\graphicspath{{figures/h1/}}

\chapter{The H1 Experiment} \label{c:h1}

The data for the measurement of the structure function $F_{2}$ to be
presented in this thesis has been collected in the year 2000 with the
H1 experiment situated at the HERA collider. After a short overview of
the accelerator this chapter concentrates on the description of the H1
detector putting special focus on the relevant subdetectors and the
online event selection.

\section{HERA Accelerator} \label{c:hera}

The HERA (Ha\-dron-Elek\-tron-Ring-An\-la\-ge) collider located at
DESY (Deut\-sches-Elek\-tro\-nen-Syn\-chro\-tron) in Hamburg is the
first storage ring for electrons or positrons\footnote{In the year
2000 relevant for this analysis positrons have been accelerated.} and
protons ever built. It started operation in 1991. The beam energies
are \mbox{$27.6\, \mathrm{GeV}$} for the electrons and \mbox{$920\,
\mathrm{GeV}$} for the protons\footnote{An increase of the proton beam
energy from \mbox{$820\, \mathrm{GeV}$} to \mbox{$920\, \mathrm{GeV}$}
was achieved at the beginning of 1998.}, respectively. This
corresponds to a centre of mass energy available for electron-proton
collisions of \mbox{$\sqrt{s} \approx 320\, \mathrm{GeV}$} which is
more than ten times larger than in fixed target experiments performed
beforehand.

The particles are accelerated in two separate beam lines located in a
tunnel of $6.3\, \mathrm{km}$ circumference. The electron (proton)
ring is equipped with normal conducting (superconducting) dipole
magnets having a maximum field strength of $0.17\, \mathrm{T}$ ($4.7\,
\mathrm{T}$). The magnetic field strength limits the reachable proton
energy. The maximum energy of the electron beam is defined by the
power of the radiofrequency system which is responsible for the
acceleration and thus has to compensate the energy losses due to
synchrotron radiation. Synchrotron radiation losses are negligible in
the case of the protons since they have a mass being more than three
orders of magnitude larger than the electron mass. Before the
particles reach the HERA machine they pass a system of several
pre-accelerators as depicted in figure~\ref{f:hera}. The last
pre-accelerator before the injection into HERA is PETRA
(Po\-si\-tron-Elek\-tron-Tan\-dem-Ring-An\-lage) accelerating
electrons and protons to energies of \mbox{$12\, \mathrm{GeV}$} and
\mbox{$40\, \mathrm{GeV}$}, respectively.

\begin{figure}
  \centering
  \includegraphics[width=0.8\textwidth]{hera.eps}
  \caption{The HERA collider facility and its pre-accelerator system.}
  \label{f:hera}
\end{figure}

The counter rotating beams collide head-on at the North and South
interaction regions where the multi-purpose detectors H1 and ZEUS are
located. Two additional experiments make use of only one of the two
beams: the \mbox{HERA-B} experiment has been designed to study the
interaction of protons with the nuclei of target wires positioned in
the halo of the proton beam aiming for a measurement of the $CP$
violation in decays of $B$ mesons. It stopped data taking at the end
of 2003. The second experiment, HERMES, explores the spin structure of
the nucleons by scattering longitudinally polarised electrons off
polarised gas atoms (hydrogen, deuterium, helium-3).

The HERA accelerator stores electrons and protons in 220 bunches of
$10^{10}$ to $10^{11}$ particles each. This beam structure defines the
collision rate of \mbox{$10.4\, \mathrm{MHz}$} corresponding to a time
interval of \mbox{$96\, \mathrm{ns}$} between two bunch
crossings. During the data taking period relevant for the analysis on
average 174 colliding bunches were filled. The remaining bunches are
either not filled or have an empty partner bunch. They can be used to
study the beam induced background (see section~\ref{c:background}).

In September 2000 the first running phase of the HERA collider ended
with a long shut down to allow for a major upgrade of the machine and
the colliding beam experiments. The major goal of the upgrade was a
fivefold increase in instantaneous luminosity\footnote{The luminosity
is a measure for the number of observable $ep$ scattering processes as
is explained in section~\ref{c:lumisystem}.} to further enhance the
physics potential of the experiments. The ongoing running phase that
started in 2002 is referred to as HERA-II.

\section{Detector Overview} \label{c:h1overview}

The H1 detector~\cite{Abt:1996hi, Abt:1996xv} has been designed for a
precise identification and reconstruction of the particles emerging
from the $ep$ interactions. It provides a hermetic coverage of almost
the entire solid angle as can be seen in figure~\ref{f:h1} which shows
a schematic view of the main setup.

\begin{figure}[t]
  \centering
  \includegraphics[width=0.9\textwidth]{h1_withCoordinates.eps}
  \caption{Schematic 3-dimensional view of the H1 detector. References to particular items of this figure are indicated by boxes in the text.}
  \label{f:h1}
\end{figure}

A right-handed Cartesian coordinate system (see figure~\ref{f:h1})
defined by the Central Tracker (see below) is used to describe the
signatures of detected particles. The positive \mbox{$z$-axis} points
into the proton beam direction, the positive \mbox{$x$-axis} towards
the centre of HERA. The geometrical centre of the Central Tracker
constitutes the origin. For the parameterisation of particle
trajectories polar coordinates are usually employed: the distance $r$
from the origin in the \mbox{$xy$-plane}, the azimuthal angle $\phi$
in the \mbox{$xy$-plane} w.r.t. the \mbox{$x$-axis} and the polar
angle $\theta$ w.r.t. the \mbox{$z$-axis}. The region of small (large)
polar angles is referred to as forward (backward) region. The H1
detector is arranged symmetrically around the beam pipe, the
asymmetric instrumentation in $z$-direction accounts for the different
beam energies causing a large fraction of the hadronic final state
particles to occupy the forward region.

A detailed description of the H1 detector can be found
in~\cite{Abt:1996hi, Abt:1996xv}. In the following only the detector
components most relevant for this analysis are discussed after a short
overview of the general layout. The numbers given below refer to the
labels in figure~\ref{f:h1}.

The interaction region is surrounded by the tracking system of the H1
detector used for the identification and momentum determination of
charged particles. The tracking system consists of two separate
modules: the forward~\fbox{3} and the central~\fbox{2} tracking device
having a polar angle acceptance\footnote{All polar angle acceptances
quoted in this chapter refer to \mbox{$z=0$}, i.e. the nominal
\mbox{$z$-position} of the interaction vertex for standard running
conditions of the HERA collider. Note however that for the data taking
period analysed in this thesis the interaction vertex has been shifted
resulting in a nominal vertex position of approximately \mbox{$70\,
\mathrm{cm}$} (see section~\ref{c:datasample}). This causes a shift of
the acceptance intervals towards larger polar angles.} of
\mbox{$7^{\circ} < \theta < 25^{\circ}$} and \mbox{$15^{\circ} <
\theta < 165^{\circ}$}, respectively. The central tracking device is
shortly referred to as Central Tracker in the following. Its wire
chambers are complemented by the Central Silicon Tracker (CST)
situated closest to the interaction region. The CST covers the polar
angle range \mbox{$30^{\circ} <
\theta < 150^{\circ}$} and provides precise information concerning the
vertex position allowing to separate vertices from primary interaction
products and decay particles. The backward region of the tracking
system is equipped with two subdetectors dedicated to the
reconstruction of the scattered electron, the Backward Silicon Tracker
(BST) and the Backward Drift Chamber (BDC).

The trackers are enclosed by a calorimeter system used to measure the
energy of the final state particles. The bulk of the acceptance
(\mbox{$4^{\circ} < \theta < 154^{\circ}$}) is occupied by a liquid
argon calorimeter (LAr calorimeter) that is composed of an
electromagnetic~\fbox{4} and a hadronic section~\fbox{5} and is
contained in a cryogenic vessel~\fbox{15}. The Spaghetti Calorimeter
(SpaCal)~\fbox{12} in the backward region (\mbox{$153^{\circ} <
\theta < 177.5^{\circ}$}) has been designed for an accurate energy
determination of the scattered electron. An additional PLUG
calorimeter~\fbox{13} is installed in the forward direction close to
the beam pipe.

All detector components mentioned so far are surrounded by a
superconducting solenoid~\fbox{6} providing a homogeneous magnetic
field of \mbox{$1.16\, \mathrm{T}$} parallel to the beam axis. It
causes the trajectories of charged particles to bend allowing for a
measurement of their momenta. Since the solenoid is located outside of
the calorimeters the amount of dead material influencing the energy
measurement is minimised.

The magnetic field lines are closed by the iron return yoke~\fbox{10}
which is instrumented with streamer tubes. Together with two
additional sets of three layers of streamer tubes~\fbox{9} mounted at
its inside and outside the instrumented iron constitutes the central
muon detector. Apart from the reconstruction of muon tracks it allows
to measure the energy leakage from hadrons not fully contained in the
calorimeters. High energetic muons with polar angles
\mbox{$3^{\circ} < \theta < 17^{\circ}$} are detected in the forward 
muon detector consisting of two sets of three double layers of drift
chambers~\fbox{9} at the front and back side of a toroidal
magnet~\fbox{11}.

In order to reduce the background caused by interactions of the beam
particles with residual gas atoms in the beam pipe or the beam pipe
material the H1 detector is equipped with a time-of-flight
system~\cite{Wissing:1998}. Several combinations of scintillators
inside and outside of the main detector provide timing information
with high precision allowing to distinguish background and signal
events by the definition of narrow time intervals.

The luminosity system is installed in negative \mbox{$z$-direction}
close to the electron beam pipe in the HERA tunnel. It consists of a
photon detector and an electron tagger to reconstruct the radiated
photon and the scattered electron of Bethe-Heitler events. The data
delivered by the individual subdetectors are processed by the trigger
and data acquisition systems.

\section{Tracking Detectors} \label{c:tracking}

For the measurement of the polar angle of the scattered electron
either the BST or a combination of Central Tracker and BDC is
employed. Apart from measuring the position of the interaction vertex
the Central Tracker provides information for the reconstruction of the
hadronic final state.

\subsection*{Central Tracker}

The main components for the track reconstruction in the central region
of the H1 detector are the two central jet chambers CJC1 and CJC2 (see
figure~\ref{f:ctradial}). These are two concentric drift chambers
having an active length of \mbox{$220\, \mathrm{cm}$} and a radial
extension of \mbox{$20 .3\, \mathrm{cm} \leq r \leq 45.1\,
\mathrm{cm}$} (CJC1) and \mbox{$53.0\, \mathrm{cm} \leq r \leq 84.4\,
\mathrm{cm}$} (CJC2).

\begin{figure}
  \centering
  \includegraphics[width=0.7\textwidth]{CTD_radialView.eps}
  \caption{View of the central tracking device in the \mbox{$r\phi$-plane}.}
  \label{f:ctradial}
\end{figure}

The track reconstruction is based on the ionisation of a gas mixture
(\mbox{$\mathrm{Ar-CO_{2}-CH_{4}}$}) by the charged particles
originating from the collision. The free electrons being produced in
the course of the ionisation are detected on 2640 signal wires strung
parallel to the \mbox{$z$-axis} and organised in 30 (CJC1) and 60
(CJC2) drift cells, respectively. The drift cells are inclined by
about $30^{\circ}$ w.r.t. the radial direction. This causes the
ionisation electrons in the presence of the magnetic field to drift
approximately perpendicular to high momentum tracks originating from
the beam axis which guarantees an optimal track resolution.

The spatial reconstruction in the \mbox{$r\phi$-plane} is based on the
measurement of the drift time of the ionisation electrons. A charge
division technique is used to determine the \mbox{$z$-coordinate}. The
3-dimensional space point corresponding to the information of a single
wire is referred to as \emph{hit}. The achieved resolutions for the
hit coordinates are \mbox{$\sigma_{r\phi} = 170\, \mathrm{\mu m}$} and
\mbox{$\sigma_{z} = 4\, \mathrm{cm}$}~\cite{Tluczykont:1999}, respectively. 

In addition to the track reconstruction the central jet chambers
provide information for the particle identification by measuring the
specific energy loss of charged particles $dE/dx$ with a resolution of
$\sigma_{dE/dx}/(dE/dx) \approx 8\%$~\cite{Steinhart:1999}.

Two thin drift chambers CIZ (central inner
\mbox{$z$-chamber}) and COZ (central outer \mbox{$z$-cham}\-ber) are attached to 
 the inside and outside of the CJC1, respectively. Their wires are
strung in polygonal support structures around the beam axis (see
figure~\ref{f:ctradial}). In \mbox{$z$-di}\-rec\-tion the CIZ (COZ) is
separated in 15 (24) rings of \mbox{$12\, \mathrm{cm}$} (\mbox{$9\,
\mathrm{cm}$}) width containing 4 layers of sense wires each. 
Since the wires are oriented perpendicular to the beam axis the
chambers are ideally suited for the reconstruction of the
\mbox{$z$-co}\-or\-di\-nate. The corresponding resolution \mbox{$\sigma_{z}
= 300\, \mathrm{\mu m}$} is significantly better than the one for the
central jet chambers. Therefore the signals of the two jet chambers
and the two \mbox{$z$-cham}\-bers are subjected to a combined track
reconstruction (see section~\ref{c:evreco}). This yields a resolution
of the \mbox{$z$-co}\-or\-di\-nate of the interaction vertex of \mbox{$1\,
\mathrm{cm}$}~\cite{Glazov:1998a} and a momentum resolution 
\mbox{$\sigma_{p}/p = 0.01\, \mathrm{GeV^{-1}} p$}.

Furthermore the Central Tracker comprises two multiwire proportional
chambers, the CIP (central inner proportional chamber) and the COP
(central outer proportional chamber). The CIP is the wire chamber
sitting closest to the beam line at an average radial distance of
\mbox{$16.2\, \mathrm{cm}$} covering the polar angle acceptance 
\mbox{$9^{\circ} < \theta < 171^{\circ}$}. Its two layers are equipped 
with 480 cathode pads each, 60 pads in \mbox{$z$-direction} and 8 pads
in azimuth. They collect the charge induced by crossing charged
particles. The layout of the COP is similar to the one of the CIP. It
is divided into 18 sectors along the \mbox{$z$-axis} and 16 sectors in
azimuth and detects charged particles in the polar angle range
\mbox{$25^{\circ} < \theta < 155^{\circ}$}.

Both multiwire proportional chambers deliver a fast timing signal with
a resolution better than the time interval of \mbox{$96\,
\mathrm{ns}$} between two successive HERA bunch crossings. These
signals are used in combination with the first proportional chamber
FPC (Forward Proportional Chamber) of the forward tracking device to
select events online based on charged particle trajectories
originating from the nominal interaction vertex.

\subsection*{Backward Drift Chamber}


The Backward Drift Chamber~\cite{Schwab:1996} has been designed to
complement the reconstruction of the scattered electron in the SpaCal
(see next section) with track information in order to improve the
precision of the polar angle measurement. Figure~\ref{f:h1back}
indicates the position of the BDC in the backward region of the H1
detector. It is mounted in front of the SpaCal at \mbox{$z = -145\,
\mathrm{cm}$} having the same polar angle acceptance of
\mbox{$153^{\circ} < \theta < 177.5^{\circ}$}. Four double layers
subdivided into eight octants are the basic construction units of the
BDC, i.e. a charged particle can cause up to eight hits on a distance
of approximately \mbox{$7\, \mathrm{cm}$}.

\begin{figure}
  \centering
  \includegraphics[width=0.7\textwidth]{backward_rzView_modified.eps}
  \caption{Backward region of the H1 detector in the \mbox{$rz$-plane}. The nominal interaction point (IAP) is indicated.}
  \label{f:h1back}
\end{figure}

In total 2048 wires are strung octagonal in planes perpendicular to
the beam line. This implies that the ionisation electrons drift in
radial direction and thus the chamber geometry is optimised for an
accurate reconstruction of the polar angle~$\theta$. The stereo effect
of the four double layers which are rotated by $11.25^{\circ}$
w.r.t. each other is employed for a coarse measurement of the
azimuthal angle~$\phi$. Since the event rate rapidly increases with
increasing polar angles drift cells of different size are used in the
inner and outer part of the BDC (see figure~\ref{f:bdcrz}) to keep the
fraction of overlaying events in the chamber (pile-up) as small as
possible. The radial wire spacing is \mbox{$1\, \mathrm{cm}$} for the
inner and \mbox{$3\, \mathrm{cm}$} for the outer cells. The
intermediate region is covered by a transition cell of \mbox{$2\,
\mathrm{cm}$} size which has a special field configuration since the
wire position is not centred w.r.t. the cell. From
figure~\ref{f:bdcrz} it can be inferred in addition that that wires in
the neighbouring planes of a double layer are shifted by half the cell
size in radial direction. This allows to resolve left-right
ambiguities of the drift origin. For the reconstruction of the polar
angle $\theta$ the BDC information is combined with the position of
interaction vertex determined by the Central Tracker (see
section~\ref{c:evreco}). The resulting resolution amounts to
\mbox{$0.57\, \mathrm{mrad}$}~\cite{Glazov:1998b, Keller:1998}.

\begin{figure}
\begin{captionbeside}{Part of one BDC double layer in the \mbox{$rz$-plane}. The numbers indicate the radial distance from the beam line in $\mathrm{mm}$. \vspace{0.2cm}}[i][0.95\textwidth][0.05\textwidth]*
\begin{minipage}[t]{0.4\textwidth}
  \centering
  \includegraphics[width=0.7\textwidth]{bdc_rzview_zoomed.eps}
\end{minipage}
\end{captionbeside}
\label{f:bdcrz}
\end{figure}

\subsection*{Backward Silicon Tracker}


The Backward Silicon Tracker measures the polar angle of the scattered
electron with high precision and is able to reconstruct the
interaction vertex independently of the Central Tracker.

Figure~\ref{f:bst} a) depicts the BST~\cite{Arkadov:2000,
Eckstein:2002} in its configuration of the years 1998-2000. It
comprises eight detector planes which are oriented perpendicular to
the beam axis and cover the \mbox{$z$-interval}
\mbox{$-95.6\, \mathrm{cm} \le z \le -35.8\, \mathrm{cm}$}. 
They are arranged in two groups of four detector planes each. The
first group (BST1) was installed in the H1 detector already in 1996,
the second group (BST2) has been added in 1998 to enlarge the BST
acceptance towards larger values of $Q^{2}$.

\begin{figure}
  \centering
  \begin{minipage}[c]{0.53\textwidth}
    \centering
    \includegraphics[width=0.9\textwidth]{bst3d.eps}
    \put(-210,111){a)}
  \end{minipage}
  \begin{minipage}[c]{0.43\textwidth}
    \centering
    \includegraphics[width=0.9\textwidth]{bstsensors_modified.eps}
    \put(-153,111){b)}
    \put(-48,111){c)}
  \end{minipage}
  \caption{a) Layout of the BST in the years 1998-2000. Following the \mbox{$z$-axis} in positive direction one can distinguish the readout electronics and the two groups of detector planes BST1 and BST2. Each detector plane is equipped with 16 \mbox{$r$-sensors} b) and one \mbox{$u$-sensor} c).}
  \label{f:bst}
\end{figure}

Each plane is equipped with 16 wedge shaped silicon strip detectors,
called \mbox{$r$-\emph{sensors}}. According to figure~\ref{f:bst} b)
their readout strips are segments of a circle concentric to the beam
line. The active material is \mbox{$280\, \mathrm{\mu m}$} thick
\mbox{n-type} silicon. About 20000 electron-hole pairs are produced by
a single minimal ionising particle scattered in the active volume of
a sensor. The wedges overlap in \mbox{$\phi$-direction} by
\mbox{$3\, \mathrm{mm}$} providing some redundancy for the track
reconstruction and a hermetic coverage of the azimuthal angle. They
extend in radial direction from \mbox{$5.9\, \mathrm{cm}$} to
\mbox{$12.0\, \mathrm{cm}$} allowing to reconstruct charged particles
in the polar angle range \mbox{$164^{\circ} < \theta < 176^{\circ}$}
with an uncertainty of \mbox{$0.2\,
\mathrm{mrad}$}~\cite{H1:draft}.

One \mbox{$\phi$-sector} (\mbox{$45^{\circ} < \phi < 67.5^{\circ}$})
of each wheel is equipped with an additional
\mbox{$u$-\emph{sensor}}. For this sensor type the readout strips are
parallel to one of the detector edges. By combining the information of
$r$- and \mbox{$u$-sensors} it is possible to measure the transverse
momentum and the charge of a track. Both sensor types have 640 readout
strips each. In order to minimise the attenuation of the small signals
five pre-amplifiers are directly bonded to the readout strips on each
sensor.

\section{Calorimetry} \label{c:calorimetry}

The energy measurement of the H1 experiment is based on the LAr
calorimeter in the central and forward region and the SpaCal in the
backward region. For the present analysis the former is employed to
reconstruct the hadronic final state while the main purpose of the
latter is the energy measurement of the scattered electron. In
addition the SpaCal provides information for the online event selection.

\subsection*{Spaghetti Calorimeter}


The Spaghetti calorimeter covers the polar angle acceptance
\mbox{$153^{\circ} < \theta < 177.5^{\circ}$}~\cite{Appuhn:1996na}. It
is a \emph{sampling} calorimeter, i.e. different materials are
employed for the absorption and detection of particles. For the SpaCal
lead is used as absorber material while the active material are
scintillating fibres. The incident particles induce a shower of
secondary particles in the lead which cause the fibres to
scintillate. The amount of light registered by photomultiplier tubes
is a measure for the energy of the primary particles. Special
photomultipliers have been chosen capable of operating in the strong
magnetic field~\cite{Janoth:1993kw}.

As can be seen from figure~\ref{f:h1back} the SpaCal is composed of an
electromagnetic and a hadronic section. The electromagnetic part
consists of 1192 cells with a dimension of \mbox{$4 .05 \times 4.05
\times 25.5\, \mathrm{cm^{3}}$}. The smallest construction units of 
the calorimeter are \mbox{2-cell} modules, called
\emph{sub-modules}. Each of these modules contains 52 layers of lead
having 90 grooves instrumented with scintillating fibres. The
lead-to-fibre ratio is \mbox{$2.27$ : $1$} by volume. Sets of eight
sub-modules in turn constitute so-called \emph{super-modules} which
have a quadratic cross-section and are the main building blocks of the
electromagnetic section as shown in figure~\ref{f:spacalrphi} a). The
innermost region of the SpaCal (see figure~\ref{f:spacalrphi} b)) is
equipped with a special arrangement of cells, called \emph{insert
module}~\cite{Dirkmann:1995}. It accounts for the space needed by the
beam pipe. The purpose of four inner cells surrounding the beam pipe,
called \emph{veto cells}, is to detect energy leakage of neighbouring
cells into the beam pipe. A tantalum layer of
\mbox{$2\, \mathrm{mm}$} thickness protects the active detector from
synchrotron radiation.

\begin{figure}
  \centering
  \begin{minipage}[c]{0.5\textwidth}
    \centering
    \includegraphics[width=0.9\textwidth]{spacal_radialView_modified.eps}
    \put(-195,180){a)}
  \end{minipage}
  \hspace{0.05\textwidth}
  \begin{minipage}[c]{0.4\textwidth}
    \centering
    \includegraphics[width=0.9\textwidth]{insert_modified.eps}
    \put(-175,171){b)}
  \end{minipage}
  \caption{a) Electromagnetic section of the SpaCal calorimeter in the \mbox{$r\phi$-plane}. The thin (thick) solid lines refer to the borders of the sub-modules (super-modules). An magnified view of the highlighted area, the insert module, is depicted in b).}
  \label{f:spacalrphi}
\end{figure}

The cross-section of the cells is well matched to the Moli\`ere radius
of \mbox{$2.55\, \mathrm{cm}$} to ensure a good spacial
resolution\footnote{$A \oplus B$ is defined as: $A \oplus B \equiv
\sqrt{A^{2} + B^{2}}$} of \mbox{$\sigma = (6.3 \pm 0.4)\, \mathrm{mm}
/\sqrt{E/\mathrm{GeV}} \oplus (1.7 \pm 0.1)\, \mathrm{mm}$} and a
reliable electron/hadron separation based on transverse shower
profiles. The cell dimension in \mbox{$z$-direction} of
\mbox{$25.5\, \mathrm{cm}$} corresponds to 28 radiation lengths. Test beam
measurements have shown that the longitudinal energy leakage is
negligible for \mbox{$30\, \mathrm{GeV}$}
electrons~\cite{Nicholls:1995di}. In addition the energy resolution of
the electromagnetic section has been determined to \mbox{$(7.1 \pm
0.2)\% / \sqrt{E/\mathrm{GeV}} \oplus (1.0 \pm
0.1)\%$}~\cite{Nicholls:1995di}.

Due to the fast response and precise timing information of better than
$1\, \mathrm{ns}$ reached by the photomultipliers the SpaCal proves to
be useful for the online event selection. Apart from suppressing beam
induced background events based on the timing information DIS events
can be selected by requiring energy depositions above a certain
threshold in the calorimeter (see section~\ref{c:trigger}).

The hadronic section of the SpaCal consists of 136 cells, each having
a dimension of \mbox{$11.93 \times 11.90 \times 25\,
\mathrm{cm^{3}}$}. It adds 1.02 nuclear interaction lengths of
material to the electromagnetic section which correspond to 1.0
interaction lengths. Therefore it can only provide a coarse hadronic
energy measurement, but it allows to distinguish between
electromagnetic and hadronic showers.

\subsection*{Liquid Argon Calorimeter}


The liquid argon calorimeter is responsible for the energy measurement
in a large range of the polar angle (\mbox{$4^{\circ} < \theta <
154^{\circ}$}). Like the SpaCal it is a sampling calorimeter, but
using LAr as active material. Choosing this technique has the
advantages of a good stability, a homogeneous response and a fine
granularity. The calorimeter is segmented into eight self-supporting
wheels in \mbox{$z$-direction} (see figure~\ref{f:larrz}) which are
in turn divided into octants in $\phi$. Six of the wheels are composed
of an electromagnetic and a hadronic section, the BBE has an
electromagnetic section only, the OF consists of two hadronic
sections.

\begin{figure}
  \centering
  \includegraphics[width=0.8\textwidth]{calo-laengs.eps}
  \caption{View of the LAr calorimeter in the \mbox{$rz$-plane} with nomenclature for the different wheels: Inner Forward (IF), Outer Forward (OF), Forward Barrel (FB1, FB2), Central Barrel (CB1, CB2, CB3) and Backward Barrel (BBE). The last letter distinguishes electromagnetic (E) and hadronic (H) sections. The nominal interaction point (WWP) is indicated.}
  \label{f:larrz}
\end{figure}

In the electromagnetic (hadronic) part of the calorimeter lead (steel)
plates are used as absorbers. In order to obtain a uniform energy
resolution their orientation is chosen such that particles originating
from the interaction region cross them with an angle of larger than
$45^{\circ}$. The absorption length of the electromagnetic part 
varies between 20 and 30 radiation lengths in the central and forward
direction, respectively. The total amount of absorbing material of the
calorimeter sums up to about five to eight nuclear interaction
lengths.

The fine granularity of the LAr calorimeter is reflected in a total
number of 44532 readout channels. The readout system provides
calibrated charges for each readout cell. A first suppression of
electronics noise is already performed online by excluding cells from
the readout for which the absolute value of the signal after the
subtraction of the pedestal does not exceed a certain threshold (for
details see section~\ref{c:simulation}). The calibrated charges are
converted to energies with the help of a complex reconstruction
software comprising several steps. Among them the correction for dead
material effects, cluster formation as well a several measures to
further suppress the noise contribution.

These reconstruction steps provide the correct energy if the incident
particle is an electron or a photon. Since the LAr calorimeter is
non-compensating the charge output for hadrons is about 30\% smaller
than for electrons\footnote{The exact value depends on the incident
particle energy.}. Hence an additional correction has to be applied for
hadrons to compensate for this deficit. For this purpose special
software weighting techniques are employed~\cite{Wellisch:1994,
Issever:1996}. They rely on the fine segmentation of the LAr
calorimeter which allows to identify the electromagnetic components
within hadronic showers.

Test beam measurements of calorimeter modules have revealed an energy
resolution of
\mbox{$12\% / \sqrt{E/\mathrm{GeV}} \oplus 1\%$} for electrons and
\mbox{$50\% / \sqrt{E/\mathrm{GeV}} \oplus 2\%$} for
hadrons~\cite{Andrieu:1994yn, Andrieu:1993tz}.

\section{Luminosity System} \label{c:lumisystem}

For a collider experiment the \emph{instantaneous luminosity}
$\mathcal{L}$ is the factor of proportionality between the observed
event rate $dN/dt$ and the cross-section $\sigma$ for a given
process:
\begin{equation}
\frac{dN}{dt} = \mathcal{L}\, \sigma
\label{e:lumi}
\end{equation}
The total number of events $N$ is related to the integrated luminosity
$L = \int \mathcal{L} dt$ in the same way. Therefore a precise
determination of the luminosity is necessary to perform a
cross-section measurement based on the observed number of events.

The luminosity is determined via the measurement of the event rate for
a process with a precisely known cross-section. H1 utilises the
Bethe-Heitler process of small-angle bremsstrahlung \mbox{$ep
\rightarrow e' \gamma p$} for this purpose which has been introduced
in section~\ref{c:radepscat}. Its cross-section is calculable to high
precision within QED. Since the angular distributions of the electrons
and the radiated photons have a strong peak in the direction of the
incoming electron the detectors of the luminosity system have to be
placed close to the electron beam line in negative
\mbox{$z$-direction}.

Figure~\ref{f:lumi} shows a typical event in the luminosity
system. The main components of the system are two electromagnetic
calorimeters: the photon detector (PD) located at \mbox{$z_{PD} =
-102.9\,\mathrm{m}$} and the electron tagger (ET) at \mbox{$z_{ET} =
-33.4\,\mathrm{m}$}. Both consist of thallium chloride / thallium
bromide crystals serving as \v{C}erenkov counters. The signals in each
crystal are registered by a separate photomultiplier.

\begin{figure}[t]
  \centering
  \includegraphics[width=0.8\textwidth, angle=270]{lumi.eps}
  \caption{The luminosity system of the H1 experiment. The top part depicts the detection of a Bethe-Heitler event schematically. In addition typical energy depositions in the electron tagger (middle left) and the photon detector (middle right) are shown as well as the positions of both detectors w.r.t. the beam line (middle centre, bottom).}
  \label{f:lumi}
\end{figure}

In total 25 crystals constitute the photon detector corresponding to
an active area of \mbox{$10 \times 10\, \mathrm{cm^{2}}$} in the
\mbox{$xy$-plane} and a depth of 22 radiation lengths. Photons 
emitted collinearly with the incoming lepton reach the photon detector
by leaving the beam pipe through an exit window at \mbox{$z =
-92.3\,\mathrm{m}$} where the beam pipe bends upwards. The photon
detector is shielded from synchrotron radiation by a lead filter (F)
of two radiation lengths depth. A water \v{C}erenkov counter (VC) with
a depth of one radiation length is used to veto events with photons
interacting in the lead absorber to guarantee a precise energy
measurement.

The electrons emerging from the bremsstrahlung process have a reduced
momentum compared to the beam electrons. Hence they are deflected by
the HERA beam magnets and reach the electron tagger after leaving the
beam pipe through an exit window at \mbox{$z =
-27.3\,\mathrm{m}$}. The electron tagger is assembled of 49 crystals
resulting in an active area of \mbox{$15.4 \times 15.4\,
\mathrm{cm^{2}}$}. The tagger acceptance is defined by the field of
the magnets and may thus vary significantly if the beam optics
changes.

Two methods are used for the luminosity measurement of the H1
experiment~\cite{Ahmed:1995cf, Gogitidze:1996}: the instantaneous
luminosity is determined online by requiring the detection of both the
scattered electron and the radiated photon. This information is used
to optimise the beam position during the operation of the HERA
accelerator. Since this method utilises the electron tagger the
measurement depends strongly on the beam optics. Hence the integrated
luminosity used for physics analyses is calculated based on the photon
detector information only. This method provides a higher precision,
but only after a precise absolute calibration and resolution
determination has been performed offline. The main background to the
Bethe-Heitler events is caused by interactions of the electrons with
residual gas atoms in the beam pipe. Their contribution is estimated
with the help of electron pilot bunches, i.e. electron bunches which
have no proton partner bunch.

Apart from the luminosity measurement the luminosity system is
employed for the identification of photoproduction events (see
section~\ref{c:phojetnorm}) and initial state radiation events (see
section~\ref{c:dissel}).

\section{Trigger System} \label{c:trigger}

Depending on the beam quality it is possible that the rate at which
background events induce a signal in the H1 detector exceeds the one
for $ep$ interactions by more than a factor of 1000. Apart from
synchrotron radiation the main background sources are interactions of
the proton or electron beam with residual gas atoms in the beam pipe
or atoms of the beam pipe itself. Cosmic muons constitute another
important background source.

Rejecting background events while at the same time efficiently
selecting $ep$ interactions of interest for physics analyses is
the task of a trigger system. For the H1 experiment in particular this
implies a rate reduction from the bunch crossing rate of
\mbox{$10.4\, \mathrm{MHz}$} to a rate of approximately \mbox{$10\,
\mathrm{Hz}$} at which the data are stored on raw data tapes. This is 
realised with the help of a multi-level trigger
system~\cite{Elsen:1993}. The decision time increases from level to
level while the rate is reduced
successively. Figure~\ref{f:triggersystem} gives an overview.

\begin{figure}
  \centering
  \includegraphics[width=0.95\textwidth]{h1_triggersystem.eps}
  \caption{Overview of the H1 trigger system. Decision times and typical input rates are shown at each level.}
  \label{f:triggersystem}
\end{figure}

Basically one has to distinguish between two sets of information: the
information that is sent from most of the subdetectors to the trigger
system and the data that are finally used for the event
reconstruction. While fast availability is of importance for the
former, emphasis is placed on precision in the case of the latter. The
signal formation in the subdetectors, signal transmission via long
cables and processing time on the first trigger level (L1) take
significantly longer than the \mbox{$96\, \mathrm{ns}$} of two
consecutive bunch crossings. Hence the subdetector systems feed their
data into a ring buffer system in order to keep the first trigger
level deadtime free.

Typical criteria to arrive at a trigger decision on L1 are the
information of the time-of-flight system, multiplicities and momenta
of charged tracks in the drift chambers or localised energy deposition
in the calorimeter. They are encoded in Boolean decisions known as
trigger elements. Up to 256 trigger elements can be sent from the
subsystems to the central trigger where they are combined to 128
subtriggers via logical operations. The L1 decision is taken based on
the subtriggers. If one of the subtriggers accepts the event the
ring buffers are frozen and the deadtime begins. The latency of
L1 is $2.3\, \mathrm{\mu s}$, the rate is reduced to \mbox{$1\,
\mathrm{kHz}$}.

The second trigger level (L2) receives all the trigger data from the
independent L1 trigger subsystems. They are analysed at a much higher
granularity compared to the L1 trigger elements and correlations
between them are taken into account. For this purpose two independent
systems are available taking a decision within a latency of $20\,
\mathrm{\mu s}$~\cite{Nicholls:1998us}: the topological trigger (L2TT) 
represents the detector geometry as a \mbox{$16 \times 16$} matrix in
the \mbox{$\theta \phi$-space}~\cite{Bizot:1992a, Bizot:1992b}. The
trigger decision is taken based on the event topology. For example it
is possible to select only events which have at least one energy
deposition in the SpaCal outside a predefined radius $r$ (see
section~\ref{c:onlinesel}). The second system (L2NN) consists of
several neural networks~\cite{Koehne:1997,Kraemerkaemper:1998}. They
are trained using previously recorded data samples of background
events and events from the physics process of interest. Both systems
can send up to 16 L2 trigger elements to the central trigger which are
used to validate L1 subtriggers. In the case of a negative trigger
decision the ring buffers stopped on L1 are started again and the
deadtime ends. If the event is accepted the readout of the ring
buffers is started.

The third trigger level (L3) is based on software algorithms
implemented on a single RISC\footnote{Reduced Instruction Set
Computing} processor. In the case of a negative trigger decision the
readout is aborted to reduce the deadtime. Due to long decision times
this system has not been active during data taking. In the course of
the luminosity upgrade the third trigger level has been realised
within the Fast Track Trigger project by a modern processor
farm~\cite{Baird:2001sz, Naumann:2002}.

The data are transferred to the fourth trigger level (L4). It has the
full detector information available and aims for a reduction of the
data logging rate and volume. L4 consists of a farm of RISC processors
operating asynchronously to the data taking and hence not contributing
to the deadtime. Fast algorithms especially designed for the processor
farm or parts of the standard offline reconstruction are run at this
level. The event processing proceeds in two steps: during the L4
\emph{trigger verification} step the L1 subtrigger decision is checked on the
basis of the refined detector information. In the case of a positive
verification an event is kept if it fulfils either one of the
\emph{hard scales} or if it is recognised by one of the \emph{finders}
dedicated to special final state signatures. The hard scale selection
aims to identify events in which a hard subprocess is involved. These
events are characterised by particles with a high momentum, high
energy jets or large values of $Q^{2}$. A small fraction of the events
rejected by L4 is kept for cross-checks. This technique is referred to
as
\emph{downscaling}.

The events accepted by L4 are written to raw data tapes with a typical
rate of $10\, \mathrm{Hz}$. Finally the raw data are subjected to the
full offline event reconstruction.

The input rate of the processor farm on L4 is limited to \mbox{$50\,
\mathrm{Hz}$}. This bandwidth has to be divided between the 128 L1
subtriggers. The rate of the various subtriggers differs significantly
and also the rate of a single subtrigger changes according to the
instantaneous luminosity and background conditions. In order to
achieve an optimal distribution of the bandwidth it is therefore
possible to downscale each of the 128 individual subtriggers generated
at L1 by a pre-settable factor, called \emph{prescale factor}. If a
prescale factor $d_{i}$ is assigned to the subtrigger $i$ only one out
of $d_{i}$ events satisfying the conditions of the subtrigger leads to
a positive L1 decision. This is realised by the introduction of
\emph{raw} and \emph{actual subtrigger bits}: if an event matches the 
requirements of the subtrigger $i$ its raw bit is set. But only for
one out of $d_{i}$ events for which the raw bit is set also the actual
bit is set. An event is accepted by the first trigger level if the
actual bit of at least one of the subtriggers is set.

To react on the changing conditions during data taking in a convenient
way an automatic optimisation procedure has been developed and
established, known as \emph{autoprescale}
program~\cite{Schultz-Coulon:1999tx}. It analyses the rate of the
individual subtriggers, estimates their future trend and calculates an
optimal set of prescale factors. The distribution of the bandwidth can
be steered via a complex strategy file.

\subsection*{Inclusive Electron Trigger}

Since in the phase space relevant to this analysis the electron is
scattered into the acceptance of the SpaCal calorimeter the
corresponding trigger subsystem, the inclusive electron trigger
(IET), provides the basis for the event selection. It compares local energy
depositions in the SpaCal with pre-defined
thresholds~\cite{Boudry:1995}.  All considered subtriggers contain at
least one of its trigger elements (see
section~\ref{c:onlinesel}). Therefore its operation principle is
explained in the following.

For triggering purposes the SpaCal is segmented into groups of
\mbox{$2 \times 2$} readout cells, so-called
\emph{trigger cells}. The energy attributed to a trigger cells is
calculated by summing up the energy depositions in the readout cells
belonging to it. Subsequently the energy in \mbox{$2 \times 2$}
trigger cells is added. To this combination of trigger cells a
\emph{cluster bit} is assigned. The deposited energy attributed to the
cluster bit is compared to pre-defined thresholds. To avoid losses at
the borders of the cluster bits a sliding window technique is applied:
Adjacent cluster bits overlap as depicted in
figure~\ref{f:ietsliding}. Their centres of gravity are separated by
\mbox{$8.1\, \mathrm{cm}$}, the transverse extension of two readout cells.

\begin{figure}
  \centering
  \includegraphics[width=0.7\textwidth]{slidingWindow.eps}
  \caption{Illustration of the sliding window technique: trigger cells are formed by combinations of four readout cells. Four of these trigger cells are in turn combined to a cluster-bit. To avoid energy losses at the borders of the cluster bits they  overlap with each of their neighbours by half the area they cover.}
  \label{f:ietsliding}
\end{figure}

Figure~\ref{f:ietliets} shows a representation of the SpaCal on
trigger level. The information whether an energy threshold is exceeded
in a certain cluster bit is encoded in bit patterns. The bits of
\mbox{$4 \times 4$} cluster bits are combined with the logical 
operation OR to a so-called \emph{LIET}\footnote{Local Inclusive
Electron Trigger} \emph{region}. If an energy threshold is exceeded
for a cluster bit, the bit of the corresponding LIET region is
set. The surface of the SpaCal is covered by 25 LIET regions. The LIET
region which contains the intersection with the nominal beam axis is
called \emph{central LIET region}.

\begin{figure}
  \centering
  \includegraphics[width=0.7\textwidth]{clusterBits.eps}
  \caption{Representation of the SpaCal on trigger level. The cross indicates the nominal position of the beam axis..}
  \label{f:ietliets}
\end{figure}

