The Fourier–Bessel expansion: application to experimental probes of gravity and feeble short-range interactions

Abstract

Two Eöt–Wash torsion balance instruments exploited optimized Fourier–Bessel geometries to test the short-distance properties of gravity and to constrain exotic dipole–dipole and monopole–dipole interactions. We discuss efficient analytic techniques for computing the expected torques in those instruments arising from Newtonian and Yukawa interactions between unpolarized test bodies and dipole–dipole and monopole–dipole torques on polarized test-bodies. We consider systematic effects induced by weak external magnetic fields on the nominally unpolarized test-bodies. We also present a new Fourier–Bessel expansion for inverse-power-law (IPL) potentials and use this to calculate the expected IPL signals in our recent short-distance test of the gravitational inverse-square law. Our results slightly improve limits on inverse-5th-power law potentials.

Novel setup for detecting short-range anisotropic corrections to gravity

“…For each fin, there were x + 1 patch boundaries along the radial direction and x + 1 boundaries along the angular direction. The calculated torque has the expected periodicity of 2π/N and is consistent with an independent calculation of the net torque using the numerical methods described in [41].…”