\chapter*{Preface}
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\markboth{Preface}{Preface}


Spectroscopic measurements and scattering experiments are the two
basic methods to investigate the structure of matter. Among
the latter the exploration of nuclei and afterwards nucleons with a
lepton as a point-like probe has played and continues to play a key
role. According to Heisenberg's uncertainty principle the negative
squared momentum transfer between the lepton and the target $Q^{2}$
defines the scale \mbox{$\lambda \simeq \hbar/\sqrt{Q^{2}}$} to which
the target structure can be resolved. The higher the energy in the
centre of mass system of the interacting particles the larger values
of $Q^{2}$ that can be reached and the finer structures of the target
that can be resolved. Therefore the development of new experiments
aims for a continuous increase of the centre of mass energy.

With the Stanford Linear Accelerator for electrons proposed in
1957~\cite{Ginzton:1957} energies large enough to probe the
substructure of the proton in a \emph{deep-inelastic scattering} (DIS)
experiment were reached. The striking feature of the first SLAC data
published in 1969 was that the \emph{structure function} $F_{2}$
parametrising the structure of the proton showed almost no dependence
on $Q^{2}$, i.e. the resolution power of the
electron~\cite{Bloom:1969kc, Breidenbach:1969kd}. Such a scale
invariant behaviour, simply called \emph{scaling}, had already been
predicted by Bjorken~\cite{Bjorken:1968dy}. Feynman gave a simple
physical interpretation of the result in the so-called \emph{parton
model}~\cite{Feynman:1969ej} where the proton is assumed to consist of
non-interacting and point-like constituents (partons), on which the
electron scatters incoherently. One then expects no dependence of
$F_{2}$ on $Q^{2}$ since the scattering centre is a point. It only
depends on a variable commonly referred to as Bjorken $x$, which can
be interpreted as the fraction of the proton's momentum carried by the
struck parton. Finally Bjorken and Paschos associated the partons with
quarks~\cite{Bjorken:1969ja}, resulting in the \emph{quark-parton
model}. Quarks had been introduced to explain the large number of
meson and baryon resonances observed in hadron
spectroscopy~\cite{Gell-Mann:1964nj, Zweig:1964}.

Despite many successful applications severe difficulties arose for the
quark parton model in the following years: It was observed in
neutrino-nucleon experiments that the quarks carry only about half of
the momentum of the nucleon~\cite{Perkins:1975}. This was evidence for
the existence of additional constituents in the proton not interacting
with the leptonic probe. The other major problem was the
non-observation of quarks in the final state. This imposes a
conceptual problem on the quark parton model: While the non-existence
of free quarks implies strong forces between them the scaling
behaviour is successfully described assuming no interactions between the
partons.

Both problems were solved with the development of Quantum
Chromodynamics (QCD), the gauge theory of the strong interaction, in
the early 1970s. It describes the interaction between the quarks via
the exchange of \emph{gluons}, which carry the missing momentum
fraction of the proton. It was discovered that due to the non-Abelian
structure of QCD the strength of the interaction between the quarks
decreases towards small distances (large~$Q^{2}$)~\cite{Gross:1973id,
Politzer:1973fx}, such that the quarks in DIS experiments are
quasi-free. This behaviour is referred to as \emph{asymptotic freedom}
and allows perturbative methods to be employed to make quantitative
predictions. At large distances (small~$Q^{2}$) the strength of the
interaction rises such that \emph{confinement} of the quarks within
the hadrons takes place. Apart from providing a theoretical
justification for the parton model QCD predicted the breaking of
Bjorken scaling. Indeed a $Q^{2}$ dependence of the structure function
$F_{2}$ was observed in muon-nucleon scattering
experiments~\cite{Fox:1974ry}.

With the HERA accelerator at DESY in Hamburg starting operation in
1991 a new class of experiments was realised: lepton-hadron collider
experiments. Electrons or positrons and protons are accelerated and
brought to collision inside the multi-purpose detectors of the H1 and
ZEUS collaborations. Compared to the previous fixed target experiments
the centre of mass energy is significantly increased, allowing for a large
extension of the kinematic range in $x$ and $Q^{2}$ and thus enabling
extensive QCD tests.

One of the most important results of the H1 and ZEUS experiments so
far is the observation of a steep rise of the proton structure
function $F_{2}$ towards low values of Bjorken $x$ at fixed
$Q^{2}$~\cite{Abt:1993cb, Derrick:1993ft}, which is caused by the
gluonic content of the proton and is successfully described by
perturbative QCD (pQCD) calculations~\cite{Gluck:1991ng}. Moreover, it
turned out that the $Q^{2}$ evolution of the proton structure function
$F_{2}(x,Q^{2})$ is well described by pQCD down to low values of
$Q^{2}$ of only a few $\mathrm{GeV^{2}}$.

At even lower $Q^{2}$ values around $1\, \mathrm{GeV^{2}}$ a
transition takes place into a domain in which quark confinement
effects start to dominate and hadrons become the relevant degrees of
freedom instead of quarks. Since pQCD is no longer applicable the
description of the transition region constitutes a challenge for the
theory and a field for phenomenological models. Successful predictions
should improve the understanding of quark confinement. If the results
of pQCD or most of the phenomenological models are extrapolated
towards smaller values of $x$ the growth of $F_{2}$ would violate
unitarity. Therefore the rise of $F_{2}$ at low $x$ is expected to be
tamed, an effect referred to as \emph{saturation}. The lowest values
of $x$ are reached at HERA for small values of $Q^{2}$.

To test the available models and to search for signs of
saturation high precision data in the transition region are
essential. Collecting them requires dedicated experimental techniques
since with the scattered electron being detected in the main detector
of H1 or ZEUS standard DIS events can only be reconstructed for
\mbox{$Q^{2} > 2\, \mathrm{GeV^{2}}$}. One possibility is to extend
the acceptance of the existing detector components towards lower
values of $Q^{2}$ by shifting the interaction region of leptons and
protons in the direction of the incoming proton. This has been done
during a special running period of the HERA collider in the year 2000,
called the \emph{shifted vertex run}. The subject of the present thesis is
the measurement of the proton structure function $F_{2}$ using the
data collected by the H1 experiment in this time interval.

The thesis is organised as follows: In chapter~\ref{c:dis} the
theoretical concepts concerning deep inelastic scattering and the
structure of the proton are introduced. Chapter~\ref{c:h1} is
concerned with the experimental foundations of the measurement, namely
the relevant aspects of the HERA accelerator and the H1
detector. Following these prerequisites the basic principles of the
cross-section determination and the extraction of the structure
function $F_{2}$ are presented in chapter~\ref{c:basics}. The chapter
also serves to distinguish the present work from complementary
analyses. All details about the data analysis are covered in
chapter~\ref{c:selection}. Finally, chapter~\ref{c:results} is devoted
to the results of the measurement and the comparison to other
experimental results and to theoretical predictions.

