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\section{Introduction}  \subsection{Muon Decay}  The muon is an elementary particle with similar properties to an electron. Muons are formed high in the Earth's atmosphere by energetic cosmic rays. The high energy rays produce an assortment of particles, some of which are negatively charged pions which eventually decay into muons (which are also negatively charged). These muons continue to travel down through Earth's atmosphere, but are unstable themselves and thus decay. Muon decay will always produce three particles, which include an electron and two different types of neutrinos. The decay will vary slightly depending on whether it is a muon($\mu^{-}$) that decays or its antiparticle, the antimuon ($\mu^{+}$) . More precisely, muons will decay into to an electron, an electron anti-neutrino, and a muon-neutrino, while an antimuon will decay into a positron, an electron anti-neutrino, and a muon-antineutrino. \cite{Rub1} \cite{Muon}  Formulaically, \begin{equation}   \mu^{-}=e^{-}+\overline{v_{e}}+v_{\mu}   \end{equation}