for the mass-dependent limit.

³⁷

BEZERRA 2014B is analogous to BEZERRA 2014. BEZERRA 2014B use the measurement of the normal and lateral Casimir forces between sinusoidally corrugated surfaces of a sphere and a plate to constrain pseudoscalar coupling to nucleons for 1 eV $<$ ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 20 eV. See their Figs. $1 - 3$ for mass-dependent limits.

³⁸

BEZERRA 2014C is analogous to BEZERRA 2014. They use the measurement of the gradient of the Casimir force between ${}^{}\mathrm {Au}$- and ${}^{}\mathrm {Ni}$-coated surfaces of a sphere and a plate to constrain pseudoscalar coupling to nucleons for $3 \times 10^{-5}$ eV $<$ ${\mathit m}_{{{\mathit A}_{{{0}}}}}$ $<$ 1 eV. See their Figs. 1, 3, and 4 for the mass-dependent limits.

³⁹	BLUM 2014 studied effects of an oscillating strong $\mathit CP$ phase induced by axion dark matter on the primordial ${}^{4}\mathrm {He}$ abundance. See their Fig. 1 for mass-dependent limits.

⁴⁰

LEINSON 2014 attributes the excessive cooling rate of the neutron star in Cassiopeia A to axion emission from the superfluid core, and found C${}^{2}_{n}{{\mathit m}^{2}}_{{{\mathit A}^{0}}}$ $\simeq{}$ $5.7 \times 10^{-6}$ eV${}^{2}$, where C$_{n}$ is the effective Peccei-Quinn charge of the neutron.

⁴¹

ALESSANDRIA 2013 used the CUORE experiment to look for 14.4 keV solar axions produced from the M1 transition of thermally excited ${}^{57}\mathrm {Fe}$ nuclei in the solar core, using the axio-electric effect. The limit assumes the hadronic axion model. See their Fig. 4 for the limit on product of axion couplings to electrons and nucleons.

⁴²	ARMENGAUD 2013 is analogous to ALESSANDRIA 2013. The limit assumes the hadronic axion model. See their Fig. 8 for the limit on product of axion couplings to electrons and nucleons.

⁴³

BELLI 2012 looked for solar axions emitted by the M1 transition of ${}^{7}\mathrm {Li}{}^{*}$ (478 keV) after the electron capture of ${}^{7}\mathrm {Be}$, using the resonant excitation ${}^{7}\mathrm {Li}$ in the ${}^{}\mathrm {LiF}$ crystal. The mass bound assumes ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ = 0.55, ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit s}}}$ = 0.029, and the flavor-singlet axial vector matrix element $\mathit S$ = 0.4.

⁴⁴

BELLINI 2012B looked for 5.5 MeV solar axions produced in the ${{\mathit p}}$ ${{\mathit d}}$ $\rightarrow{}^{3}\mathrm {He}{{\mathit A}^{0}}$.The limit assumes the hadronic axion model. See their Figs. 6 and 7 for mass-dependent limits on productsof axion couplings to photons, electrons, and nucleons.

⁴⁵

DERBIN 2011 looked for solar axions emitted by the M1 transition of thermally excited ${}^{57}\mathrm {Fe}$ nuclei in the Sun, using their possible resonant capture on ${}^{57}\mathrm {Fe}$ in the laboratory. The mass bound assumes ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ = 0.56 and the flavor-singlet axial vector matrix element ${{\mathit S}}$ = 3${{\mathit F}}−{{\mathit D}}$ $\simeq{}$ 0.5.

⁴⁶

BELLINI 2008 consider solar axions emitted in the M1 transition of ${}^{7}\mathrm {Li}{}^{*}$ (478 keV) and look for a peak at 478 keV in the energy spectra of the Counting Test Facility (CTF), a Borexino prototype. For ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ 450 keV they find mass-dependent limits on products of axion couplings to photons, electrons, and nucleons.

⁴⁷	ADELBERGER 2007 use precision tests of Newton's law to constrain a force contribution from the exchange of two pseudoscalars. See their Fig. 5 for limits on the pseudoscalar coupling to nucleons, relevant for ${\mathit m}_{{{\mathit A}^{0}}}$ below about 1 meV.

References

Except where otherwise noted, content of the 2025 Review of Particle Physics is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. The publication of the Review of Particle Physics is supported by US DOE, MEXT (Japan), INFN (Italy) and CERN. Individual collaborators receive support for their PDG activities from their respective institutes or funding agencies. © 2025. See LBNL disclaimers.

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