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cau-ath-djf-0007_i1-0/performance-analysis.tex

@@ -266,22 +266,20 @@ Based on the analysis above we have decided that \textbf{a Cherenkov is recommen
 
 \begin{itemize}
     \item The high-accuracy data products limit the opening angle by requiring all detectors to be hit by a particle. This limits the opening angle and thus the geometric factor leading to lower statistics compared to the high-statistics channels. The benefit, however, is a reduced contamination (i.e. of protons in the electron channel) leading to lower systematic uncertainties.
-    \item The high-statistics data products do not require all detectors to be hit, improving the opening angle and thus the statistics on the cost of a higher contamination.
+    \item The high-statistics data products do not require all detectors to be hit, improving the opening angle and thus the statistics on the cost of a higher contamination (i.e. the Cherenkov detectors can not be utilized for particles with oblique trajectories).
 \end{itemize}
-Since these data products will be produced in parallel, measurements over a prolonged time period can be utilized to validate and/or improve the high-statistics channel by comparing the fluxes to the high-accuracy mode. In addition, the high-statistics data products can be used to monitor temporal variations over a time period of interest. If no variations are observed, this information allows the usage of the high-accuracy mode in that given time period by accumulating statistics.\newline
-
-In order to provide estimates on the uncertainties
-Furthermore, particle identification and expected count rates (statistical uncertainties) have been investigated as summarized below. 
-
+Since these data products will be produced in parallel, the high-statistics data products can be used to monitor temporal variations over a time period of interest. If no variations are observed, this information allows the usage of the high-accuracy mode in that given time period by accumulating statistics.\newline
+In addition, measurements over a prolonged time period can be utilized to validate and/or improve the high-statistics channel by comparing the fluxes to the high-accuracy mode. This is especially important for the electron measurements due to the proton contamination. This contamination will be corrected for by using the measured proton spectrum and the simulated response (i.e. the likely-hood of a proton to end up in the electron channel) in order to estimate the number of protons in the electron channels and subtract this from the measured electron channel count rate. A detailed mathematical description of the systematic uncertainties introduced by this method is given in section \ref{sec:error_estimation_eq}.\newline
 
+The derived uncertainties for the protons and electrons in their corresponding high-accuracy and high-statistics data products are summarized below. Note that while the proton uncertainty is derived from the expected counting statistics, the electron uncertainties also include the systematic uncertainties caused by proton contamination.
 
 
 
 \subsubsection*{High-accuracy proton channels}
 It has been shown that requiring a coincidence from SDA up to SDE for protons allows for utilizing the Cherenkov in order to separate at 2~GeV. Using this coincidence, protons from 150~MeV up to 2~GeV can be detected in
 \begin{itemize}
-    \item five channels on 10ks time resolution with 2.7\% uncertainty
-    \item two channels on 3ks time resolution with 3.1\% uncertainty
+    \item five channels on 10ks time resolution with 2.7\% stat. uncertainty
+    \item two channels on 3ks time resolution with 3.1\% stat. uncertainty
 \end{itemize}
 This would also provide an integral channel for protons above 2~GeV.
 Note that the protons up to 150~MeV can also improve the statistics utilizing the stopping channels. \newline