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

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.