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\overline{\nu_{\mu}} \rightarrow \overline{\nu_{e}}  \end{equation}  TheNuMI  beam of neutrinos being used  is an "off-axis" \footnote{Fore more information see section ***}neutrino  beam created by colliding protons from Fermilab's Main Injector into a long cylindrical graphite target. While many different particles are generated during these collisions, of most interest are the postive pions that emerge, in the following process   PION PRODUCTION FEYNMAN DIAGRAM