add a section about the backgrounds

2 files changed, 154 insertions, 0 deletions

diff --git a/Makefile b/Makefile
index 96fe01c..2082cdb 100644
--- a/Makefile
+++ b/Makefile
@@ -9,6 +9,8 @@ default: all
 
 all: sddm.pdf
 
+all: sddm.pdf
+
 calculate_limits: calculate_limits.c
 
 sddm.pdf: sddm.tex
diff --git a/sddm.tex b/sddm.tex
index c7da970..1f3fa96 100644
--- a/sddm.tex
+++ b/sddm.tex
@@ -4,6 +4,9 @@
 \usepackage{tikz}
 \usepackage{hyperref}
 \usepackage{amsfonts}
+\usepackage{algorithmic}
+\renewcommand{\algorithmiccomment}[1]{\# #1}
+\usepackage{algorithm}
 \newcommand*\diff{\mathrm{d}}
 \usetikzlibrary{shapes}
 \author{Anthony LaTorre}
@@ -487,6 +490,151 @@ where in the last expression we define
 t_0(x) \equiv \frac{l(x)n(\lambda_0)}{c}
 \end{equation}
 
+\section{Backgrounds}
+\subsection{External Muons}
+Both cosmic ray muons and muons created from atmospheric neutrinos interacting
+in the surrounding rock present a background for this analysis. In both cases,
+it is necessary to cut events which start \emph{outside} the PSUP and enter the
+detector.
+
+During SNO, these events were cut using the MUON cut which tagged events with
+at least 150 hits, 5 or more outward-looking (OWL) PMT hits, and with a time
+RMS of less than 90 nanoseconds. This cut would have a negligible sacrifice for
+any contained atmospheric or dark matter candidate events, but could
+potentially cut events which produce an energetic muon which then exits the
+detector. Therefore, I have slightly modified this cut to \emph{also} require
+that at least 1 OWL tube is both early and has a high charge relative to the
+nearby normal PMTs. We define a early and high charge tube by creating an array
+of the ECA calibrated hit times (we can't use PCA calibrated times since the
+OWL tubes were never calibrated via PCA) and of the best uncalibrated charge
+(FIXME: footnote?) for all normal PMTs within 3 meters of each hit OWL PMT. We
+then compute the median charge and time for these normal PMTs. We then compute
+how many OWL PMT hits are \emph{both} earlier than the median normal PMT time
+and have a higher charge than the surrounding PMTs. If at least 1 OWL PMT hit
+satisfies this criteria and all the other criteria from the SNO MUON cut are
+satisifed (except the time RMS part) then it's tagged as a muon.
+
+\subsection{Noise Events}
+
+There are several sources of noise events which refers to events triggered by
+sources which do not actually create light in the detector. The two most common
+sources are "ringing" after large events and electrical pickup on deck.
+
+These events are tagged by the QvNHIT and ITC cuts which are identical to their
+SNO counterparts aside from minor updates\footnote{The ITC cut uses the pt1
+time which is the time without the charge walk calibration since otherwise the
+cut may fail to tag an event which consists of mostly electronics noise which
+has charge too low to apply PCA. The QvNHIT cut does not require good
+calibrations for the hits for a similar reason.}.
+
+\subsection{Neck Events}
+
+Neck events are caused by light produced in or leaking through the glove box on
+top of the detector\cite{sonley}. The SNO neck event cut is defined
+as\cite{snoman_companion}:
+
+\begin{quotation}
+This cuts events containing neck tubes. It requires that either both tubes in
+the neck fire, or that one of those tubes fires and it has a high charge and is
+early. High charge is defined by a neck tube having a pedestal subtracted
+charge greater than 70 or less than -110. Early if defined by the neck tube
+having an ECA time 70ns or more before the average ECA time of the PSUP PMTS
+with z les than 0. After the cable changes to the neck tubes this time
+difference changes to 15ns. 
+\end{quotation}
+
+Similarly to the MUON cut, I've used these criteria but added an additional
+requirement to avoid tagging high energy upwards going events. The NECK cut I
+use also has a requirement that 50\% of the hit PMTs must have a z coordinate
+of less than 4.25 meters \emph{or} 50\% of the ECA calibrated QHS charge must
+be below z = -4.25 meters.
+
+\subsection{Flashers}
+
+Flashers are probably the most difficult and common source of instrumental
+background for this analysis. A flasher event occurs when there is an
+electrical short in the PMT base or dynode stack which causes light to be
+emitted from the PMT and hit the opposite side of the
+detector\textsuperscript{[citation needed]}. Because this event is caused by
+actual light in the detector it is particularly hard to cut while also
+maintaining a small signal sacrifice.
+
+The cut algorithm is sufficiently complex that it is easier to describe in
+pseudocode. A description of the algorithm is shown in
+Algorithm~\ref{flasher_algorithm}.
+
+\begin{algorithm}
+\caption{Flasher Cut Algorithm}
+\label{flasher_algorithm}
+\begin{algorithmic}
+  \IF{nhit $< 31$} \RETURN 0 \ENDIF
+
+  \COMMENT{This condition is similar to the SNO QvT cut except we require that 70\% of the normal hit PMTs be 12 meters from the high charge channel and that 70\% of the normal hit PMTs be at least 50 ns after the high charge channel.}
+
+  \IF{highest QLX $>$ second highest QLX $+ 80$}
+     \STATE {Collect all hit times from the same slot as the high charge channel and compute the median hit time}
+     \IF{At least 4 hits in the slot \AND 70\% of the normal hit PMTs with good calibration are more than 12 meters from the high charge channel \AND 70\% of the normal hit PMTs with good calibration are more than 50 ns after the median hit time in the slot}
+       \RETURN 1
+     \ENDIF
+  \ENDIF
+  \FOR{All PC with at least 4 hits}
+    \STATE {Collect the QHS, QHL, and QLX charges and the ECA calibrated hit times (EPT) for each PMT in the PC sending charge values below 300 to 4095}
+    \STATE {$t \leftarrow \textrm{median}(\textrm{EPT})$}
+    \STATE {$\textrm{QHS}_1 \leftarrow \textrm{max}(\textrm{QHS})$}
+    \STATE {$\textrm{QHL}_1 \leftarrow \textrm{max}(\textrm{QHL})$}
+    \STATE {$\textrm{QLX}_1 \leftarrow \textrm{max}(\textrm{QLX})$}
+    \STATE {$\textrm{QHS}_2 \leftarrow \textrm{second highest}(\textrm{QHS})$}
+    \STATE {$\textrm{QHL}_2 \leftarrow \textrm{second highest}(\textrm{QHL})$}
+    \STATE {$\textrm{QLX}_2 \leftarrow \textrm{second highest}(\textrm{QLX})$}
+    \IF{$\textrm{QHS}_1 > \textrm{QHS}_2 + 1000$}
+      \IF{70\% of the normal hit PMTs with good calibration are more than 12 meters from the high charge channel \AND 70\% of the normal hit PMTs with good calibration are more than 50 ns after $t$}
+        \RETURN 1
+      \ENDIF
+    \ELSIF{$\textrm{QHL}_1 > \textrm{QHL}_2 + 1000$}
+      \IF{70\% of the normal hit PMTs with good calibration are more than 12 meters from the high charge channel \AND 70\% of the normal hit PMTs with good calibration are more than 50 ns after $t$}
+        \RETURN 1
+      \ENDIF
+    \ELSIF{$\textrm{QLX}_1 > \textrm{QLX}_2 + 80$}
+      \IF{70\% of the normal hit PMTs with good calibration are more than 12 meters from the high charge channel \AND 70\% of the normal hit PMTs with good calibration are more than 50 ns after $t$}
+        \RETURN 1
+      \ENDIF
+    \ELSE
+      \FOR{All normal PMT channels \emph{not} hit in PC}
+        \IF{more hits in slot than surrounding 4 meters or median hit time in slot is 10 ns earlier than PMTs within 4 meters}
+          \IF{70\% of the normal hit PMTs with good calibration are more than 12 meters from the high charge channel \AND 70\% of the normal hit PMTs with good calibration are more than 50 ns after $t$}
+            \RETURN 1
+          \ENDIF
+        \ENDIF
+      \ENDFOR
+    \ENDIF
+  \ENDFOR
+  \RETURN 0
+\end{algorithmic}
+\end{algorithm}
+
+\subsection{Breakdowns}
+
+Breakdowns are very similar to flashers except that they produce \emph{much}
+more light\footnote{In fact, I think there is a continuous spectrum between
+flashers and breakdowns, but the distinction is still helpful since the way to
+tag the two are very different}.
+
+Since breakdowns often cause many of the electronics to saturate, it is
+\emph{very} difficult to find a single common characteristic on which to cut.
+However, the one thing that does seem to be common among almost all breakdowns
+is that the crate with the channel that breaks down all has pickup from the
+breaking down channel and thus comes much earlier in the event than the rest of
+the PMT hits.
+
+Therefore, the breakdown cut tags any event which has at least 1000 PMT hits
+and in which the crate with the highest median TAC has at least 256 hits and is
+500 TAC counts away from the next highest crate (with at least 20 hits).
+
+Occasionally a breakdown is so big that it causes issues with the TAC
+measurement and many of them end up reading outside of the linear TAC region.
+Therefore we also tag any events in which less than 70\% of the PMT hits have a
+TAC value above 400.
+
 \begin{thebibliography}{9}
 \bibitem{grossman2017}
     Grossman, et al. \textit{Self-Destructing Dark Matter}. \href{https://arxiv.org/abs/1712.00455}{{\tt arXiv:1712.00455}}. Dec 2017.
@@ -496,5 +644,9 @@ t_0(x) \equiv \frac{l(x)n(\lambda_0)}{c}
     T. Caldwell. \textit{Searching for Dark Matter with Single Phase Liquid Argon}. \url{https://repository.upenn.edu/dissertations/1632}. 2015.
 \bibitem{pdg2017}
     C. Patrignani et al. (Particle Data Group), Chin. Phys. C, 40, 100001 (2016) and 2017 update.
+\bibitem{sonley}
+    T. Sonley. \textit{A Measurement of the Atmospheric Neutrino Flux and Oscillation Parameters at the Sudbury Neutrino Observatory}. Feb 2009. \url{https://www.sno.phy.queensu.ca/sno/papers/Sonley_phd_physics_2009.pdf}. Access Date: Oct 5, 2019.
+\bibitem{snoman_companion}
+    \textit{SNOMAN Companion}. Last updated: Nov. 8, 2006. \url{http://hep.uchicago.edu/~tlatorre/snoman_companion/}. Access Date: Oct 5, 2019.
 \end{thebibliography}
 \end{document}