Systematic Uncertainties of the Firez Interference Term in the Free Neutron Beta Decay of the Nab Experiment

The Nab experiment is under construction at the SNS, with the goal to measure two parameters in free neutron beta decay: (a) the electron-antineutrino correlation $a$ to a precision of $\delta a / a = 10^{-3}$ and (b) the Fierz interference term $b$ to $\delta b = 3\times10^{-3}$. The Fierz interference term $b$ will be extracted from a measurement of the neutron beta decay spectrum. These results will be used to determine the ratio of nucleon axial-vector coupling to vector coupling up to a precision of $0.03\%$, and thus test the unitarity of CKM matrix, as well as to search for beyond the Standard Model Physics through S,T interactions. We will present simulations required for a thorough analysis of the systematic uncertainties in the Fierz term measurement.