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\@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces  The neutrino energy and reconstructed neutrino energy distribution of single electron-like ring events originating from QE.}}{3}{}}
\newlabel{fig:erecQE}{{1}{3}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  The neutrino energy and reconstructed neutrino energy distribution of single electron-like ring events originating from all the charged current interactions.}}{4}{}}
\newlabel{fig:erecCC}{{2}{4}{}{}{}}
\citation{ref:Barszczek}
\citation{ref:polfit}
\citation{ref:Barszczek}
\citation{ref:polfit}
\citation{ref:ATMFull}
\citation{ref:BNLVLB}
\@writefile{toc}{\contentsline {section}{\numberline {II}Monte Carlo Event Sample}{6}{}}
\citation{ref:BNLVLB}
\citation{ref:Barszczek}
\@writefile{toc}{\contentsline {section}{\numberline {III}POLfit}{7}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  Reconstructed $\pi ^0$ mass of single e-like ring events from neutral current single $\pi ^0$ production using \textit  {POLfit}{}.}}{8}{}}
\newlabel{fig:pi0massdist}{{3}{8}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  $\pi ^0$ reconstruction efficiency with (1- and 2-ring events, solid circles) and without (2-ring events only,open circles) \textit  {POLfit}{}.}}{9}{}}
\newlabel{fig:pi0effic}{{4}{9}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {IV}Quantities used to distinguish the signal from the background}{10}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {A}Reconstructed $\pi ^0$ mass $m_{\gamma \gamma }$ ($m_{\gamma \gamma }$)}{10}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces  Distributions of reconstructed $\pi ^0$ mass of single e-like ring events for signal (solid line) and background (dotted line).}}{11}{}}
\newlabel{fig:pi0mass}{{5}{11}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {B}Fraction of energy in the second ring (E$_{frac}$)}{11}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  E$_{frac}$: The distributions of the energy fraction of the second ring found by \textit  {POLfit}{} in 1-ring events for the signal (solid line) and background (dotted line).}}{12}{}}
\newlabel{fig:efrac}{{6}{12}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {C}Difference in log $\pi ^0$ likelihood ratio ($\Delta \mathop {\mathgroup \symoperators log}\nolimits \pi ^0$-lh)}{12}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces  $\Delta \mathop {\mathgroup \symoperators log}\nolimits \pi ^0$-lh: The distributions of the difference in log $\pi ^0$ likelihood between the two algorithms. The larger this quantity, the more likely an event is $\pi ^0$ background. The distribution in solid line is for the signal and that in dotted line is for the background.}}{13}{}}
\newlabel{fig:dpi0likelihood}{{7}{13}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {D}Direction cosine of the e-like ring ($\mathop {\mathgroup \symoperators cos}\nolimits \theta $)}{13}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces  $\mathop {\mathgroup \symoperators cos}\nolimits \theta $: The distributions of the directional cosine of the primary e-like ring with respect to the neutrino beam direction. The distribution in solid is for the signal and that in dotted is for the background.}}{14}{}}
\newlabel{fig:costh}{{8}{14}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {E}Ratio: Total charge to ring energy (Q/E)}{14}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces  Q/E: the distributions of the ratio, the total charge in pe to the ring energy in MeV are shown. The distribution in solid is for the signal and that in dotted line is for the background.}}{15}{}}
\newlabel{fig:poa}{{9}{15}{}{}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {F}log pid-likelihood (log pid-lh)}{16}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {G}$\mathop {\mathgroup \symoperators log}\nolimits \pi ^0$-likelihood ($\mathop {\mathgroup \symoperators log}\nolimits \pi ^0$-lh)}{16}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {H}Cherenkov angle (Cangle)}{16}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {I}Log ring-count likelihood ratio ($\Delta \mathop {\mathgroup \symoperators log}\nolimits $ ring-lh)}{16}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces  log pid-lh: The distributions of the log-likelihood ratio between e-like and $\mu $-like of the primary e-like ring The distribution in solid line is for the signal and that in dotted line is for the background.}}{17}{}}
\newlabel{fig:elike}{{10}{17}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {V}Discriminator: Likelihood function and likelihood ratio}{17}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces  $\mathop {\mathgroup \symoperators log}\nolimits \pi ^0$-lh: The distributions of the $\pi ^0$-likelihood of the primary e-like ring. The distribution in solid line is for the signal and that in dotted line is for the background.}}{18}{}}
\newlabel{fig:pi0like}{{11}{18}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces  Cangle: The distributions of the measured Cherenkov angle of the primary e-like ring. The distribution in solid line is for the signal and that in dotted line is for the background.}}{19}{}}
\newlabel{fig:Cangle}{{12}{19}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces  $\Delta \mathop {\mathgroup \symoperators log}\nolimits $ ring-lh: The distributions of log-likelihood ratio of two hypotheses on the number of Cherenkov ring in an event: there is only one Cherenkov ring or more. If the log-likelihood ratio is negative, the event is less likely to have an additional ring. The distributions in solid line are for the signal and that in dotted line are for the background.}}{20}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces The distributions of log-likelihood ratio of two hypotheses on the origin of events: signal vs. background. The distributions in solid line are for the signal and that in dotted line are for the background.}}{21}{}}
\newlabel{fig:dlogL}{{14}{21}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {VI}Reconstructed neutrino energy distributions with a cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$}{21}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces The distribution of the reconstructed neutrino energy with the standard Super-Kamiokande cuts before the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied. The distribution in dashed line is for the signal and those in dotted (dash-dotted) line is for the background 1(2). $\delta _{CP}=+45^{o}$ and the baseline is 2,540 km.}}{22}{}}
\newlabel{fig:P100Erec}{{15}{22}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 50\% of the signal events survive by this cut. The distribution in dashed line is for the signal and that in dotted (dash-dotted) line is for the background. $\delta _{CP}=+45^{o}$ and the baseline is 2,540 km.}}{23}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distribution in dashed line is for the signal and that in dotted (dash-dotted) line is for the background 1(2). $\delta _{CP}=+45^{o}$ and the baseline is 2,540 km.}}{24}{}}
\newlabel{fig:P40Erec+45}{{17}{24}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {VII}$E_{rec}$ distributions and CP-violating phase $\delta _{CP}$}{24}{}}
\@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Summary of the numbers of the signal and background events, and the signal-to-background ratio using events from background 1 with the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ to retain 40\% of the signal events. The CP-violating phase is assumed to be $45^{o}$ and the baseline is 2,540 km.}}{25}{}}
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\@writefile{lot}{\contentsline {table}{\numberline {II}{\ignorespaces Summary of the numbers of the signal and background events for different values of $\delta _{CP}$ using events from background 1 with the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ to retain 40\% of the signal events with the baseline of 2,540 km.}}{25}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distributions in dashed line is for the signal and that in dotted (dash-dotted) line is for the background 1(2). $\delta _{CP}=+135^{o}$ and the baseline is 2,540 km.}}{26}{}}
\newlabel{fig:P40Erec+135}{{18}{26}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {VIII}$E_{rec}$ distributions and baseline}{26}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distribution in dashed line is for the signal and that in dotted (dash-dotted) line is for the background 1(2). $\delta _{CP}=0^{o}$ and the baseline 2,540 km.}}{27}{}}
\newlabel{fig:P40Erec0}{{19}{27}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {IX}Sources of background events}{27}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {20}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distribution in dashed line is for the signal and that in dotted (dash-dotted) line is for the background. $\delta _{CP}=-45^{o}$ and the baseline is 2,540 km}}{28}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {21}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distribution in dashed line is for the signal and that in dotted (dash-dotted) line is for the background 1(2). $\delta _{CP}=-135^{o}$ and the baseline is 2,540 km.}}{29}{}}
\newlabel{fig:P40Erec-135}{{21}{29}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {22}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distributions in dashed line is for the signal and that in dotted (dash-dotted) line is for the background 1(2). $\delta _{CP}=+135^{o}$ and the baseline is 1,480 km.}}{30}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {23}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distributions in dashed line is for the signal and that in dotted (dash-dotted) line is for the background. $\delta _{CP}=+45^{o}$ and the baseline is 1,480 km.}}{31}{}}
\newlabel{fig:P40Erec+45FH}{{23}{31}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {X}Detector size and granularity}{31}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {24}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distributions in dashed line is for the signal and that in dotted (dash-dotted) lines is for the background. $\delta _{CP}=0^{o}$ and the baseline is 1,480km.}}{32}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {25}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distribution in dashed line is for the signal and that in dotted (dashed-dotted) line is for the background 1(2). $\delta _{CP}=-45^{o}$ and the baseline is 1,480 km.}}{33}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {26}{\ignorespaces The distribution of the reconstructed neutrino energy, in addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distribution in dashed line is for the signal and that in dotted (dash-dotted) line is for the background 1(2). $\delta _{CP}=-135^{o}$ and the baseline is 1,480 km.}}{34}{}}
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\@writefile{lot}{\contentsline {table}{\numberline {III}{\ignorespaces Summary of the numbers of signal and background events for different values for $\delta _{CP}$ using events from background 1 with the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ to retain 40\% of the signal events with the baseline of 1,480 km.}}{35}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {27}{\ignorespaces The distribution of the neutrino energies that produced the signal, background 1 and background 2 events. In addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distribution in dashed line is for the signal and that in dotted (dash-dotted) is for the background 1(2). $\delta _{CP}=+45^{o}$ and the baseline is 2,540 km.}}{36}{}}
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\bibcite{ref:BNLVLB}{{1}{}{{}}{{}}}
\@writefile{lof}{\contentsline {figure}{\numberline {28}{\ignorespaces The distribution of the neutrino energies that produced the signal, background 1 and background 2 events. In addition to the standard Super-Kamiokande cuts, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ is applied in such a way to retain 40\% of the signal events survive by this cut. The distribution in dashed line is for the signal and that in dotted (dash-dotted) is for the background 1(2). $\delta _{CP}=+45^{o}$ and the baseline is 1,480 km.}}{37}{}}
\newlabel{fig:enuspec1480}{{28}{37}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {}Acknowledgments}{37}{}}
\bibcite{ref:SKSoft}{{2}{}{{}}{{}}}
\bibcite{ref:ATMFull}{{3}{}{{}}{{}}}
\bibcite{ref:Barszczek}{{4}{}{{}}{{}}}
\bibcite{ref:polfit}{{5}{}{{}}{{}}}
\@writefile{lot}{\contentsline {table}{\numberline {IV}{\ignorespaces Summary of the percent contributions from events produced by different interactions for signal events and for background 1 events are summarized in the cases for $\delta _{CP}=+45^o$, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ to retain 40\% of the signal events and the baseline of 2,540 km.}}{38}{}}
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\@writefile{lot}{\contentsline {table}{\numberline {V}{\ignorespaces Summary of the percent contributions from events produced by different interactions for signal events and for background 1 events are summarized in the cases for $\delta _{CP}=+45^o$, the cut on $\Delta \mathop {\mathgroup \symoperators log}\nolimits L$ to retain 40\% of the signal events and the baseline of 1,480 km.}}{39}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {29}{\ignorespaces The $\pi ^0$ detection efficiency as a function of the two photon opening angle for three ranges of the distance from the $\pi ^0$ production vertex to the closest PMT surface in the direction of $\pi ^0$.}}{40}{}}
\newlabel{fig:pi0size}{{29}{40}{}{}{}}