Constraining Light Scalar Field with Torsion-Balance Gravity Experiments

The light scalar field with a coupling to standard model particles provide a possible source of the dark matter, long-range Yukawa forces or violation of the weak equivalence principle, which can be potentially explored by precision gravity experiments. We describe the searches for such light scalar fields with the three types of gravity experiments, including the $G$-measurement experiments, Inverse-Square Law (ISL) experiments, and equivalence principle experiments. We investigate the potential influences of the scalar field as a function of its mass, and focus on the experimental constraints from torsion-balance gravity experiments. HUST-18 $G$-measurement torsion-balance experiments place bounds on the photon coupling and electron coupling at up to $\Lambda_{\gamma}=7\times10^{17}$ GeV and $\Lambda_{e}=1\times10^{17}$ GeV in the mass ranges $10^{-9}-10^{-4}$ eV. Results from the ISL experiments by the Universities of Washington, Stanford, IUPUI, HUST, Colorado, Irvine, Yale and others allow us to set limits on the photon coupling and electron coupling at up to $\Lambda_{\gamma}=5\times10^{17}$ GeV and $\Lambda_{e}=3\times10^{16}$ GeV for scalar field mass ranges between $10^{-5}$ and $10^{-1}$ eV. Additionally, we also discuss the limits from equivalence principle experiments, and $MICROSCOPE$ final result updates the constrains on the coupling parameters at up to $\Lambda_{\gamma}=7\times10^{22}$ GeV and $\Lambda_{e}=4\times10^{21}$ GeV for mass ranges $\lesssim 10^{-13}$ eV. These results contribute experimental constraints to relatively unexplored mass regions of {light scalar field} parameter space and improve upon previous limits in some mass ranges. This work paves the way for long-range Yukawa forces mediated by light scalar fields in future high-precision gravity experiments.