\section{\lhcb Experiment}


\subsection{\lhc}

The Large Hadron Collider (\lhc) is a proton-proton synchrotron situated nearly $200\m$ below the surface in a tunnel. The ring of superconducting magnets has a total length of $27\km$ containing two beam pipes filled with protons that are brought to collision at several points. Those collisions occurred at a total centre-of-mass energy of $\sqs = 7\tev$ in 2011 and $8\tev$ in 2012. After an upgrade, the energy has been increased to the centre-of-mass energy of $13\tev$ in 2015 and 2016.
The proton beams interact simultaneously in four detector points in the \lhc ring which experiments built around, \atlas, \cms, \lhcb and \alice. Two of them, \cms and \atlas, are more general-purpose experiments with a toroidal structure covering the whole space around the interaction point and operating at the full collision rate. With another goal in mind, there is also \alice, an experiment designed to study gluon-plasma and high-density events. For a fraction of the running time, the \lhc is filled with lead-ions in order to create lead-proton or lead-lead interactions.

%
%
%
\subsection{Detector}
The Large Hadron Collider beauty (\lhcb) is one out of four experiments situated at the \lhc at CERN\cite{Alves:2008zz}.
The \lhcb~ is designed to perform high-precision measurements of particles containing \bquark and \cquark quarks to study rare decays and \CP violation. In contrast to the other experiments located at the \lhc, the \lhcb is a single-arm forward spectrometer. This allows for measurements in the region of the \mbox{pseudorapidity} range $2<\eta <5$, the predominant flight direction of \bbbar-production.\newline
%
%
%
\begin{figure}[b]
	\centering
	\includegraphics[width=0.75\textwidth]{img/lhcb_side.png}
	\caption{A schematic view of the non-bending plane of the \lhcb detector. Particles are produced in the collision point on the left side inside the vertex locator and are bent by the magnet afterwards.}
	\label{fig:lhcb_schematic}
\end{figure}

\subsubsection{Vertex locator}
An important aspect of the \bquark and \cquark physics is the tracking of the particles close to the interaction point in order to precisely determine the primary and secondary vertices of heavy mesons. At the \lhcb this is achieved with the vertex locator (\velo), a series of modules with sensors made up of lightweight, radiation-hard silicon-strips. Each sensor is able to either measure the azimuthal coordinate or the radial distance to the beam axis, a single module contains both complementary sensors. The tracker is located about $8\mm$ from the aligned beam and is placed inside a beam-pipe independent vacuum system.

\subsubsection{Tracking system}
In addition to the \velo, several other tracking stations measure the tracks and bending of the particles. In front of the 4 Tm dipole magnets, the Tracker Turicensis is installed. It consists of four layers of silicon-strip detectors and allows for the detection of low-momenta particles which will be bent away in the magnetic field.

After the dipole magnet, the three tracking stations T1, T2 and T3 are placed. Each of them consists of an inner tracker situated close to the beam pipe and an outer tracker, covering the largest area of the tracker plane. The inner tracker is a silicon-strip detector covering the area with a high density of tracks. Another detector technique is used in the outer tracker as it covers a greater area without the need for the same precision as required in the inner tracker. In this case four layers of straw tubes filled with gas are used as drift chambers.

\subsubsection{\rich}
In \bquark physics it is important to have a good discrimination between charged particles, \eg\ \kaon and \pion. In order to achieve a good particle identification, there is a ring imaging Cherenkov detector (\rich) on each side of the magnet, which measure the Cherenkov emission angle $\theta_c$. The Cherenkov radiation is detected by pixel hybrid photon detectors. As the angle of the radiation relative to the particles flight direction depends on the velocity of the passing particle only, using additionally the information about the momentum from the tracker allows to determine the mass of the particle and therefore its identity. The Cherenkov angle also depends on the materials refractive index the charged particle is passing through. In order to cover a large momentum range with a good angle resolution, the \rich detectors are filled with materials of different refractive indices.

\subsubsection{Calorimeter}
A calorimeter measures the total as well as the differential energy loss by completely absorbing it through interactions with the material. For the \lhcb, a  classical architecture of an electromagnetic calorimeter (\ecal) in front of a hadronic calorimeter (\hcal) was chosen. Both are optimized for particle identification, mostly for \electron/\pion and \piz/\g discrimination, as well as for a fast readout. The information will be used, among others, in the first trigger stage (see Sec. \ref{sec:trigger}).

In front of the \ecal, a scintillator pad detector is placed to detect the pass-through of charged particles followed by a pre-shower detector. The \ecal itself is built of a sampling scintillator/lead structure (shashlik technology) and has a total depth of $25\Xrad$. As the hit density rapidly drops with increasing distance from the beam pipe, the \ecal is split into three different sections with appropriate cell sizes.

The \hcal of the \lhcb is a sampling calorimeter with a special structure. It consists of lead/scintillator tiles directed \textit{parallel} to the beam-pipe. Each thin row consisting of several tiles has a neighbour-row with inverted lead/scintillator tiles. The scintillation light is detected by photomultiplier tubes and collected by fibres. The total length equals to 5.6 hadronic interaction lengths.

\subsubsection{Muon system}

The muon system is responsible for the identification of muons and provides a standalone, fast signal to the trigger in case of muons with high transverse momentum (\pt) passing it. The whole system is composed of the five stations M1--M5. M1 is placed in front of the calorimeters to improve the \pt resolution whereas the others are located downstream. The stations are separated by iron absorbers to prevent any non-muons from passing through the detectors. All systems provide spatial resolved hit information with decreasing segmentation scale for increasing distance to the beam pipe. M4 and M5 are mostly used for penetration testing and offer only sparsely location informations.

\subsection{Trigger}
\label{sec:trigger} 
At the nominal \lhc conditions, the bunch crossing frequency can reach up to $40\mhz$ which leaves $25\ns$ in between two crossings. This high frequency has to be reduced down to $1\khz$ in order to be able to store the data for offline analysis. Two trigger-systems, a low-level trigger (L0) and a high-level trigger (\hlt) consisting of two stages, \hltone and \hlttwo select which events to keep.

The L0 stage is a hardware implemented trigger and consists of a custom electronics set-up built with \fpga. It takes information from three different sources into account. The first is a pile-up system inside the \velo, estimating the number of events that occurred during the collision. Information from the calorimeter is used to estimates the transverse energy (\et) of certain particles and decides to keep the event in case of high \et. The muon system feeds the trigger with information about the \pt of muons in order to trigger on a certain threshold.

The next stage is the \hltone. It reconstructs some parts of the tracks to confirm the L0 decision as well as to further reduce the event rate. This is now low enough to allow the \hlttwo to reconstruct \bquark events and make more refined decisions. The events which pass \hlttwo with a frequency of around $1\khz$ are then stored for offline analysis.

A general distinction is made on whether an event passed the trigger because of the events signature itself (trigger on signal, \TOS) or because of some other particles signature (trigger independent of signal, \TIS).

\subsection{Software}
Once the events are stored, offline tools are used to reconstruct and fit tracks and apply sets of exclusive selections prior to the data manipulation.


\subsubsection{Track reconstruction and fit}
For the event reconstruction, information from the tracking system (including the \velo) is used. First of all, a clustering algorithm determines \textit{track seeds} by searching for candidates in a low magnetic field region of the spectrometer. A Kalman filter algorithm is then fitted to the data using the track seeds as initialisation. An advantage of reconstructing and fitting with this algorithm is that the result is equivalent to a least square fit of the tracks to the hits. For the particle propagation with the Kalman filter, the inhomogeneous magnetic field as well as multiple scattering occurring from detector material is taken into account.
