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

Constraints on the Yukawa-type corrections to Newton's gravitational law and on the coupling constant of axionlike particles to nucleons obtained from different laboratory experiments are reviewed and compared. The constraints on non-Newtonian gravity under discussion cover the wide interaction range from nanometers to millimeters and follow from the experiments on neutron scattering, measuring the Casimir force and Cavendish-type experiments. The constraints on the axion-to-nucleon coupling constant following from the magnetometer measurements, Cavendish-type experiments, Casimir physics, and experiments with beams of molecular hydrogen are considered which refer to the region of axion masses from $10^{-10}$ eV to 200 eV. Particular attention is given to the recent constraints obtained from measuring the Casimir force at nanometer separation distance between the test bodies. Several proposed experiments focused on constraining the non-Newtonian gravity, axionlike particles and other hypothetical weakly interacting particles, such as chameleons and symmetrons, are discussed.