  The abBA collaboration proposes to conduct a comprehensive program of precise
measurements of neutron $\beta$-decay coefficients $a$ (the correlation between
the neutrino momentum and the decay electron momentum), $b$ (the electron
energy spectral distortion term), $A$ (the correlation between the neutron spin
and the decay electron momentum), and $B$ (the correlation between the neutron
spin and the decay neutrino momentum) at a cold neutron beam facility. We have
used a GEANT4-based code to simulate the propagation of decay electrons and
protons in the electromagnetic spectrometer and study the energy and timing
response of a pair of Silicon detectors. We used these results to examine
systematic effects and find the uncertainties with which the physics parameters
$a$, $b$, $A$, and $B$ can be extracted from an over-determined experimental
data set.
