\section{Response Matrices for MIND analysis}
\label{app:response}
This appendix summarises the response matrices of signal (wrong sign $\nu_\mu$ and $\overline{\nu}_\mu$ appearance) and all backgrounds ($\overline{\nu}_\mu$, $\nu_\mu$ CC, $\overline{\nu}_e$, $\nu_e$ CC and NC) in bins of true and reconstructed neutrino energy, relevant to an oscillation analysis. Each entry in the table is the survival probability for each species. In all tables, columns represent the true neutrino energy in GeV and rows the reconstructed energy, also in GeV. The overflow bin in reconstructed energy represents all events with a reconstructed energy greater than the known maximum.
\vspace{0.25cm}

{\large {\bf $\nu_\mu$ appearance} }
\vspace{0.25cm}

\hspace{1.0cm}    {\large Signal Efficiency }

\begin{table}[!ht]
  \caption{
    $\nu_\mu$ appearance detection efficiency. 
    All values $\times 10^{-4}$.
  }
  \begin{center}
  \begin{tabular}{|l||c|c|c|c|c|c|c|c|c|c|c|}
    \hline
    & {\tiny 0-2.0} & {\tiny 2.0-3.0} & {\tiny 3.0-4.0} & {\tiny 4.0-5.0} & {\tiny 5.0-6.0} & {\tiny 6.0-8.0} & {\tiny 8.0-10.0} & {\tiny 10.0-12.5} & {\tiny 12.5-15.0} & {\tiny 15.0-20.0} & {\tiny 20.0-25.0}\\
    \hline
    \hline
    {\tiny 0-2.0} & {\scriptsize211.8} & {\scriptsize331.0} & {\scriptsize48.55} & {\scriptsize13.92} & {\scriptsize5.73} & {\scriptsize2.371} & {\scriptsize0.790} & {\scriptsize0.377} & {\scriptsize0.142} & {\scriptsize0.076} & {\scriptsize0.039}\\
\hline
{\tiny 2.0-3.0} & {\scriptsize154.4} & {\scriptsize1379} & {\scriptsize522.0} & {\scriptsize118.0} & {\scriptsize42.03} & {\scriptsize15.18} & {\scriptsize4.903}
& {\scriptsize1.916} & {\scriptsize1.049} & {\scriptsize0.572} & {\scriptsize0.156}\\
\hline
{\tiny 3.0-4.0} & {\scriptsize45.17} & {\scriptsize906.6} & {\scriptsize1408} & {\scriptsize554.5} & {\scriptsize145.6} & {\scriptsize41.82} & {\scriptsize13.36}
& {\scriptsize4.334} & {\scriptsize2.211} & {\scriptsize0.934} & {\scriptsize0.429}\\
\hline
{\tiny 4.0-5.0} & {\scriptsize17.93} & {\scriptsize422.1} & {\scriptsize1377} & {\scriptsize1352} & {\scriptsize544.5} & {\scriptsize105.4} & {\scriptsize26.26}
& {\scriptsize8.951} & {\scriptsize3.288} & {\scriptsize1.449} & {\scriptsize0.722}\\
\hline
{\tiny 5.0-6.0} & {\scriptsize7.509} & {\scriptsize155.6} & {\scriptsize744.7} & {\scriptsize1476} & {\scriptsize1233} & {\scriptsize318.5} & {\scriptsize49.26}
& {\scriptsize14.82} & {\scriptsize4.535} & {\scriptsize2.307} & {\scriptsize0.761}\\
\hline
{\tiny 6.0-8.0} & {\scriptsize2.017} & {\scriptsize70.17} & {\scriptsize421.2} & {\scriptsize1469} & {\scriptsize2729} & {\scriptsize2010} & {\scriptsize447.4} & {\scriptsize71.04} & {\scriptsize18.31} & {\scriptsize7.302} & {\scriptsize3.025}\\
\hline
{\tiny 8.0-10.0} & {\scriptsize0.112} & {\scriptsize7.406} & {\scriptsize46.89} & {\scriptsize230.1} & {\scriptsize850.6} & {\scriptsize2371} & {\scriptsize1823} & {\scriptsize380.8} & {\scriptsize56.63} & {\scriptsize13.65} & {\scriptsize5.212}\\
\hline
{\tiny 10.05-12.5} & {\scriptsize0} & {\scriptsize2.134} & {\scriptsize12.61} & {\scriptsize37.15} & {\scriptsize134.9} & {\scriptsize963.9} & {\scriptsize2756} & {\scriptsize2011} & {\scriptsize416.5} & {\scriptsize48.96} & {\scriptsize11.50}\\
\hline
{\tiny 12.5-15.0} & {\scriptsize0} & {\scriptsize0.126} & {\scriptsize2.739} & {\scriptsize11.20} & {\scriptsize27.05} & {\scriptsize127.4} & {\scriptsize886.8} & {\scriptsize2519} & {\scriptsize1788} & {\scriptsize242.5} & {\scriptsize22.84}\\
\hline
{\tiny 15.0-20.0} & {\scriptsize0} & {\scriptsize0.126} & {\scriptsize0.498} & {\scriptsize2.346} & {\scriptsize7.930} & {\scriptsize36.72} & {\scriptsize173.2} & {\scriptsize1207} & {\scriptsize3621} & {\scriptsize2840} & {\scriptsize340.5}\\
\hline
{\tiny 20.0-25.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.083} & {\scriptsize0.076} & {\scriptsize0.088} & {\scriptsize1.186} & {\scriptsize11.52} & {\scriptsize61.27} & {\scriptsize380.2} & {\scriptsize2665} & {\scriptsize2562}\\
\hline
{\tiny overflow} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.514} & {\scriptsize0.757} & {\scriptsize5.685} & {\scriptsize31.86} & {\scriptsize477.2} & {\scriptsize3338}\\
\hline
  \end{tabular}
  \end{center}
\end{table}
\newpage

\hspace{1.0cm}       {\large $\overline{\nu}_\mu$ CC background }

\begin{table}[!ht]
  \begin{center}
  \begin{tabular}{|l||c|c|c|c|c|c|c|c|c|c|c|}
    \hline
    & {\tiny 0-2.0} & {\tiny 2.0-3.0} & {\tiny 3.0-4.0} & {\tiny 4.0-5.0} & {\tiny 5.0-6.0} & {\tiny 6.0-8.0} & {\tiny 8.0-10.0} & {\tiny 10.0-12.5} & {\tiny 12.5-15.0} & {\tiny 15.0-20.0} & {\tiny 20.0-25.0}\\
    \hline
    \hline
    {\tiny 0-2.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.096} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.041} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 2.0-3.0} & {\scriptsize0.346} & {\scriptsize0.546} & {\scriptsize0} & {\scriptsize0.083} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.039} & {\scriptsize0.020}\\
\hline
{\tiny 3.0-4.0} & {\scriptsize0.173} & {\scriptsize0.273} & {\scriptsize0.096} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.084} & {\scriptsize0} & {\scriptsize0.065} & {\scriptsize0.029} & {\scriptsize0.077} & {\scriptsize0.020}\\
\hline
{\tiny 4.0-5.0} & {\scriptsize0.173} & {\scriptsize0.546} & {\scriptsize0.192} & {\scriptsize0.166} & {\scriptsize0} & {\scriptsize0.042} & {\scriptsize0.068} & {\scriptsize0.065} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.020}\\
\hline
{\tiny 5.0-6.0} & {\scriptsize0} & {\scriptsize0.273} & {\scriptsize0.384} & {\scriptsize0.083} & {\scriptsize0.187} & {\scriptsize0.042} & {\scriptsize0.034} & {\scriptsize0} & {\scriptsize0.029} & {\scriptsize0.039} & {\scriptsize0.039}\\
\hline
{\tiny 6.0-8.0} & {\scriptsize0} & {\scriptsize0.273} & {\scriptsize0.288} & {\scriptsize0.249} & {\scriptsize0.468} & {\scriptsize0.209} & {\scriptsize0.068}
& {\scriptsize0.097} & {\scriptsize0.115} & {\scriptsize0.096} & {\scriptsize0.039}\\
\hline
{\tiny 8.0-10.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.096} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.084} & {\scriptsize0.137} & {\scriptsize0.129} & {\scriptsize0.086} & {\scriptsize0.116} & {\scriptsize0.020}\\
\hline
{\tiny 10.0-12.5} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.094} & {\scriptsize0.042} & {\scriptsize0.205} & {\scriptsize0.032} & {\scriptsize0.086} & {\scriptsize0.019} & {\scriptsize0.138}\\
\hline
{\tiny 12.5-15.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.083} & {\scriptsize0.094} & {\scriptsize0} & {\scriptsize0.102} & {\scriptsize0}
& {\scriptsize0.058} & {\scriptsize0.058} & {\scriptsize0.079}\\
\hline
{\tiny 15.0-20.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.084} & {\scriptsize0.068} & {\scriptsize0.065}
& {\scriptsize0.029} & {\scriptsize0.116} & {\scriptsize0.079}\\
\hline
{\tiny 20.0-25.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.042} & {\scriptsize0} & {\scriptsize0.032} & {\scriptsize0.086} & {\scriptsize0.058} & {\scriptsize0.059}\\
\hline
{\tiny overflow} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.019} & {\scriptsize0.098}\\
\hline
  \end{tabular}
  \end{center}
  \caption{\emph{$\overline{\nu}_\mu$ CC background. All values $\times 10^{-4}$.}}
\end{table}
\vspace{0.25cm}

\hspace{1.0cm}       {\large $\nu_e$ CC background }

\begin{table}[!ht]
  \begin{center}
  \begin{tabular}{|l||c|c|c|c|c|c|c|c|c|c|c|}
    \hline
    & {\tiny 0-2.0} & {\tiny 2.0-3.0} & {\tiny 3.0-4.0} & {\tiny 4.0-5.0} & {\tiny 5.0-6.0} & {\tiny 6.0-8.0} & {\tiny 8.0-10.0} & {\tiny 10.0-12.5} & {\tiny 12.5-15.0} & {\tiny 15.0-20.0} & {\tiny 20.0-25.0}\\
    \hline
    \hline
    {\tiny 0-2.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.020} &
{\scriptsize0.013} & {\scriptsize0}\\
\hline
{\tiny 2.0-3.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.023} & {\scriptsize0.045} & {\scriptsize0.040} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 3.0-4.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.013} & {\scriptsize0.055}\\
\hline
{\tiny 4.0-5.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.028} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}
& {\scriptsize0} & {\scriptsize0.014}\\
\hline
{\tiny 5.0-6.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.014}\\
\hline
{\tiny 6.0-8.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.020}
& {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 8.0-10.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 10.0-12.5} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.054} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 12.5-15.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 15.0-20.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.022} & {\scriptsize0.020} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 20.0-25.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny overflow} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
  \end{tabular}
  \end{center}
  \caption{\emph{$\nu_e$ CC background. All values $\times 10^{-4}$.}}
\end{table}
\newpage

\hspace{1.0cm}       {\large NC background }

\begin{table}[!ht]
  \begin{center}
  \begin{tabular}{|l||c|c|c|c|c|c|c|c|c|c|c|}
    \hline
    & {\tiny 0-2.0} & {\tiny 2.0-3.0} & {\tiny 3.0-4.0} & {\tiny 4.0-5.0} & {\tiny 5.0-6.0} & {\tiny 6.0-8.0} & {\tiny 8.0-10.0} & {\tiny 10.0-12.5} & {\tiny 12.5-15.0} & {\tiny 15.0-20.0} & {\tiny 20.0-25.0}\\
    \hline
    \hline
    {\tiny 0-2.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.035} & {\scriptsize0} & {\scriptsize0.026} & {\scriptsize0.050} & {\scriptsize0.022} & {\scriptsize0.015} & {\scriptsize0}\\
\hline
{\tiny 2.0-3.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.034} & {\scriptsize0.061} & {\scriptsize0.070} & {\scriptsize0.016} & {\scriptsize0.052} &
{\scriptsize0.050} & {\scriptsize0.034} & {\scriptsize0.030} & {\scriptsize0.039}\\
\hline
{\tiny 3.0-4.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.061} & {\scriptsize0.070} & {\scriptsize0} & {\scriptsize0.052} & {\scriptsize0.076} & {\scriptsize0.056} & {\scriptsize0.068} & {\scriptsize0.055}\\
\hline
{\tiny 4.0-5.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.034} & {\scriptsize0.030} & {\scriptsize0.106} & {\scriptsize0.157} & {\scriptsize0.210} & {\scriptsize0.088} & {\scriptsize0.146} & {\scriptsize0.106} & {\scriptsize0.086}\\
\hline
{\tiny 5.0-6.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.030} & {\scriptsize0.035} & {\scriptsize0.031} & {\scriptsize0.026} & {\scriptsize0.076} & {\scriptsize0.067} & {\scriptsize0.030} & {\scriptsize0.023}\\
\hline
{\tiny 6.0-8.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.094} & {\scriptsize0.105} & {\scriptsize0.113} & {\scriptsize0.067} & {\scriptsize0.046} & {\scriptsize0.047}\\
\hline
{\tiny 8.0-10.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.035} & {\scriptsize0.047} & {\scriptsize0.026} & {\scriptsize0.088} & {\scriptsize0.011} & {\scriptsize0.015} & {\scriptsize0.023}\\
\hline
{\tiny 10.0-12.5} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.013} & {\scriptsize0.025} & {\scriptsize0.034} & {\scriptsize0.046} & {\scriptsize0.055}\\
\hline
{\tiny 12.5-15.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.034} & {\scriptsize0.015} & {\scriptsize0.008}\\
\hline
{\tiny 15.0-20.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.013} & {\scriptsize0.011} & {\scriptsize0.030} & {\scriptsize0.016}\\
\hline
{\tiny 20.0-25.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.008}\\
\hline
{\tiny overflow} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
  \end{tabular}
  \end{center}
  \caption{\emph{NC background. All values $\times 10^{-4}$.}}
\end{table}
\newpage
{\large {\bf $\overline{\nu}_\mu$ appearance } }

\hspace{1.0cm}       {\large Signal Efficiency }

\begin{table}[!ht]
  \begin{center}
  \begin{tabular}{|l||c|c|c|c|c|c|c|c|c|c|c|}
    \hline
    & {\tiny 0-2.0} & {\tiny 2.0-3.0} & {\tiny 3.0-4.0} & {\tiny 4.0-5.0} & {\tiny 5.0-6.0} & {\tiny 6.0-8.0} & {\tiny 8.0-10.0} & {\tiny 10.0-12.5} & {\tiny 12.5-15.0} & {\tiny 15.0-20.0} & {\tiny 20.0-25.0}\\
    \hline
    \hline
    {\tiny 0-2.0} & {\scriptsize169.5} & {\scriptsize228.4} & {\scriptsize47.07} & {\scriptsize9.966} & {\scriptsize3.558} & {\scriptsize1.170} & {\scriptsize0.648} & {\scriptsize0.485} & {\scriptsize0.173} & {\scriptsize0.077} & {\scriptsize0}\\
\hline
{\tiny 2.0-3.0} & {\scriptsize378.0} & {\scriptsize1007} & {\scriptsize392.8} & {\scriptsize103.1} & {\scriptsize24.72} & {\scriptsize7.939} & {\scriptsize2.594} & {\scriptsize1.260} & {\scriptsize0.490} & {\scriptsize0.270} & {\scriptsize0.157}\\
\hline
{\tiny 3.0-4.0} & {\scriptsize310.3} & {\scriptsize1762} & {\scriptsize1234} & {\scriptsize435.1} & {\scriptsize115.1} & {\scriptsize22.06} & {\scriptsize4.983}
& {\scriptsize2.197} & {\scriptsize0.951} & {\scriptsize0.481} & {\scriptsize0.216}\\
\hline
{\tiny 4.0-5.0} & {\scriptsize97.66} & {\scriptsize1271} & {\scriptsize2188} & {\scriptsize1306} & {\scriptsize448.7} & {\scriptsize79.27} & {\scriptsize12.66} & {\scriptsize3.521} & {\scriptsize1.729} & {\scriptsize0.828} & {\scriptsize0.452}\\
\hline
{\tiny 5.0-6.0} & {\scriptsize24.41} & {\scriptsize419.5} & {\scriptsize1627} & {\scriptsize2009} & {\scriptsize1188} & {\scriptsize258.6} & {\scriptsize30.55}
& {\scriptsize8.561} & {\scriptsize2.825} & {\scriptsize1.367} & {\scriptsize0.748}\\
\hline
{\tiny 6.0-8.0} & {\scriptsize6.926} & {\scriptsize146.9} & {\scriptsize895.2} & {\scriptsize2620} & {\scriptsize3790} & {\scriptsize2173} & {\scriptsize386.3}
& {\scriptsize51.72} & {\scriptsize12.80} & {\scriptsize4.622} & {\scriptsize2.715}\\
\hline
{\tiny 8.0-10.0} & {\scriptsize0.346} & {\scriptsize12.01} & {\scriptsize87.04} & {\scriptsize400.3} & {\scriptsize1451} & {\scriptsize3242} & {\scriptsize2012} & {\scriptsize354.2} & {\scriptsize48.22} & {\scriptsize12.81} & {\scriptsize5.371}\\
\hline
{\tiny 10.0-12.5} & {\scriptsize0.173} & {\scriptsize3.274} & {\scriptsize25.27} & {\scriptsize70.34} & {\scriptsize224.4} & {\scriptsize1460} & {\scriptsize3617} & {\scriptsize2256} & {\scriptsize393.9} & {\scriptsize49.64} & {\scriptsize15.19}\\
\hline
{\tiny 12.5-15.0} & {\scriptsize0} & {\scriptsize0.136} & {\scriptsize5.283} & {\scriptsize26.99} & {\scriptsize55.52} & {\scriptsize199.2} & {\scriptsize1243} & {\scriptsize3171} & {\scriptsize1971} & {\scriptsize249.2} & {\scriptsize29.33}\\
\hline
{\tiny 15.0-20.0} & {\scriptsize0} & {\scriptsize0.136} & {\scriptsize0.384} & {\scriptsize2.907} & {\scriptsize14.79} & {\scriptsize68.24} & {\scriptsize273.2} &
{\scriptsize1634} & {\scriptsize4485} & {\scriptsize3151} & {\scriptsize357.7}\\
\hline
{\tiny 20.0-25.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.281} & {\scriptsize1.713} & {\scriptsize19.83} & {\scriptsize95.11} & {\scriptsize528.3} & {\scriptsize3212} & {\scriptsize2766}\\
\hline
{\tiny overflow} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.209} & {\scriptsize1.058} & {\scriptsize7.980} & {\scriptsize44.73} & {\scriptsize631.9} & {\scriptsize3982}\\
\hline
  \end{tabular}
  \end{center}
  \caption{\emph{$\overline{\nu}_\mu$ appearance detection efficiency. All values $\times 10^{-4}$}}
\end{table}

\hspace{1.0cm}       {\large $\nu_\mu$ CC background }

\begin{table}[!ht]
  \begin{center}
  \begin{tabular}{|l||c|c|c|c|c|c|c|c|c|c|c|}
    \hline
    & {\tiny 0-2.0} & {\tiny 2.0-3.0} & {\tiny 3.0-4.0} & {\tiny 4.0-5.0} & {\tiny 5.0-6.0} & {\tiny 6.0-8.0} & {\tiny 8.0-10.0} & {\tiny 10.0-12.5} & {\tiny 12.5-15.0} & {\tiny 15.0-20.0} & {\tiny 20.0-25.0}\\
    \hline
    \hline
    {\tiny 0-2.0} & {\scriptsize0} & {\scriptsize0.251} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 2.0-3.0} & {\scriptsize0.112} & {\scriptsize0.251} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.039}\\
\hline
{\tiny 3.0-4.0} & {\scriptsize0.224} & {\scriptsize0.126} & {\scriptsize0} & {\scriptsize0.076} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.020}\\
\hline
{\tiny 4.0-5.0} & {\scriptsize0} & {\scriptsize0.628} & {\scriptsize0.249} & {\scriptsize0.076} & {\scriptsize0.176} & {\scriptsize0.079} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 5.0-6.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.166} & {\scriptsize0.378} & {\scriptsize0.088} & {\scriptsize0.040} & {\scriptsize0.033} & {\scriptsize0} & {\scriptsize0.028} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 6.0-8.0} & {\scriptsize0} & {\scriptsize0.251} & {\scriptsize0.249} & {\scriptsize0.605} & {\scriptsize0.529} & {\scriptsize0.119} & {\scriptsize0.329}
& {\scriptsize0.126} & {\scriptsize0.057} & {\scriptsize0.095} & {\scriptsize0.098}\\
\hline
{\tiny 8.0-10.0} & {\scriptsize0} & {\scriptsize0.126} & {\scriptsize0} & {\scriptsize0.151} & {\scriptsize0.176} & {\scriptsize0.316} & {\scriptsize0.099} & {\scriptsize0.063} & {\scriptsize0.028} & {\scriptsize0.057} & {\scriptsize0.078}\\
\hline
{\tiny 10.0-12.5} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.076} & {\scriptsize0.088} & {\scriptsize0.277} & {\scriptsize0.066} & {\scriptsize0.063} & {\scriptsize0.142} & {\scriptsize0.076} & {\scriptsize0.098}\\
\hline
{\tiny 12.5-15.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.088} & {\scriptsize0.119} & {\scriptsize0.197} & {\scriptsize0.126} & {\scriptsize0.113} & {\scriptsize0.057} & {\scriptsize0.098}\\
\hline
{\tiny 15.0-20.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.033} & {\scriptsize0.063} & {\scriptsize0.085} & {\scriptsize0.038} & {\scriptsize0.078}\\
\hline
{\tiny 20.0-25.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.031} & {\scriptsize0.028} & {\scriptsize0.057} & {\scriptsize0.059}\\
\hline
{\tiny overflow} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.057} & {\scriptsize0.038} & {\scriptsize0.078}\\
\hline
  \end{tabular}
  \end{center}
  \caption{\emph{$\overline{\nu}_\mu$ CC background. All values $\times 10^{-4}$.}}
\end{table}
\newpage

\hspace{1.0cm}       {\large $\overline{\nu}_e$ CC background }

\begin{table}[!ht]
  \begin{center}
  \begin{tabular}{|l||c|c|c|c|c|c|c|c|c|c|c|}
    \hline
    & {\tiny 0-2.0} & {\tiny 2.0-3.0} & {\tiny 3.0-4.0} & {\tiny 4.0-5.0} & {\tiny 5.0-6.0} & {\tiny 6.0-8.0} & {\tiny 8.0-10.0} & {\tiny 10.0-12.5} & {\tiny 12.5-15.0} & {\tiny 15.0-20.0} & {\tiny 20.0-25.0}\\
    \hline
    \hline
    {\tiny 0-2.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.030} & {\scriptsize0} & {\scriptsize0} &
{\scriptsize0.017} & {\scriptsize0.018}\\
\hline
{\tiny 2.0-3.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.037} & {\scriptsize0} & {\scriptsize0.029} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.053}\\
\hline
{\tiny 3.0-4.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 4.0-5.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.035} & {\scriptsize0}\\
\hline
{\tiny 5.0-6.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.026} & {\scriptsize0} & {\scriptsize0.018}\\
\hline
{\tiny 6.0-8.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 8.0-10.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.017} & {\scriptsize0}\\
\hline
{\tiny 10.0-12.5} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.037} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 12.5-15.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 15.0-20.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny 20.0-25.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
{\tiny overflow} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0}\\
\hline
  \end{tabular}
  \end{center}
  \caption{\emph{$\overline{\nu}_e$ CC background. All values $\times 10^{-4}$.}}
\end{table}
\vspace{0.25cm}

\hspace{1.0cm}       {\large NC background }

\begin{table}[!ht]
  \begin{center}
  \begin{tabular}{|l||c|c|c|c|c|c|c|c|c|c|c|}
    \hline
    & {\tiny 0-2.0} & {\tiny 2.0-3.0} & {\tiny 3.0-4.0} & {\tiny 4.0-5.0} & {\tiny 5.0-6.0} & {\tiny 6.0-8.0} & {\tiny 8.0-10.0} & {\tiny 10.0-12.5} & {\tiny 12.5-15.0} & {\tiny 15.0-20.0} & {\tiny 20.0-25.0}\\
    \hline
    \hline
    {\tiny 0-2.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.070} & {\scriptsize0.016} & {\scriptsize0.013} & {\scriptsize0.038} & {\scriptsize0.056} & {\scriptsize0.023} & {\scriptsize0.055}\\
\hline
{\tiny 2.0-3.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.068} & {\scriptsize0.030} & {\scriptsize0.070} & {\scriptsize0.094} & {\scriptsize0.026} &
{\scriptsize0.038} & {\scriptsize0.079} & {\scriptsize0.061} & {\scriptsize0.063}\\
\hline
{\tiny 3.0-4.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.137} & {\scriptsize0.091} & {\scriptsize0.106} & {\scriptsize0.110} & {\scriptsize0.092} & {\scriptsize0.088} & {\scriptsize0.213} & {\scriptsize0.129} & {\scriptsize0.117}\\
\hline
{\tiny 4.0-5.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.068} & {\scriptsize0.122} & {\scriptsize0.317} & {\scriptsize0.268} & {\scriptsize0.275} & {\scriptsize0.189} & {\scriptsize0.213} & {\scriptsize0.236} & {\scriptsize0.250}\\
\hline
{\tiny 5.0-6.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.030} & {\scriptsize0} & {\scriptsize0.063} & {\scriptsize0.079} & {\scriptsize0.101} & {\scriptsize0.067} & {\scriptsize0.084} & {\scriptsize0.055}\\
\hline
{\tiny 6.0-8.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.070} & {\scriptsize0.094} & {\scriptsize0.171} & {\scriptsize0.076} & {\scriptsize0.180} & {\scriptsize0.137} & {\scriptsize0.156}\\
\hline
{\tiny 8.0-10.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.016} & {\scriptsize0.105} & {\scriptsize0.076} & {\scriptsize0.101} & {\scriptsize0.084} & {\scriptsize0.117}\\
\hline
{\tiny 10.0-12.5} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.039} & {\scriptsize0.06} & {\scriptsize0.056} & {\scriptsize0.053} & {\scriptsize0.055}\\
\hline
{\tiny 12.5-15.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.025} & {\scriptsize0.011} & {\scriptsize0.053} & {\scriptsize0.031}\\
\hline
{\tiny 15.0-20.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.011} & {\scriptsize0.023} & {\scriptsize0.047}\\
\hline
{\tiny 20.0-25.0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.008}\\
\hline
{\tiny overflow} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0} & {\scriptsize0.008}\\
\hline
  \end{tabular}
  \end{center}
  \caption{\emph{NC background. All values $\times 10^{-4}$.}}
\end{table}
