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

Limits are for the axion mass in eV.

VALUE (eV) CL% DOCUMENT ID TECN  COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
1
 2021
CASP Nucleon EDM
2
 2021
Solar axion
3
 2021
NMR Axion dark matter
4
 2021
Molecular EDM
5
 2021 B
ASTR Neutron star inspiral
$<24$ 90 6
 2020
CNTR Solar axion
7
 2020
CNTR Solar axion
8
 2020
XE1T Solar axion
9
 2020
Casimir effect
$<7.3$ 90 10
 2020 A
CDEX Solar axion
$<0.03$ 11
 2019
ASTR Neutron star cooling
$<9.6 \times 10^{-3}$ 95 12
 2019
ASTR ${{\mathit \gamma}}$ -rays from NS
13
 2019
${{\overline{\mathit p}}}$ $\mathit g$-factor
14
 2019
NMR Axion dark matter
$<65$ 95 15
 2018
CNTR Solar axion
$<6.6$ 90 16
 2018
EDE3 Solar axion
$<0.085$ 90 17
 2018
ASTR Neutron star cooling
$<12.7$ 95 18
 2018
CNTR Solar axion
$<0.01$ 19
 2018
ASTR Neutron star cooling
20
 2017
Neutron EDM
$<93$ 90 21
 2017
HPGE Solar axion
$<4$ 90 22
 2017 A
PNDX Solar axion
23
 2017 A
Casimir effect
$<177$ 90 24
 2017 A
CDEX Solar axion
$<0.079$ 95 25
 2016
ASTR ${{\mathit \gamma}}$ -rays from NS
$< 100$ 95 26
 2015
CNTR Solar axion
27
 2015
Casimir-less
28
 2014
Casimir effect
29
 2014 A
Casimir effect
30
 2014 B
Casimir effect
31
 2014 C
Casimir effect
32
 2014
COSM ${}^{4}\mathrm {He}$ abundance
33
 2014
ASTR Neutron star cooling
$<250$ 95 34
 2013
CNTR Solar axion
$<155$ 90 35
 2013
EDEL Solar axion
$<8.6 \times 10^{3}$ 90 36
 2012
CNTR Solar axion
$<1.4 \times 10^{4}$ 90 37
 2012 B
BORX Solar axion
$<145$ 95 38
 2011
CNTR Solar axion
39
 2008
CNTR Solar axion
40
 2007
Test of Newton's law
 1 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.
 2 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.
 3 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.
 4 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.
 5 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.
 6 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).
 7 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).
 8 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.
 9 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.
 10 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.
 11 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 $\mathit g_{Ann}$ $<$ $1.0 \times 10^{-10}$.
 12 LLOYD 2019 is analogous to BERENJI 2016 . They highlight that the limit obtained with this technique strongly depends on the assumed NS core temperature.
 13 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.
 14 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.
 15 AKHMATOV 2018 is an update of GAVRILYUK 2015 .
 16 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.
 17 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 $\mathit g_{Ann}$ $<$ $2.8 \times 10^{-10}$.
 18 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.
 19 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$_{n}$ = $-0.02$.
 20 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.
 21 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.
 22 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.
 23 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.
 24 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.
 25 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.
 26 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.
 27 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.
 28 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.
 29 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.
 30 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.
 31 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.
 32 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.
 33 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.
 34 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.
 35 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.
 36 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.
 37 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.
 38 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.
 39 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.
 40 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:
 AYBAS 2021
PRL 126 141802 Search for Axionlike Dark Matter Using Solid-State Nuclear Magnetic Resonance
 BHUSAL 2021
PRL 126 091601 Searching for Solar Axions Using Data from the Sudbury Neutrino Observatory
 JIANG 2021
NATP 17 1402
 ROUSSY 2021
PRL 126 171301 Experimental Constraint on Axionlike Particles over Seven Orders of Magnitude in Mass
 ZHANG 2021B
PRL 127 161101
 ABDELHAMEED 2020
EPJ C80 376 New limits on the resonant absorption of solar axions obtained with a $^\mathbf {169}$Tm-containing cryogenic detector
 APRILE 2020
PR D102 072004 Excess electronic recoil events in XENON1T
 KLIMCHITSKAYA 2020
PR D101 056013 Constraints on non-Newtonian gravity and axionlike particles from measuring the Casimir force in nanometer separation range
 WANG 2020A
PR D101 052003 Improved limits on solar axions and bosonic dark matter from the CDEX-1B experiment using the profile likelihood ratio method
 LEINSON 2019
JCAP 1911 031 Constraints on axions from neutron star in HESS J1731-347
 LLOYD 2019
PR D100 063005 Constraining the axion mass through gamma-ray observations of pulsars
 SMORRA 2019
NAT 575 310 Direct limits on the interaction of antiprotons with axion-like dark matter
 WU 2019
PRL 122 191302 Search for Axionlike Dark Matter with a Liquid-State Nuclear Spin Comagnetometer
 AKHMATOV 2018
PPN 49 599 Results of Searching for Solar Hadronic Axions Emitted in the M1 Transition in$^{83}$Kr Nuclei
 ARMENGAUD 2018
PR D98 082004 Searches for electron interactions induced by new physics in the EDELWEISS-III Germanium bolometers
 BEZNOGOV 2018
PR C98 035802 Constraints on Axion-like Particles and Nucleon Pairing in Dense Matter from the Hot Neutron Star in HESS J1731-347
 GAVRILYUK 2018
JETPL 107 589 New Constraints on the Axion?Photon Coupling Constant for Solar Axions
 HAMAGUCHI 2018
PR D98 103015 Limit on the Axion Decay Constant from the Cooling Neutron Star in Cassiopeia A
 ABEL 2017
PR X7 041034 Search for Axionlike Dark Matter through Nuclear Spin Precession in Electric and Magnetic Fields
 ABGRALL 2017
PRL 118 161801 New limits on Bosonic Dark Matter, Solar Axions, Pauli Exclusion Principle Violation, and Electron Decay from the Majorana Demonstrator
 FU 2017A
PRL 119 181806 Limits on Axion Couplings from the First 80 Days of Data of the PandaX-II Experiment
 KLIMCHITSKAYA 2017A
PR D95 123013 Constraints on Axionlike Particles and non-Newtonian Gravity from Measuring the Difference of Casimir Forces
 LIU 2017A
PR D95 052006 Constraints on Axion Couplings from the CDEX-1 Experiment at the China Jinping Underground Laboratory
 BERENJI 2016
PR D93 045019 Constraints on Axions and Axionlike Particles from Fermi Large Area Telescope Observations of Neutron Stars
 GAVRILYUK 2015
JETPL 101 664 New Experiment on Search for the Resonance Absorption of Solar Axion Emitted in the M1 Transition of ${}^{83}\mathrm {Kr}$ Nuclei
 KLIMCHITSKAYA 2015
EPJ C75 164 Improved Constraints on the Coupling Constants of Axion-like Particles to Nucleons from Recent Casimir-less Experiment
 BEZERRA 2014C
PR D89 075002 Stronger Constraints on an Axion from Measuring the Casimir Interaction by Means of a Dynamic Atomic Force Microscope
 BEZERRA 2014B
PR D90 055013 Constraints on Axion-Nucleon Coupling Constants from Measuring the Casimir Force between Corrugated Surfaces
 BEZERRA 2014A
EPJ C74 2859 Constraining Axion-Nucleon Coupling Constants from Measurements of Effective Casimir Pressure by Means of Micromachined Oscillator
 BEZERRA 2014
PR D89 035010 Constraints on the Parameters of an Axion from Measurements of the Thermal Casimir-Polder Force
 BLUM 2014
PL B737 30 Constraining Axion Dark Matter with Big Bang Nucleosynthesis
 LEINSON 2014
JCAP 1408 031 Axion Mass Limit from Observations of the Neutron Star in Cassiopeia A
 ALESSANDRIA 2013
JCAP 1305 007 Search for 14.4 keV Solar Axions from M1 Transition of ${}^{57}\mathrm {Fe}$ with CUORE Crystals
 ARMENGAUD 2013
JCAP 1311 067 Axion Searches with the EDELWEISS-II Experiment
 BELLI 2012
PL B711 41 Search for ${}^{7}\mathrm {Li}$ Solar Axions using Resonant Absorption in LiF Crystal: Final Results
 BELLINI 2012B
PR D85 092003 Search for Solar Axions Produced in the ${{\mathit p}}$ (${{\mathit d}}$ ,${}^{3}\mathrm {He}$)A Reaction with Borexino Detector
 DERBIN 2011
PAN 74 596 New limit on the Mass of 14.4-keV Solar Axions Emitted in an $\mathit M$1 Transition in ${}^{57}\mathrm {Fe}$ Nuclei
 BELLINI 2008
EPJ C54 61 Search for Solar Axions Emitted in the M1-Transition of ${}^{7}\mathrm {Li}^{*}$ with Borexino CTF