Submillimeter tests of the gravitational inverse-square law

Abstract

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 $137\ensuremath{\mu}\mathrm{m}$ 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 ${R}_{*}<~160\ensuremath{\mu}\mathrm{m},$ and on two equal-sized large extra dimensions of ${R}_{*}<~130\ensuremath{\mu}\mathrm{m}.$ Yukawa interactions with $|\ensuremath{\alpha}|>~1$ are ruled out at 95% confidence for $\ensuremath{\lambda}>~197\ensuremath{\mu}\mathrm{m}.$ 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 $V(r)\ensuremath{\propto}{r}^{\ensuremath{-}k}$ with k between 2 and 5 and on the ${\ensuremath{\gamma}}_{5}$ couplings of pseudoscalars with $m<~10\mathrm{meV}{/c}^{2}.$