# The State of the Art in Constraining Axion-to-Nucleon Coupling and Non-Newtonian Gravity from Laboratory Experiments

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## Abstract

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## 1. Introduction

## 2. The Yukawa-Type Correction to Newtonian Gravity and Constraints on It from the Casimir Effect

## 3. Constraints on the Coupling of Axions to Nucleons from the Casimir Effect

## 4. Constraints from Measuring the Casimir Force in Nanometer Separation Range and Other Laboratory Experiments

## 5. Proposed Experiments

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The schematic of two sinusoidally corrugated plates having the phase shift $\mathsf{\Phi}$ between corrugations.

**Figure 2.**Schematic diagram of the experimental setup using an atomic force microscope for measuring the lateral Casimir force between corrugated surfaces (see the text for further discussion).

**Figure 3.**The constraints on Yukawa-type correction to Newton’s gravitational law following from measuring the lateral and normal Casimir forces between corrugated surfaces (lines 1 and 2, respectively), the effective Casimir pressure (line 3), from the second and first Casimir-less experiments (lines 4 and 5, respectively), from sensing the difference of lateral forces (line 6), and from the torsion-pendulum experiment (line 7) are shown as functions of the interaction range. The regions above each line are excluded and below each line are allowed.

**Figure 4.**Schematic diagram of the experimental setup using an atomic force microscope for measuring the normal Casimir force between corrugated surfaces (see the text for further discussion).

**Figure 5.**Schematic diagram of the experimental setup using a micromechanical oscillator for determination of the effective Casimir pressure between two parallel plates (see the text for further discussion).

**Figure 6.**The constraints on the coupling constant of axion to nucleon following from the Casimir-less experiment, experiments on measuring the Casimir pressure and lateral Casimir force (lines 1, 2, and 3, respectively) and from experiments on measuring the difference of Casimir forces, gradient of the Casimir force and Casimir-Polder force (lines 4, 5, and 6, respectively) are shown as functions of the axion mass. The regions above each line are excluded and below each line are allowed.

**Figure 7.**The constraints on Yukawa-type correction to Newton’s gravitational law following from recent measuring the Casimir force at nanometer separations (line labeled “new”), from experiments on neutron scattering (lines labeled “n”), and from the Cavendish-type experiment (line labeled “gr”) are shown as functions of the interaction range. The lines 1–4, which also indicate the strongest constraints within the respective interaction ranges, are reproduced from Figure 3. The regions above each line are excluded and below each line are allowed.

**Figure 8.**The constraints on the coupling constant of axion to nucleon following from recent measuring the Casimir force at nanometer separations (line labeled “new”), from the magnetometer measurements (line labeled “m”), from the Cavendish-type experiment (line labeled “gr”), and from the experiment using beams of molecular hydrogen (line labeled “H${}_{2}$”) are shown as functions of the axion mass. The lines 1–3, where line 1 indicates the strongest constraints within some range of axion masses, are reproduced from Figure 6. The regions above each line are excluded and below each line are allowed.

**Figure 9.**The constraints on Yukawa-type correction to Newton’s gravitational law, which can be obtained from the proposed CANNEX test are shown by the line “proposed” as a function of the interaction range. For comparison purposes, the lines 4–7 and the line labeled “gr” are reproduced from Figure 3 and Figure 7, respectively. The regions above each line are excluded and below each line are allowed.

**Figure 10.**The constraints on the coupling constant of axion to nucleon, which can be obtained from the proposed CANNEX test, are shown by the line “proposed” as a function of the axion mass. For comparison purposes, the lines 1, 2 and “gr” are reproduced from Figure 6 and Figure 8, respectively. The regions above each line are excluded and below each line are allowed.

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Mostepanenko, V.M.; Klimchitskaya, G.L.
The State of the Art in Constraining Axion-to-Nucleon Coupling and Non-Newtonian Gravity from Laboratory Experiments. *Universe* **2020**, *6*, 147.
https://doi.org/10.3390/universe6090147

**AMA Style**

Mostepanenko VM, Klimchitskaya GL.
The State of the Art in Constraining Axion-to-Nucleon Coupling and Non-Newtonian Gravity from Laboratory Experiments. *Universe*. 2020; 6(9):147.
https://doi.org/10.3390/universe6090147

**Chicago/Turabian Style**

Mostepanenko, Vladimir M., and Galina L. Klimchitskaya.
2020. "The State of the Art in Constraining Axion-to-Nucleon Coupling and Non-Newtonian Gravity from Laboratory Experiments" *Universe* 6, no. 9: 147.
https://doi.org/10.3390/universe6090147