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| -rw-r--r-- | doc/sddm.tex | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/doc/sddm.tex b/doc/sddm.tex index 1f3fa96..7da66e9 100644 --- a/doc/sddm.tex +++ b/doc/sddm.tex @@ -1,4 +1,4 @@ -\documentclass{article} +\documentclass{book} \usepackage{amsmath} % for \text command \usepackage{fullpage} \usepackage{tikz} @@ -14,8 +14,8 @@ \title{Searching for Dark Matter with the Sudbury Neutrino Observatory} \begin{document} \maketitle -\section{Introduction} -\section{Estimating the Event rate in the SNO detector} +\chapter{Introduction} +\chapter{Estimating the Event rate in the SNO detector} The event rate of self destructing dark matter events, $R$, in the SNO detector is given by first integrating over the detector. \begin{equation} R = \int_\mathrm{SNO} \mathrm{d}^3r \, R(r) @@ -109,7 +109,7 @@ where $\theta_\text{min}$ is equal to: where $R$ is the radius of the earth and $\text{depth}$ is the distance from the surface of the earth to the SNO detector. -\section{Cross Section} +\chapter{Cross Section} In \cite{grossman2017} the differential scattering cross section for dark matter off a nucleus is calculated as \begin{equation} @@ -157,7 +157,7 @@ and the cross section for the dark matter to annihilate is: \frac{\diff \sigma_\text{scatter}}{\diff q^2} \simeq \frac{1}{4 \mu_p^2 v^2} \sigma_p |F_D(q)|^2 Z^2 F^2(q). \end{equation} -\subsection{Nuclear Form Factor} +\section{Nuclear Form Factor} The nuclear form factor, $F(q)$, characterizes the loss of coherence as the de Broglie wavelength of the WIMP approaches the radius of the nucleus\cite{caldwell2015}. The most commonly used form factor calculation used @@ -206,7 +206,7 @@ r_1 &= \sqrt{c^2 + \frac{7}{3}\pi^2 a^2 - 5 s^2} \end{tikzpicture} \end{figure} -\section{Event Reconstruction} +\chapter{Event Reconstruction} In order to reconstruct the physical parameters associated with an event we compute a likelihood for that event given a proposed energy, position, direction, and initial time. The likelihood may be written as: @@ -490,8 +490,8 @@ 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} +\chapter{Backgrounds} +\section{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 @@ -514,7 +514,7 @@ 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} +\section{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 @@ -527,7 +527,7 @@ 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} +\section{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 @@ -549,7 +549,7 @@ 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} +\section{Flashers} Flashers are probably the most difficult and common source of instrumental background for this analysis. A flasher event occurs when there is an @@ -612,7 +612,7 @@ Algorithm~\ref{flasher_algorithm}. \end{algorithmic} \end{algorithm} -\subsection{Breakdowns} +\section{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 |