Effects of the Nab Spectrometer on the Measurement of the Electron-Antineutrino Correlation Parameter a.

The Nab experiment aims to measure the neutron beta decay electron-neutrino correlation coefficient \textit{a} and the Fierz interference term \textit{b}. Measurement of \textit{a} to a relative uncertainty of $10^{-3}$ provides $ \lambda$, the ratio of axial to vector coupling constant, at roughly the same precision level as the vector coupling determined from the superallowed decays. A measurement of \textit{b} with an uncertainty of $3 \times 10^{-3}$ would reach physics beyond standard model. In Nab, the parameter \textit{a} is extracted from the electron energy and proton momentum using an asymmetric magnetic spectrometer and two large-area highly pixelated Si detectors. To reach the goal of $10^{-3}$ relative uncertainty in \textit{a}, Nab requires a detailed understanding of its systematic effects. The largest systematic uncertainty comes from the proton path length in the magnetic field. The proton momentum is measured via time of flight (TOF), triggered by the detection of an electron. The TOF only measures the momentum along the field lines; any gyroscopic motion of the proton is a loss of information. The spectrometer field is designed to adiabatically align the proton momentum along the field lines, such that this uncertainty is limited to $10^{-4}$. However, correcting for the path length requires a detailed mapping and analytic expansion of the magnetic field. My research focuses on the design, construction, and application of the mapping system, fitting the field data using Modified Bessel Function expansion, and using said expansion to create a numerically calculated spectrometer response function for an independent extraction of \textit{a}.