Limits on Possible Mesoscopic Spin-Dependent Forces using Neutron Spin Rotation

We discuss experiments using polarized slow neutrons to investigate possible spin-dependent forces of \lq\lq mesoscopic\rq\rq range (millimeters to microns). We describe the limits on two potentials that could give rise to such forces (Dobrescu, 2006). The first is proportional to $g_Vg_A\vec{\sigma}\cdot\vec{p}$, with $\sigma$ and $p$ the neutron spin and momentum, respectively. This interaction would lead to a phase difference in the amplitude of positive and negative helicity states, causing the spin of transversely polarized neutrons to rotate through an angle $\phi_{PNC}$. A search for neuron spin rotation in $^{4}$He provides the current limit on the product of vector and axial couplings $g_vg_A<10^{-32}$ at 1 mm (Yan and Snow, 2013). The second potential is proportional to ${g_A}^2\vec{\sigma}\cdot{(\vec{p}\times \vec{r})}$, where $r$ is the distance between the neutrons and the bulk material. We discuss an apparatus to search for this interaction using thin sheets of various mass densities made to rotate about a longitudinal symmetry axis as a target. The current limit on the product of axial vector couplings is ${g_A}^2<6\times10^{-13}$ (Piegsa and Pignol, 2012), which we hope to improve by at least two orders of magnitude.