First Full Dalitz Plot Measurement in Neutron $\beta$-Decay using the Nab Spectrometer and Implications for New Physics
Precision measurements of observables in neutron $\beta$-decay are used to test the Standard Model description of the weak interaction and search for evidence of new physics. The Nab experiment at the Fundamental Neutron Physics Beamline at the Spallation Neutron Source was constructed to measure correlations in neutron decay by utilizing an asymmetric spectrometer and novel detection system to accurately reconstruct the proton momentum and electron energy for each $\beta$-decay. This work describes the detection of neutron $\beta$-decay products in the Nab spectrometer and presents the first full Dalitz plot representation of the phase space of neutron $\beta$-decay for all electrons >100 keV. In addition, new constraints are placed on a possible excited neutron state, hypothesized to explain the disagreement between the appearance and disappearance neutron lifetime techniques.