Overview of Fierz Interference Analysis from UCNA Experiment

A non-zero Fierz interference term, the $b$ coefficient in the expansion of the beta decay rate in the Standard Model, can signify contributions to scalar and tensor interactions from physics beyond the Standard Model. In practice, $b \neq 0$ causes shifts in the shape of the electron energy spectra, primarily at low energies since Fierz interference scales like $\frac{m_e}{E}$. In 2010 the UCNA experiment at the Ultracold Neutron facility at Los Alamos Neutron Science Center took data for a beta decay asymmetry $A$ measurement. This same dataset can be used to extract the $b$ coefficient by comparing shifts in the nominal, i.e. $b = 0$, spectra to the data. Here we discuss Monte Carlo simulation methods used in both extracting a value of and estimating an error on $b$. We use Monte Carlo methods to generate the kinematics for beta decay corresponding to a range of $b$ values and input those kinematics to a GEANT4 simulation of the UCNA apparatus to create simulated beta spectra. This analysis focuses on the systematic errors due to non-linearities in the detector energy response which are modeled by converting simulated spectra into ``data-like'' spectra. The simulated spectra are compared against each other to extract a value of $b$ and an associated error.