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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. • •

CASP

Nucleon EDM

Solar axion

NMR

Axion dark matter

Molecular EDM

ASTR

Neutron star inspiral

$<24$

90

CNTR

Solar axion

CNTR

Solar axion

XE1T

Solar axion

Casimir effect

$<7.3$

90

CDEX

Solar axion

$<0.03$

ASTR

Neutron star cooling

$<9.6 \times 10^{-3}$

95

ASTR

${{\mathit \gamma}}$ -rays from NS

${{\overline{\mathit p}}}$ $\mathit g$-factor

NMR

Axion dark matter

$<65$

95

CNTR

Solar axion

$<6.6$

90

EDE3

Solar axion

$<0.085$

90

ASTR

Neutron star cooling

$<12.7$

95

CNTR

Solar axion

$<0.01$

ASTR

Neutron star cooling

Neutron EDM

$<93$

90

HPGE

Solar axion

$<4$

90

PNDX

Solar axion

Casimir effect

$<177$

90

CDEX

Solar axion

$<0.079$

95

ASTR

${{\mathit \gamma}}$ -rays from NS

$< 100$

95

CNTR

Solar axion

Casimir-less

Casimir effect

Casimir effect

Casimir effect

Casimir effect

COSM

${}^{4}\mathrm {He}$ abundance

ASTR

Neutron star cooling

$<250$

95

CNTR

Solar axion

$<155$

90

EDEL

Solar axion

$<8.6 \times 10^{3}$

90

CNTR

Solar axion

$<1.4 \times 10^{4}$

90

BORX

Solar axion

$<145$

95

CNTR

Solar axion

CNTR

Solar axion

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.

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