\section{Mu3e experiment}

\subsection{Requirements}

The ultimate goal of this experiment is to observe a $\mu \rightarrow eee$ event. As we strive for a sensitivity of $10^{-16}$ , we should be able to observe this process if its branching ratio would be higher than our sensitivity. Otherwise we want to exclude a branching ratio $>10^{-16}$ with a $90\%$ certainty.\\
To get to this sensitivity, more than $5.5 \cdot 10^{16}$ muon decays have to be observed. To reach this goal within one year, a muon stopping rate of $2 \cdot 10^9 Hz$ in combination with a high geometrical acceptance as well as a high efficiency of the experiment is required.

\subsection{Phase I}

Phase I of the experiment serves as an exploratory phase to gain more experience with the new technology and validate the experimental concept. At the same time it already strives to produce competitive measurements with a sensitivity of $10^{-15}$. \footnote{Current experiments are in the $10^{-12}$ sensitivity range} This will be done, by making use of the already existing muon beams at PSI with around $1$-$1.5\cdot10^{8}Hz$ of muons on target. The lowered sensitivity also allows for some cross-checks as the restrictions on the system are much more relaxed than in phase II.

\subsection{Phase II}

Phase II strives to reach the maximum sensitivity of $10^{-16}$. To achieve this in a reasonable time a new beamline will be used which delivers more than $2\cdot10^{9}Hz$ of muons.

\subsection{Experimental setup}

The detector is of cylindrical shape around the beam. It has a total length of around $2m$ and is situated inside a $1T$ solenoid magnet with $1m$ of inner radius and a total length of $2.5m$.

\begin{figure}[H]
\begin{center}
\begin{subfigure}{0.8\textwidth}
\includegraphics[width=1\textwidth]{img/setup-Ia.png}
\caption{Setup of the detector in the first part of phase I}
\label{setup_Ia}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\includegraphics[width=0.8\textwidth]{img/tracks-phase_I.png}
\caption{Tracks in the detector in the first part of phase I}
\label{tracks_Ia}
\end{subfigure}
\begin{subfigure}{0.45\textwidth}
\includegraphics[width=0.8\textwidth]{img/tracks-phase_II.png}
\caption{Tracks in the detector in the second part of phase I and Phase II}
\label{tracks_Ib,_II}
\end{subfigure}
\begin{subfigure}{1\textwidth}
\includegraphics[width=1\textwidth]{img/setup-Ib.png}
\caption{Setup of the detector in the second part of phase I}
\label{setup_Ib}
\end{subfigure}
\begin{subfigure}{1\textwidth}
\includegraphics[width=1\textwidth]{img/setup-II.png}
\caption{Setup of the detector in phase II}
\label{setup_II}
\end{subfigure}
\end{center}
\end{figure}\newpage

As seen in figure \ref{setup_II}, the final version of the detector can be divided into 5 separate parts in the longitudinal direction. There is the central part with the target, two inner silicon pixel layers, a fibre tracker and two outer silicon layers. The forward and backward parts, called recurl stations, consist only of a tile timing detector surrounded by two silicon recurl layers.\\\\

The target itself is a big surfaced double cone with a surface length of $10cm$ and a width of $2cm$. The target was chosen specifically to be of this shape to facilitate separating tracks coming from different muons.\\\
The two inner detector layers, also called vertex layers, span a length $12cm$. The innermost layer consists of 12 tiles while the outer vertex layer consists of 18 tiles. The tiles are each of $1cm$ width, with the inner layer having an average radius of $1.9cm$, respectively $2.9cm$. They are supported by two half cylinder made up of $25\mu m$ thin Kapton foil mounted on plastic. The detector layers itself are $50\mu m$ thin and cooled by gaseous helium. The vertex detectors are read out at a rate of $20MHz$, giving us a time resolution of $20ns$.\\
After the particles pass through the fibre tracker (see Figure \ref{tracks_Ib,_II}, \ref{setup_II}).