Constraints on axion-nucleon coupling constants from measuring the Casimir force between corrugated surfaces

We obtain stronger laboratory constraints on the coupling constants of axion-like particles to nucleons from measurements of the normal and lateral Casimir forces between sinusoidally corrugated surfaces of a sphere and a plate. For this purpose, the normal and lateral additional forces arising in the experimental configurations due to the two-axion exchange between protons and neutrons are calculated. Our constraints following from measurements of the normal and lateral Casimir forces are stronger than the laboratory constraints reported so far for masses of axion-like particles larger than 11 and 8 eV, respectively. A comparison between various laboratory constraints on the coupling constants of axion-like particles to nucleons obtained from the magnetometer measurements, Eötvos- and Cavendish-type experiments, and from the Casimir effect is performed over the wide range of masses of axion-like particles from $10^{-10}$ to 20 eV.

Figure 1

Constraints on the coupling constants of axion-like particles to nucleons are shown as functions of the axion mass. The regions above each line are prohibited and below each line are allowed. (a) Constraints from measurements of the normal Casimir force between corrugated surfaces of a sphere and a plate. The lines from bottom to top are plotted under the conditions $g_{ap}^2=g_{an}^2$, $g_{an}^2\gg g_{ap}^2$, and $g_{ap}^2\gg g_{an}^2$, respectively. (b) Constraints from measurements of the normal Casimir force between corrugated surfaces of a sphere and a plate and from the experiment using a micromachined oscillator are plotted under the condition $g_{ap}^2=g_{an}^2$ by the black and gray lines, respectively.

Figure 2

Constraints on the coupling constants of axion-like particles to nucleons are shown as functions of the axion mass. The regions above each line are prohibited and below each line are allowed. (a) Constraints from measurements of the lateral Casimir force between corrugated surfaces of a sphere and a plate. The lines from bottom to top are plotted under the conditions $g_{ap}^2=g_{an}^2$, $g_{an}^2\gg g_{ap}^2$, and $g_{ap}^2\gg g_{an}^2$, respectively. (b) Constraints from measurements of the lateral and normal Casimir forces between corrugated surfaces of a sphere and a plate are plotted under the condition $g_{ap}^2=g_{an}^2$ by the solid and dashed black lines, respectively. The constraints from measuring the Casimir pressure by means of a micromachined oscillator are shown by the gray line.

Figure 3

The laboratory constraints on the coupling constants of axion-like particles to a neutron obtained from different experiments are shown by the lines 1–8 as functions of the axion mass. The line 1 follows from the magnetometer measurements [28]. The lines 2–4 are found [29, 34] from the gravitational experiments [30, 31, 32, 33, 35], and the lines 5–8 are obtained in Refs. [36, 37, 38] and in this paper from the Casimir effect [39, 40, 41, 45, 46, 51, 52] (see text for further discussion). The regions above each line are prohibited and below each line are allowed.