The limit is for the coupling $\mathit g$ = $\mathit g_{{\mathrm {p}}}$ $\mathit g_{{\mathrm {s}}}$ in a $\mathit T$-violating potential between nucleons, nucleon and electron, or electrons of the form $\mathit V$ = ${\mathit g\hbar{}{}^{2}\over 8{{\mathit \pi}}{\mathit m}_{{{\mathit p}}}}(\mathbf {\sigma }\cdot{}\mathbf {\hat{{\mathit r}}}$) (${1\over \mathit r{}^{2}}+{1\over \lambda \mathit r}$) $\mathit e{}^{−\mathit r/\lambda }$, where $\mathit g_{{\mathrm {s}}}$ and $\mathit g_{{\mathrm {p}}}$ are dimensionless scalar and pseudoscalar coupling constants, ${\mathit m}_{{{\mathit p}}}$ is the fermion mass with the pseudoscalar coupling (whereas the mass ${\mathit m}_{{{\mathit s}}}$ of the fermion with the scalar coupling does not explicitly appear), and $\lambda $ = $\hbar{}/({\mathit m}_{{{\mathit A}}}\mathit c$) is the range of the force.

VALUE DOCUMENT ID TECN  COMMENT • • We do not use the following data for averages, fits, limits, etc. • • 1 CRESCINI 2022 SQID paramagnetic GSO crystal 2 FENG 2022 NMR polarized ${}^{129}\mathrm {Xe}$ and ${}^{131}\mathrm {Xe}$ 3 AFACH 2021 GNME Optical magnetometers 4 DZUBA 2018 THEO atomic EDM 5 STADNIK 2018 THEO atomic and molecular EDMs 6 CRESCINI 2017 SQID paramagnetic GSO crystal 7 AFACH 2015 ultracold neutrons 8 STADNIK 2015 THEO nucleon spin contributions for nuclei 9 TERRANO 2015 torsion pendulum 10 BULATOWICZ 2013 NMR polarized ${}^{129}\mathrm {Xe}$ and ${}^{131}\mathrm {Xe}$ 11 CHU 2013 polarized ${}^{3}\mathrm {He}$ 12 TULLNEY 2013 SQID polarized ${}^{3}\mathrm {He}$ and ${}^{129}\mathrm {Xe}$ 13 RAFFELT 2012 stellar energy loss 14 HOEDL 2011 torsion pendulum 15 PETUKHOV 2010 polarized ${}^{3}\mathrm {He}$ 16 SEREBROV 2010 ultracold neutrons 17 IGNATOVICH 2009 RVUE ultracold neutrons 18 SEREBROV 2009 RVUE ultracold neutrons 19 BAESSLER 2007 ultracold neutrons 20 HECKEL 2006 torsion pendulum 21 NI 1999 paramagnetic ${}^{}\mathrm {Tb}{}^{}\mathrm {F}_{3}$ 22 POSPELOV 1998 THEO neutron EDM 23 YOUDIN 1996 24 RITTER 1993 torsion pendulum 25 VENEMA 1992 nuclear spin-precession frequencies 26 WINELAND 1991 NMR 1  CRESCINI 2022 is an update of CRESCINI 2017 , and find ${{\mathit g}_{{p}}^{e}}{{\mathit g}_{{s}}^{N}}{}\leq{}$ $5.7 \times 10^{-32}$ and ${{\mathit g}_{{p}}^{e}}{{\mathit g}_{{s}}^{e}}{}\leq{}$ $1.6 \times 10^{-31}$ for $\lambda $ ${ {}\gtrsim{} }$ 10 cm at 95$\%$ CL. See their Fig. 4 for limits as a function of $\lambda $. 2  FENG 2022 look for changes of the ratio of precession frequencies between ${}^{129}\mathrm {Xe}$ and ${}^{131}\mathrm {Xe}$ when a BGO crystal is positioned near the atomic cell. They find ${{\mathit g}_{{p}}^{n}}{{\mathit g}_{{s}}^{N}}$ $<$ $2 \times 10^{-20} - 3 \times 10^{-24}$ for $\lambda $ = $0.11 - 0.55$ mm. See their Fig. 4 for limits as a function of $\lambda $. 3  AFACH 2021 look for axion domain walls coupled to atomic spins by using the global network of optical magnetometers. Assuming that the axion domain walls make up all dark matter, they exclude the effective decay constant below $4 \times 10^{5}$ GeV for ${\mathit m}_{{{\mathit A}^{0}}}$ in the range of $10^{-15} - 10^{-11}$ eV. See their Fig. 4 for the mass-dependent limits. 4  DZUBA 2018 used atomic EDM measurements to derive limits on the product of the pseudoscalar coupling to nucleon and the scalar coupling to electron, which improved on the laboratory bounds for ${\mathit m}_{{{\mathit A}^{0}}}$ $>$ 0.01 eV. See their Fig. 1 for mass-dependent limits. 5  STADNIK 2018 used atomic and molecular EDM experiments to derive limits on the product of the pseudoscalar couplings to electron and the scalar coupling to nucleon and electron. See their Fig. 2 for mass-dependent limits, which improved on the laboratory bounds for ${\mathit m}_{{{\mathit A}^{0}}}$ $>$ 0.01 eV. 6  CRESCINI 2017 use the QUAX-${{\mathit g}_{{p}}}{{\mathit g}_{{s}}}$ experiment to look for variation of a paramagnetic GSO crystal magnetization when rotating lead disks are positioned near the crystal, and find $\mathit g$ = ${{\mathit g}_{{p}}^{e}}{{\mathit g}_{{s}}^{N}}$ $<$ $4.3 \times 10^{-30}$ for $\lambda $ = $0.1 - 0.2$ m at 95$\%$ CL. See their Fig. 6 for limits as a function of $\lambda $. 7  AFACH 2015 look for a change of spin precession frequency of ultracold neutrons when a magnetic field with opposite directions is applied, and find ${{\mathit g}}$ $<$ $2.2 \times 10^{-27}$ (m/$\lambda ){}^{2}$ at 95$\%$ CL for 1 $\mu $m $<$ $\lambda $ $<$ 5 mm. See their Fig. 3 for their limits. 8  STADNIK 2015 studied proton and neutron spin contributions for nuclei and derive the limits $\mathit g$ $<$ $10^{-28} - 10^{-23}$ for $\lambda $ $>$ $3 \times 10^{-4}$ m using the data of TULLNEY 2013 . See their Figs. 1 and 2 for $\lambda $-dependent limits. 9  TERRANO 2015 used a torsion pendulum and rotating attractor, and derived a restrictive limit on the product of the pseudoscalar coupling to electron and the scalar coupling to nucleons, ${{\mathit g}}$ $<$ $9 \times 10^{-29} - 5 \times 10^{-26}$ for ${\mathit m}_{{{\mathit A}^{0}}}$ $<$ $1.5 - 400$ $\mu $eV. See their Fig. 5 for mass-dependent limits. 10  BULATOWICZ 2013 looked for NMR frequency shifts in polarized ${}^{129}\mathrm {Xe}$ and ${}^{131}\mathrm {Xe}$ when a zirconia rod is positioned near the NMR cell, and find $\mathit g$ $<$ $1 \times 10^{-19} - 1 \times 10^{-24}$ for $\lambda $ = $0.01 - 1$ cm. See their Fig. 4 for their limits. 11  CHU 2013 look for a shift of the spin precession frequency of polarized ${}^{3}\mathrm {He}$ in the presence of an unpolarized mass, in analogy to YOUDIN 1996 . See Fig.$~$3 for limits on ${{\mathit g}}$ in the approximate ${\mathit m}_{{{\mathit A}^{0}}}$ range $0.02 - 2$ meV. 12  TULLNEY 2013 look for a shift of the precession frequency difference between the colocated ${}^{3}\mathrm {He}$ and ${}^{129}\mathrm {Xe}$ in the presence an unpolarized mass, and derive limits g $<$ $3 \times 10^{-29} - 2 \times 10^{-22}$ for $\lambda $ $>$ $3 \times 10^{-4}$ m. See their Fig. 3 for $\lambda $-dependent limits. 13  RAFFELT 2012 show that the pseudoscalar couplings to electron and nucleon and the scalar coupling to nucleon are individually constrained by stellar energy-loss arguments and searches for anomalous monopole-monopole forces, together providing restrictive constraints on $\mathit g$. See their Figs. 2 and 3 for results. 14  HOEDL 2011 use a novel torsion pendulum to study the force by the polarized electrons of an external magnet. In their Fig.$~$3 they show restrictive limits on $\mathit g$ in the approximate ${\mathit m}_{{{\mathit A}^{0}}}$ range $0.03 - 10$ meV. 15  use spin relaxation of polarized ${}^{3}\mathrm {He}$ and find $\mathit g$ $<$ $3 \times 10^{-23}$ (cm/$\lambda ){}^{2}$ at 95$\%$ CL for the force range $\lambda $ = $10^{-4} - 1$ cm. 16  SEREBROV 2010 use spin precession of ultracold neutrons close to bulk matter and find $\mathit g~<$ $2 \times 10^{-21}$ (cm/$\lambda ){}^{2}$ at 95$\%$ CL for the force range $\lambda $ = $10^{-4} - 1$ cm. 17  IGNATOVICH 2009 use data on depolarization of ultracold neutrons in material traps. They show $\lambda $-dependent limits in their Fig. 1. 18  SEREBROV 2009 uses data on depolarization of ultracold neutrons stored in material traps and finds ${{\mathit g}}<2.96 \times 10^{-21}$ (cm/${{\mathit \lambda}}){}^{2}$ for the force range ${{\mathit \lambda}}$ = $10^{-3} - 1$ cm and ${{\mathit g}}<3.9 \times 10^{-22}$ (cm/${{\mathit \lambda}}){}^{2}$ for ${{\mathit \lambda}}$ = $10^{-4} - 10^{-3}$ cm, each time at 95$\%$ CL, significantly improving on BAESSLER 2007 . 19  BAESSLER 2007 use the observation of quantum states of ultracold neutrons in the Earth's gravitational field to constrain $\mathit g$ for an interaction range 1 $\mu $m$-$a few mm. See their Fig.$~$3 for results. 20  HECKEL 2006 studied the influence of unpolarized bulk matter, including the laboratory's surroundings or the Sun, on a torsion pendulum containing about $9 \times 10^{22}$ polarized electrons. See their Fig. 4 for limits on $\mathit g$ as a function of interaction range. 21  NI 1999 searched for a $\mathit T$-violating medium-range force acting on paramagnetic ${}^{}\mathrm {Tb}{}^{}\mathrm {F}_{3}$ salt. See their Fig.$~$1 for the result. 22  POSPELOV 1998 studied the possible contribution of $\mathit T$-violating Medium-Range Force to the neutron electric dipole moment, which is possible when axion interactions violate $\mathit CP$. The size of the force among nucleons must be smaller than gravity by a factor of $2 \times 10^{-10}$ (1$~$cm/$\lambda _{\mathit A}$), where $\lambda _{\mathit A}=\hbar{}/{\mathit m}_{{{\mathit A}}}\mathit c$. 23  YOUDIN 1996 compared the precession frequencies of atomic ${}^{199}\mathrm {Hg}$ and ${}^{}\mathrm {Cs}$ when a large mass is positioned near the cells, relative to an applied magnetic field. See Fig.$~$3 for their limits. 24  RITTER 1993 studied the influence of bulk mass with polarized electrons on an unpolarized torsion pendulum, providing limits in the interaction range from 1 to 100 cm. 25  VENEMA 1992 looked for an effect of Earth's gravity on nuclear spin-precession frequencies of ${}^{199}\mathrm {Hg}$ and ${}^{201}\mathrm {Hg}$ atoms. 26  WINELAND 1991 looked for an effect of bulk matter with aligned electron spins on atomic hyperfine resonances in stored ${}^{9}\mathrm {Be}{}^{+}$ ions using nuclear magnetic resonance.

References:

CRESCINI 2022 PR D105 022007 Search of spin-dependent fifth forces with precision magnetometry FENG 2022 PRL 128 231803 Search for Monopole-Dipole Interactions at the Submillimeter Range with a Xe129-Xe131-Rb Comagnetometer AFACH 2021 NATP 17 1396 Search for topological defect dark matter with a global network of optical magnetometers DZUBA 2018 PR D98 035048 New constraints on axion-mediated P,T-violating interaction from electric dipole moments of diamagnetic atoms STADNIK 2018 PRL 120 013202 Improved Limits on Axionlike-Particle-Mediated $\mathit P$, $\mathit T$-Violating Interactions between Electrons and Nucleons from Electric Dipole Moments of Atoms and Molecules CRESCINI 2017 PL B773 677 Improved Constraints on Monopole-Dipole Interaction Mediated by Pseudo-Scalar Bosons AFACH 2015 PL B745 58 Constraining Interactions Mediated by Axion-Like Particles with Ultracold Neutrons STADNIK 2015 EPJ C75 110 Nuclear spin-dependent interactions: Searches for WIMP, Axion and Topological Defect Dark Matter, and Tests of Fundamental Symmetries TERRANO 2015 PRL 115 201801 Short-Range Spin-Dependent Interactions of Electrons: a Probe for Exotic Pseudo-Goldstone Bosons BULATOWICZ 2013 PRL 111 102001 A Laboratory Search for a Long-Range $\mathit T$-odd, $\mathit P$-odd Interaction from Axion-Like Particles using Dual Species Nuclear Magnetic Resonance with Polarized ${}^{129}\mathrm {Xe}$ and ${}^{131}\mathrm {Xe}$ Gas CHU 2013 PR D87 011105 Laboratory Search for Spin-Dependent Short-Range Force from Axionlike Particles using Optically Polarized ${}^{3}\mathrm {He}$ Gas TULLNEY 2013 PRL 111 100801 Constraints on Spin-Dependent Short-Range Interaction between Nucleons RAFFELT 2012 PR D86 015001 Limits on a $\mathit CP$-Violating Scalar Axion-Nucleon Interaction HOEDL 2011 PRL 106 041801 Improved Constraints on an Axion-Mediated Force PETUKHOV 2010 PRL 105 170401 Polarized ${}^{3}\mathrm {He}$ as a Probe for Short-Range Spin-Dependent Interactions SEREBROV 2010 JETPL 91 6 Search for Macroscopic $\mathit CP$ Violating Forces using a Neutron EDM Spectrometer IGNATOVICH 2009 EPJ C64 19 Limits on a Nucleon-Nucleon Monopole-Dipole Coupling from Spin Relaxation of Polarized Ultra-Cold Neutrons in Traps SEREBROV 2009 PL B680 423 New Constraints for $\mathit CP$-Violating Forces between Nucleons in the Range 1 Micrometer to 1 Centimeter BAESSLER 2007 PR D75 075006 Constraint on the Coupling of Axionlike Particles to Matter via an Ultracold Neutron Gravitational Experiment HECKEL 2006 PRL 97 021603 New $\mathit CP$-Violation and Preferred-Frame Tests with Polarized Electrons NI 1999 PRL 82 2439 Search for an Axionlike Spin Coupling using a Paramagnetic Salt with a dc SQUID POSPELOV 1998 PR D58 097703 $\mathit CP$ Odd Interaction of Axion with Matter YOUDIN 1996 PRL 77 2170 Limits on Spin $−$ Mass Couplings within the Axion Window RITTER 1993 PRL 70 701 Search for Anomalous Spin-Dependent Forces with a Polarized-Mass Torsion Pendulum VENEMA 1992 PRL 68 135 Search for a Coupling of the Earth's Gravitational Field to Nuclear Spins in Atomic Mercury WINELAND 1991 PRL 67 1735 Search for Anomalous Spin Dependent Forces Using Stored Ion Spectroscopy