deletions | additions       diff --git a/underlying_physics.tex b/underlying_physics.tex  index c30bc3f..a574529 100644  --- a/underlying_physics.tex  +++ b/underlying_physics.tex 
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\overline{\nu_{\mu}} \rightarrow \overline{\nu_{e}}  \end{equation}  The beam of neutrinos being used is an "off-axis" \footnote{Fore more information see section ***} \ref{sect:osc-twoflavor}  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, as seen in figure \ref{fig:pionprod}.     These pions are selected out of the heap of products using a carefully calibrated magnetic field. After making it past the selector, the relatively short lived particles decay into muon and muon neutrinos, which correspond to the Feynman fiagram seen in figure \ref{fig:piondecay}.