Submillimeter tests of the gravitational inverse-square law

Motivated by a variety of theories that predict new effects, we tested the gravitational ${1/r}^2$ law at separations between 10.77 mm and $137\mu \mathrm{m}$ using two different 10-fold azimuthally symmetric torsion pendulums and rotating 10-fold symmetric attractors. Our work improves upon other experiments by up to a factor of about 100. We found no deviation from Newtonian physics at the 95% confidence level and interpret these results as constraints on extensions of the standard model that predict Yukawa or power-law forces. We set a constraint on the largest single extra dimension (assuming toroidal compactification and that one extra dimension is significantly larger than all the others) of $R_{*}<~160\mu \mathrm{m},$ and on two equal-sized large extra dimensions of $R_{*}<~130\mu \mathrm{m}.$ Yukawa interactions with $|\alpha |>~1$ are ruled out at 95% confidence for $\lambda >~197\mu \mathrm{m}.$ Extra-dimensions scenarios stabilized by radions are restricted to unification masses $M_{*}>~3.0\mathrm{TeV}{/c}^2,$ regardless of the number of large extra dimensions. We also provide new constraints on power-law potentials $V\left(r\right)\mathrm{}\propto r^{-k}$ with k between 2 and 5 and on the ${\gamma }_5$ couplings of pseudoscalars with $m<~10\mathrm{meV}{/c}^2.$