New Experimental Limits on Non-Newtonian Forces in the Micrometer Range

We report measurements of the short-range forces between two macroscopic gold-coated plates using a torsion pendulum. The force is measured for separations between 0.7 and $7\mu \mathrm{m}$ and is well described by a combination of the Casimir force, including the finite-temperature correction, and an electrostatic force due to patch potentials on the plate surfaces. We use our data to place constraints on the Yukawa-type “new” forces predicted by theories with extra dimensions. We establish a new best bound for force ranges 0.4–$4\mu \mathrm{m}$ and, for forces mediated by gauge bosons propagating in ($4+n$) dimensions and coupling to the baryon number, extract a ($4+n$)-dimensional Planck scale lower limit of $M_{*}>70\mathrm{TeV}$.

Figure 1

The binned experimental short-range force between gold-coated plates. The error bars include contributions from statistical scatter, and uncertainties in the applied corrections, discussed in the text. The dashed blue line shows the theoretical Casimir force, calculated by using the Lifshitz formalism at 300 K, with the Drude model permittivity extrapolation to zero frequency. The red line shows the force, including the electrostatic patch-potential contribution, with two free fitting parameters, as described in the text. Inset: The force residuals, used to place constraints on the new short-range forces.

Figure 2

Experimental upper limits on the Yukawa force strength $\alpha$, together with some theoretical predictions. The area shaded in light blue is experimentally excluded. The curves labeled A–E correspond to results in Refs. 6, 7, present work, and Refs. 4, 5, respectively. The hatched area labeled “gauge bosons” is the parameter space for forces mediated by gauge bosons that propagate in ($4+n$) dimensions and couple to the standard model baryon number.