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 AYRES 02   EDM ultracold neutrons 2 PODDAR 02   ASTR solar system 3 ZHANG 02   NMR polarized ${}^{129}\mathrm {Xe}$ and ${}^{131}\mathrm {Xe}$ 4 CRESCINI 02   SQID paramagnetic GSO crystal 5 FENG 02   NMR polarized ${}^{129}\mathrm {Xe}$ and ${}^{131}\mathrm {Xe}$ 6 AFACH 02   GNME Optical magnetometers 7 DZUBA 01   THEO atomic EDM 8 STADNIK 01   THEO atomic and molecular EDMs 9 CRESCINI 01   SQID paramagnetic GSO crystal 10 AFACH 01   ultracold neutrons 11 STADNIK 01   THEO nucleon spin contributions for nuclei 12 TERRANO 01   torsion pendulum 13 BULATOWICZ 01   NMR polarized ${}^{129}\mathrm {Xe}$ and ${}^{131}\mathrm {Xe}$ 14 CHU 01   polarized ${}^{3}\mathrm {He}$ 15 TULLNEY 01   SQID polarized ${}^{3}\mathrm {He}$ and ${}^{129}\mathrm {Xe}$ 16 RAFFELT 01   stellar energy loss 17 HOEDL 01   torsion pendulum 18 PETUKHOV 01   polarized ${}^{3}\mathrm {He}$ 19 SEREBROV 01   ultracold neutrons 20 IGNATOVICH 00   RVUE ultracold neutrons 21 SEREBROV 00   RVUE ultracold neutrons 22 BAESSLER 00   ultracold neutrons 23 HECKEL 00   torsion pendulum 24 NI 99   paramagnetic ${}^{}\mathrm {Tb}{}^{}\mathrm {F}_{3}$ 25 POSPELOV 99   THEO neutron EDM 26 YOUDIN 99   27 RITTER 99   torsion pendulum 28 VENEMA 99   nuclear spin-precession frequencies 29 WINELAND 99   NMR 1  AYRES 2023 at PSI use their neutron EDM setup to look for a mm to micron-range spin-dependent force between ultracold spin-polarized neutrons stored in vacuum and the unpolarised nucleons in the surrounding apparatus. They constrain a nucleon-neutron monopole-dipole interaction parameterised by the coupling ${{\mathit g}_{{{s}}}^{N}}{{\mathit g}_{{{p}}}^{n}}$. They set a limit of ${{\mathit g}_{{{s}}}^{N}}{{\mathit g}_{{{p}}}^{n}}$ $<$ $10^{-20}$ (95$\%$ CL) for a 1 meV mass axion, see Fig. 6. 2  PODDAR 2023 search for long-range monopole-dipole forces between the polarized population of electrons inside the Earth and the unpolarised nucleons in the Sun, which would affect the precession of orbital perihelion. However, the most competitive limit is obtained by combining the monopole-monopole force constraints on ${{\mathit g}^{N}_{s}}$ from planetary precession with the strongest stellar bound on the pseudoscalar electron coupling (${{\mathit g}^{e}_{p}}$), shown in Fig. 5. 3  ZHANG 2023 look for changes of the ratio of precession frequencies between ${}^{129}\mathrm {Xe}$ and ${}^{131}\mathrm {Xe}$ as the bias field is flipped in Earth's gravitational field after Earth roation effect is subtracted. They find ${{\mathit g}_{{{p}}}^{n}}{{\mathit g}_{{{s}}}^{N}}$ $<$ $1 \times 10^{-26} - 3.7 \times 10^{-36}$ for $\lambda $ = $0.3 - 1 \times 10^{10}$ m. See their Fig. 4 for limits as a function of $\lambda $. 4  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 $. 5  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 $. 6  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. 7  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. 8  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. 9  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 $. 10  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. 11  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. 12  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. 13  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. 14  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. 15  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. 16  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. 17  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. 18  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. 19  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. 20  IGNATOVICH 2009 use data on depolarization of ultracold neutrons in material traps. They show $\lambda $-dependent limits in their Fig. 1. 21  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. 22  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. 23  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. 24  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. 25  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 $\lambda _{\mathit A}=\hbar{}/{\mathit m}_{{{\mathit A}}}\mathit c$. 26  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. 27  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. 28  VENEMA 1992 looked for an effect of Earth's gravity on nuclear spin-precession frequencies of ${}^{199}\mathrm {Hg}$ and ${}^{201}\mathrm {Hg}$ atoms. 29  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.

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