We surrounded a rotating torsion pendulum containing $9.8\times {10}^{22}$ polarized electrons by 2 or 4 stationary sources, each with a net spin of $6.0\times {10}^{24}$ polarized electrons. Multiple source configurations gave sensitivity to hypothetical dipole-dipole, spin-dot-spin, and spin-cross-spin exchange interactions mediated by bosons with masses up to $20\mu \mathrm{eV}$. For bosons with masses $\le 0.1\mu \mathrm{eV}$ our null results for the dipole-dipole, spin-dot-spin, and spin-cross-spin forces imply $1\sigma$ upper limits on $(g_P^e{)}^2/(\hslash c)$, $(g_A^e{)}^2/(\hslash c)$ and $(g_V^e{g}_A^e)/(\hslash c)$ of $2.2\times {10}^{-16}$, $3.8\times {10}^{-40}$, and $1.2\times {10}^{-28}$, respectively. We also constrain, for the first time, any possible linear combination of static spin-spin interactions. In this case our upper limits relax to $5.6\times {10}^{-16}$, $9.8\times {10}^{-40}$, and $1.2\times {10}^{-28}$, respectively.

• Received 1 August 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.151802