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\subsection{The NO$\nu$A Experiment}  The confirmed probability of a muon neutrino to "oscillate" into an electron neutrino is given by a function of the following arguments,  \begin{align}  P(\nu_{\mu} \rightarrow \nu_{e}) = f ( &\sin^2 \theta_{23} \sin^2 2\theta_{13}, \nonumber \\  & \frac{\Delta_{31}}{\Delta_{31} \mp a L} \sin (\Delta_{31} \mp aL), \nonumber \\  & \sin \delta_{CP} )  \end{align}  where $i$ and $j$ carry values 1,2,3 and stand for electron, muon, and tau quantities respectively; $\theta_{ij}$ is the "mixing angle" between the various flavors; $\Delta_{ij} = \Delta m_{ij}^2 L / 4E $; L is the length over which the oscillations occur; $a = G_F N_e \sqrt{2} \simeq (4000 \rm{km})^{-1}$; the $\delta_{CP}$ is a measure of the amount by which charge and parity conversation are allowed to be violated; the $\mp$ correspond to neutrinos and antineutrinos respectively. It is important to note that the aL term comes about because of the initial momentum of the neutrinos in the beam and allows for close study of the mass hierarchy since a larger L gives a bigger probability for muon antineutrinos to oscillate \cite{Paley_2012}.  NO$\nu$A is the latest in the long, rich history of particle detectors specialized to study neutrinos. It is a long baseline experiement managed by the Fermi National Accelerator Laboratory (Fermilab) near Chicago, Illinois and takes advantage of the NuMI (Neutrinos at Main Injector) neutrino beam that was constructed for the MINOS project. With the start of NO$\nu$A, along with other improvements, the NuMI beam was upgraded to nearly twice the power with a new graphite target and magnetic horns to provide a narrow-band neutrino beam with a high intensity whose energy peaks at the maximum probability for neutrino oscillation \cite{Paley_2012}.