A Search for Possible Weakly-Coupled $Z^{\prime}$ Bosons to the Neutron Using Slow Neutron Spin Rotation*

An exotic axial vector interaction with a mm to $\mu$m range that couples weakly to the neutron through exchange of a $Z^{\prime}$ boson can appear in some extensions of the Standard Model [1]. We present the current status and systematic uncertainty analysis for an experiment to search for an interaction of the form $V_{5}=\frac{g^{2}_{A}}{4\pi m}\frac{e^{-m_{0}r}}{r}(\frac{1}{r}+\frac{1}{\lambda_{c}})\vec\sigma\cdot(\vec v\times\hat r)$. We plan to employ slow neutron polarimetry [2] to look for a spin rotation of transversely polarized slow neutrons which pass through a series of open parallel slots bounded by flat rectangular plates of tungsten, copper, and glass [3]. The goal of our experiment is to improve the sensitivity of $\varphi'=[2.8\pm4.6(stat.)\pm4.0(sys.)]\times10^{-5}$ rad/m achieved in [4] by at least two orders of magnitude at the NIST NG-C beamline. We will discuss our work using pT-sensitivity B-field maps of the plate surfaces to bound the main source of systematic uncertainty arising from residual magnetic fields.\\\\{[1]} F. M. Piegsa and G. Pignol, Phys. Rev. Lett. 108 (2012)\\{[2]} W. M. Snow et al., Rev. Sci. Inst. 86, 055101 (2015)\\{[3]} C. Haddock et al., Nucl. Inst. Meth. A 885 (2018)\\{[4]} C. Haddock et al., Phys. Lett. B 783 (2018)