Effect of Beam Polarization in the Nab Experiment at the SNS

The Nab Experiment on the Fundamental Physics Beamline (FnPB) at the Spallation Neutron Source (SNS) aims to precisely measure the electron-neutrino correlation parameter \textit{a},  and the Fierz interference term \textit{b}, associated with the beta decay of free neutrons. This measurement provides a cross-check and independent measurement of  $\lambda$, the ratio of vector to axial-vector coupling constants in the Standard Model. A potential source of systematic error in this experiment stems from residual polarization in the incident neutron beam. Whether or not such a polarization exists, and its possible size, is unknown.  Estimating the degree to which this polarization could affect the outcome of the experiment requires the integration of neutron beam polarization into ongoing studies of the systematic errors associated with the Nab Experiment. To further verify the extent of this effect the polarization of the FnPB can be measured using a polarized $^3$He spin filter and an Adiabatic Fast Passage Spin Flipper.