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\newcommand{\GeV}{\rm GeV}
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\newcommand{\pb}{\rm pb}
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\newcommand{\hdick}{\noalign{\hrule height1.4pt}}
\newcommand{\pbinv}{\mbox{${\rm pb^{-1}}$}}

\newcommand{\tg}{\theta_{\gamma}}
\newcommand{\te}{\theta_e}

\def\gsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex%
\raise 0.55ex\hbox{$\scriptstyle >$}\,}
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\def\lsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex%
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\newcommand{\qsq}{\mbox{$Q^2$}}
\newcommand{\wsq} {$W^2$}
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% choix articles classique
\def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4}

\def\NCA{\em Nuovo Cimento}
\def\NIM{\em Nucl. Instrum. Methods}
\def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}}
\def\NPB{{\em Nucl. Phys.} {\bf B}}
\def\PLB{{\em Phys. Lett.} {\bf B}}
\def\PRL{\em Phys. Rev. Lett.}
\def\PRD{{\em Phys. Rev.} {\bf D}}
\def\ZPC{{\em Z. Phys.} {\bf C}}
\def\EPJ{{\em Eur. Phys. J.} {\bf C}}
\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
\begin{small}
\begin{tabular}{llrr}
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                32nd International Conference 
                on High Energy Physics, ICHEP04},
                August~16,~2004,~Beijing} \\
                 & Abstract:        & {\bf 6-0182}    &\\
                 & Parallel Session & {\bf 6}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf
    Deeply Virtual Compton Scattering at HERA
  }

  \vspace*{1cm}
    {\Large H1 Collaboration}
\end{center}

\begin{abstract}

\noindent The cross section for the Deeply Virtual Compton
Scattering (DVCS) process $\gamma^* p \rightarrow \gamma p$ has
been measured with the H1 detector at HERA in an extended
kinematic domain. Using an integrated luminosity of 26 $\pbinv$,
the cross section is determined as a function of the photon
virtuality $Q^2$ and of the photon-proton centre-of-mass energy
$W$ in the kinematic region $4 < Q^2 < 80\,$GeV$^2$ and $30 < W <
140\,$GeV. The measurement is compared with next-to-leading order
perturbative QCD calculations and Colour Dipole model predictions.
\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction}

Deeply Virtual Compton Scattering (DVCS), sketched in
figure~\ref{fig:dvcs}a, consists of the hard diffractive
scattering of a virtual photon off a proton. It contributes to the
reaction $e^+p \rightarrow e^+ \gamma p$ which also receives
contributions from the purely electromagnetic Bethe-Heitler
process (figures~\ref{fig:bh}b and c) and the interference between
the two processes. Previous DVCS measurements at HERA can be found
in references~\cite{h1-dvcs, zeus-dvcs, hermes-dvcs}.

The interest in the DVCS process results from the particular
insight it gives into the applicability of perturbative Quantum
Chromo-Dynamics (QCD) to the field of diffractive interactions. In
the presence of a hard scale, the DVCS scattering amplitude
factorises~\cite{Radyushkin:1997ki,Collins:1999be,Ji:1998xh} into
a hard scattering part calculable in perturbative QCD and parton
distributions which contain the non-perturbative effects due to
the structure of the proton structure. The DVCS process is similar
to diffractive vector meson electroproduction, but with a real
photon replacing the final state vector meson. This allows the
theoretical complications and uncertainties associated with the
unknown vector meson wave function to be avoided. However, even at
photon virtualities $Q^2$ above a few GeV$^2$, non-perturbative
effects influence the predictions and have to be modelled. The
wide kinematic range in the photon virtuality, \qsq, accessible at
HERA, provides a powerful probe for the interplay between the
perturbative and non-perturbative regimes in QCD. Furthermore, the
DVCS process gives access to the Generalised Parton Distributions
(GPDs)~\cite{Muller:1994fv, Ji:1997ek, Radyushkin:1997ki}, which
are generalisations of the familiar parton distributions and
incorporate information on correlations between the momenta of
partons in the proton.

This paper presents a new measurement of the DVCS process, in
which the cross section is extracted as a function of $Q^2$ and of
the photon-proton centre-of-mass energy $W$. The measurements
extend to larger $Q^2$ and $W$ values than has been previously
possible. The data used were taken at HERA in the year 2000 in
which 920\,GeV protons collided with 27.5\,GeV positrons. The
integrated luminosity of 26.0 $\pbinv$ is 3.5 times larger than
the that used in the previously published H1 cross section
measurements~\cite{h1-dvcs, rainer}.


\section{H1 detector}

A detailed description of the H1 detector can be found
in~\cite{h1dect}. Here only the detector components relevant to
the present analysis are described.
%
The SpaCal calorimeter covers the backward\footnote{H1 uses a
right-handed coordinate system with the $z$ axis pointing along
the beam direction, the $+z$ or ``forward" direction being that of
the outgoing proton beam. Polar angles $\theta$ are measured with
respect to the $z$ axis. The pseudo-rapidity is defined by
$\eta=-\ln \tan \theta /2$.} region of the H1 detector ($153 ^{\rm
\circ} < \theta < 177.5 ^{\rm \circ}$). Its energy resolution for
electromagnetic showers is $\sigma(E)/E \simeq 7.1\%/\sqrt{E/GeV}
\oplus 1\%$. The liquid argon (LAr) calorimeter ($4^{\rm \circ}
\leq \theta \leq 154^{\rm \circ}$) is situated inside a solenoidal
magnet. The energy resolution of the LAr for electromagnetic
showers is $\sigma(E)/E \simeq 11\%/\sqrt{E/GeV}$.
%
The major components of the central tracking detector are two
\mbox{2\,m} long coaxial cylindrical drift chambers with wires
parallel to the beam direction which form the Central Jet Chamber
(CJC). The measurement of charged particle transverse momenta is
performed in a magnetic field of 1.15~T, uniform over the full
tracker volume. The forward components of the detector, used here
to tag hadronic activity at high pseudorapidity ($5 \lsim \eta
\lsim 7$), are the forward muon spectrometer (FMD) and the proton
remnant tagger (PRT). The FMD, designed to identify and measure
the momentum of muons emitted in the forward direction, contains
six active layers, each made of a pair of planes of drift cells.
The three layers between the main calorimeter and the toroidal
magnet can be reached by secondary particles arising from the
interaction of particles scattered under small angles hitting the
beam collimators or the beam pipe walls. Secondary particles or
the scattered proton at large $|t|$ can also be detected by the
Proton Remnant Tagger (PRT), located at 24\,m from the interaction
point and consisting of double layers of scintillator surrounding
the beam pipe.

\section{Event selection}
%%%%%%%%%%%%%%%%%%%%%%%%%
The cross section for the Bethe-Heitler (BH) process, which
proceeds via Bremsstrahlung from the positron lines, is largest
when the positron and the photon are both produced in the backward
direction. In the DVCS case, the final state photon does not
originate from the positron and therefore the ratio of the DVCS to
the BH cross section is expected to increase when the photon is
found in the forward direction. The analysis is thus restricted to
the case where the photon is detected in the central or in the
forward parts of the detector, i.e.~in the LAr calorimeter. A data
sample dominated by Bethe-Heitler events is used as a reference
sample to monitor the detector's performance and the simulation
thereof.
%
Two event samples are selected according to:
\begin{itemize}
\item {\bf DVCS candidate sample:} The photon candidate is
detected in the LAr calorimeter and the positron candidate in the
SpaCal calorimeter. Both DVCS and Bethe-Heitler processes are
expected to contribute to this sample with similar magnitudes.
\item {\bf BH dominated sample:} The photon candidate is detected
in the SpaCal calorimeter and the positron candidate in the LAr
calorimeter. The contribution of DVCS to this sample is
negligible.
\end{itemize}


The event selection is based on the detection of exactly two
electromagnetic clusters, corresponding to the final state photon
and positron. One cluster is required to be detected in the SpaCal
calorimeter with energy larger than $15\,{\rm GeV}$ and the other
in the LAr calorimeter ($25^{\circ} - 145^\circ$) with a
transverse momentum $p_t > 2\,{\rm GeV}$. Events with more than
one track reconstructed in the CJC are rejected. Events with one
track are only kept if the track is associated with one of the
clusters and hence identifies the positron candidate. In order to
reject inelastic and proton dissociation events, no further
cluster in the LAr calorimeter with energy above $0.5\,{\rm GeV}$
is allowed and an absence of activity above the noise level in
forward detectors PRT and FMD is required. The influence of
radiative corrections is reduced by requirements on the
longitudinal momentum balance\footnote{The quantity $\sum E - P_z$
is required to be above $45\,{\rm GeV}$, where $E$ denotes the
energy and $P_z$ the momentum along the beam axis of the final
state particles. The sum is calculated for the final state
positron and photon.}. To enhance the DVCS signal with respect to
the Bethe-Heitler contribution and to maintain a large detector
acceptance, the kinematic domain is explicitly restricted to $Q^2
> 4\,{\rm GeV}^2 $, $ |t| < 1\,{\rm GeV}^2$ and $30 < W <
140\,{\rm GeV}$. The kinematic variables are reconstructed as
described in section~\ref{sec:kin}. Note that for the BH process,
the $Q^2$ and $W$ variables cannot be associated with the photon
virtuality and the $\gamma^*p$ centre-of-mass energy.


\section{Theoretical predictions}

Calculations of the DVCS cross section have been published based
on both NLO QCD
calculations~\cite{Freund:2001hm,Freund:2001hd,Freund:2003qs} and
on Colour Dipole models~\cite{Donnachie:2000px, Favart:2003cu}.
Both approaches contain ``soft" (non-perturbative) and ``hard"
contributions.

Freund and McDermott~\cite{Freund:2001hm,Freund:2001hd} have
calculated the NLO QCD amplitude at leading twist. The soft
contribution is based on the aligned jet
model~\cite{Bjorken:1973gc}. In a recent publication,
Freund~\cite{Freund:2003qs} has included the twist-3 contribution
and proposes a parametrisation of the GPD based on standard
(forward) parton densities and a squared four-momentum transfer to
the proton ($t$) dependence of the form $\exp(bt)$ with
$b=b_0(1-0.15 \log(Q^2/2))$.

Colour Dipole models are based on the factorisation of the
incoming photon wave function, the $q\bar q$-p cross section and
the outgoing photon wave function. The main difference between the
models is the way the $q\bar q$-p dipole cross section is
parameterised. Donnachie and Dosch~\cite{Donnachie:2000px}
associate soft pomerons with large dipole sizes and hard pomerons
with small dipoles. Favart and Machado~\cite{Favart:2003cu} apply
the saturation model of Golec-Biernat et
al.~\cite{Golec-Biernat:1999qd} to the DVCS process, including the
possibility of DGLAP evolution~\cite{Bartels:2002es}. These
predictions only provide the scattering amplitude at $t = t_{min}
\simeq -m^2_p Q^4/W^4$. In both cases an exponential
$t$-dependence, $e^{bt}$, is assumed.

\section{Kinematic variables and Monte Carlo simulation}
\label{sec:kin}

The reconstruction of the kinematic variables $Q^2$ and Bjorken
$x$ relies on the polar angle measurements of the final state
electron, $\te$, and photon, $\tg$, (double angle method):
\begin{eqnarray}
Q^2 & = & 4 E_0^2\, \frac{\sin\ \tg\ (1+\cos \te)}
                {\sin\ \tg\ + \sin\ \te\ - \sin\ (\te\ + \tg)} \; ;\\
x & = & \frac{E_0}{E_p} \, \frac{\sin\ \tg\ + \sin\ \te\ + \sin\ (\te\ +
\tg)}
                {\sin\ \tg\ + \sin\ \te\ - \sin\ (\te\ + \tg)} \; ;\\
   W^2 & =&  \frac{Q^2}{x}\, (1-x) \; ,
\end{eqnarray}
where $E_0$ and $E_p$ are the electron and the proton beam
energies, respectively. If no event vertex is reconstructed, the
nominal $ep$ interaction vertex position is assumed for the
reconstruction of these angles. The variable $t$ is very well
approximated by the negative square of the transverse momentum of
the outgoing proton. The latter is computed as the vector sum of
the transverse momenta of the final state photon $\vec
p_{t_{\gamma}}$ and of the scattered positron $\vec p_{t_{e}}$:
%
\begin{equation}
  t \simeq - |\vec p_{t_{\gamma}} + \vec p_{t_{e}}|^2 \ .
\label{eq:t}
\end{equation}

% Monte Carlo
Monte Carlo simulations are used to estimate the corrections that
must be applied to the data due to the effects of the acceptance
and resolution of the detector. The generated events are passed
through a detailed simulation of the H1 detector and are subject
to the same reconstruction and analysis chain as the data. The
Monte Carlo TINTIN~\cite{rainer} is used to model the DVCS and BH
processes and their interference. These contributions are
simulated according the prediction of Frankfurt, Freund and
Strikman~\cite{Frankfurt:1998at}, denoted FFS in the following. In
order to subtract the small background contributions,
DIFFVM~\cite{diffvm} is to simulate diffractive vector meson
electroproduction and GRAPE~\cite{grape} to model electron pair
production via photon-photon interactions.

\section{BH dominated sample}
%%%%%%%%%%%%%%%%%%%%%%%%
In order to monitor the detector response in the energy and
angular range relevant for the DVCS sample, the kinematic cuts on
$Q^2$ and $W$ used in that case are also applied to this sample,
treating the photon candidate in the SpaCal as the scattered
positron and the positron candidate in the LAr calorimeter as the
photon. Background contributions from inelastic Bethe-Heitler
events, diffractive $\rho$ meson production and electron pair
production are considered. In figure~\ref{fig:bhcont} the
distributions of several basic quantities are compared with the
simulation. A good description of the data by the sum of the
different MC samples is achieved, showing that the detector
response is well described by the simulation.
Figure~\ref{fig:bhcont}f), in which the transverse momentum of the
positron measured by the LAr calorimeter is compared with that
measured using the track curvature, illustrates the good
calibration of the LAr calorimeter.

\section{DVCS candidate sample}

This sample is dominated by the DVCS contribution, although the
contribution of the Bethe-Heitler process is not negligible.
Significant contamination arises from the DVCS process with proton
dissociation:
\begin{equation}
e^+ + p \rightarrow e^+ + \gamma + Y,
\end{equation}
\label{eq:reac2} when the decay products of the baryonic system
$Y$ are not detected in the forward detectors. This typically
occurs if the mass of the system for $Y$ is below 1.6\,GeV. The
sum of the DVCS and BH contributions in which the proton does not
survive intact has been estimated to be $11\pm 6\,\%$ of the final
sample. The other sources of background considered are diffractive
$\omega$ and $\phi$ production as the $\omega$ and $\phi$ have
decay modes to final states including photons (directly or from
$\pi^0$ decays) or $K^0_L$ mesons.

Figure~\ref{fig:dvcscont} shows both data distributions and the
sum of the predictions of the FFS calculation and the expected
backgrounds. All contributions are normalised to the luminosity of
the data sample, using a $t$ slope of $b = 7$ GeV$^{-2}$ for the
FFS prediction. The pure Bethe-Heitler contribution is also shown.
The kinematic distribution of the DVCS signal is different to that
of the Bethe-Heitler contribution, in particular in the polar
angle of the LAr cluster (figure~\ref{fig:dvcscont}e) and in the
coplanarity (figure~\ref{fig:dvcscont}c), which is defined as the
difference of the azimuthal angles of the two clusters and is
related to the $p_t$-balance of the positron-photon system. For
$|t| > |t_{min}|$, the coplanarity is expected to deviate slightly
from 180$\degr$ since the $e\gamma$ system must balance the
transverse momentum of the scattered proton. The coplanarity
distribution is found to be broader in the DVCS candidate sample
than in the Bethe-Heitler dominated sample
(figure~\ref{fig:bhcont}c). This is attributed to the
electromagnetic nature of the BH process, which implies a steeper
$t$ distribution for this process than for the DVCS signal. The
distributions of the kinematic variables $Q^2$, $W$ and $t$ are
shown in figure~\ref{fig:dvcskin} as are the same distributions
for the sum of the predictions of the FFS calculation and the
expected backgrounds.

\section{Cross section measurement}

To extract the cross section, the DVCS candidate sample is
corrected for detector effects and for the initial state radiation
of real photons from the positron line using the Monte Carlo
simulation. The contamination resulting from inelastic BH and DVCS
events with proton dissociation is subtracted statistically bin by
bin. The background contributions from diffractive $\omega$ and
$\phi$ production, estimated to be 3.5\% on average and below
$6\,\%$ in all bins, are also subtracted bin by bin.

In the leading twist approximation, the contribution of the
interference term to the cross section is proportional to the
cosine of the angle between the plane formed by the incoming and
the scattered positron and the $\gamma^*$-proton plane. Since the
present measurement is integrated over this angle, the overall
contribution of the interference term is negligible. Therefore the
Bethe-Heitler cross section can be subtracted from the total cross
section in order to obtain the DVCS cross section. The DVCS
$e^+p\rightarrow e^+\gamma p$ cross section is then converted to a
DVCS $\gamma^* p \rightarrow \gamma p$ cross section using the
equivalent photon approximation (as used in~\cite{h1_rho}):
\begin{equation}
 \frac{d\sigma_{e^+ p\rightarrow e^+ p \gamma}}{dQ^2dy}
  =
 \Gamma(Q^2,y) \; \sigma_{\gamma^* p\rightarrow \gamma p}(Q^2,y)\; ,
\end{equation}
where $\Gamma(Q^2,y)$ is the virtual photon flux factor. In order
to apply bin centre corrections, $\sigma_{\gamma^* p\rightarrow
\gamma p}$ is parameterised as:
\begin{equation}
\sigma_{\gamma^* p\rightarrow \gamma p}(Q^2,y) \sim
  y^a \; (\frac{1}{Q^2})^n.
\end{equation}
The values of the parameters $a$ and $n$ are obtained from an
iterative fit procedure, yielding $a=0.49 \pm 0.22$ and $ n = 1.72
\pm 0.31$. This corresponds to the data following a dependence
$\sigma(W) \sim W^{\delta}$, with $\delta=0.98\pm 0.44$.

The dominant systematic uncertainties arise from the following
sources:
\begin{itemize}
 \item uncertainty on the proton dissociation subtraction ($11\pm6\%$);
 \item uncertainty on the acceptance and bin centre corrections
 ($\pm 7\%$);
 \item energy calibration of the two clusters (SpaCal $\pm 1\%$,
   LAr $\pm 2\%$), yielding an error of 5\% in both cases;
 \item $\theta$ measurement of the two clusters (positron $\pm 1.3$mrad,
  photon $\pm 3$mrad), yielding errors of 5\% and 2\%, respectively;
 \item uncertainty on the $t$ slope used in the MC for the correction
  of detector effects ($b \pm 2$ GeV$^{-2}$), yielding an error of 4\%;
 \item uncertainty on the noise in the forward detectors ($2.7 \pm
 0.1\%$);
 \item uncertainty on the CJC random noise ($\pm 2\%$);
 \item uncertainty on the luminosity measurement ($\pm 1.5\%$).
\end{itemize}

\section{Results}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The $\gamma^* p$ cross section for the DVCS process is shown in
figures~\ref{fig:gpsig1}, \ref{fig:gpsig2} and \ref{fig:gpsig3} as
a function of $Q^2$ for $W = 82\,$GeV and as a function of $W$ for
$Q^2 = 8\,$GeV$^2$. In figure~\ref{fig:gpsig1}, the measurement is
compared to the NLO QCD prediction using two different GPD
parameterisations~\cite{Freund:2003qs}. The bands presented in the
plot, corresponding to $5 < b_0 < 9\,$GeV$^{-2}$, represent the
normalisation uncertainty associated with the predictions. The NLO
QCD predictions are in good agreement with the data for both GPD
parameterisations. The main difference between the results
obtained using the two parameterisations is a change in the
overall normalisation, emphasizing the need for a direct
measurement of the $t$ dependence. In figure~\ref{fig:gpsig2}, the
measurement is compared to two different Colour Dipole model
predictions, by Donnachie and Dosch~\cite{Donnachie:2000px} and by
Favart and Machado~\cite{Favart:2003cu}. For clarity's sake,  no
normalisation uncertainty band is shown in the figure. The
predictions are presented for $b = 7$ GeV$^{-2}$. All the Colour
Dipole model predictions shown describe the data well in both
shape and normalisation for the same $b$ value. The value of $b =
7\,$GeV$^{-2}$ is chosen as it leads to a good representation of
the normalisation and also to a good description of the
uncorrected $t$ distribution (see figure~\ref{fig:dvcskin}c).
Figure~\ref{fig:gpsig3} shows a comparison of the new measurement
with the previous measurements of H1~\cite{h1-dvcs} and
ZEUS~\cite{zeus-dvcs}. The two H1 measurements are in good
agreement. The new H1 measurement is in fair agreement with the
ZEUS results. In the region around $W \sim 70\,$GeV, the ZEUS
points lie above those of, the discrepancy being at about the two
standard deviation level.

\section{Conclusion}
%%
The $\gamma^* p \rightarrow \gamma p$ cross section for the DVCS
process is measured in an extended kinematic regime, $4 <Q^2
<80\,$GeV$^2$, $40 < W < 140\,$GeV and $|t| < 1\,$GeV$^2$, using a
data sample taken with the H1 detector which corresponds to an
integrated luminosity of 26 $\pbinv$. The measured cross section
is in reasonable agreement with previous H1 and ZEUS measurements.
The cross section has been compared with NLO QCD
predictions~\cite{Freund:2001hm} using GPD parameterisations based
on MRST2001 and CTEQ6~\cite{Freund:2003qs} parton distribution
functions, and to Colour Dipole model
predictions~\cite{Donnachie:2000px, Favart:2003cu} which all
describe the measured $Q^2$ and $W$ distributions within errors,
assuming a $t$ slope parameter $b = 7\,$GeV$^{-2}$.

%
%   References
%
\begin{thebibliography}{99}

\bibitem{h1-dvcs}
%\bibitem{Adloff:2001cn}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Measurement of deeply virtual Compton scattering at HERA,''
 \Journal{\PLB}{517}{2001}{47},
[hep-ex/0107005].
%%CITATION = HEP-EX 0107005;%%

\bibitem{zeus-dvcs}
%\bibitem{:2003ya}
 ZEUS Collaboration,
%``Measurement of deeply virtual Compton scattering at HERA,''
DESY-03-059, [hep-ex/0305028].

\bibitem{hermes-dvcs}
%\bibitem{Airapetian:2001yk}
A.~Airapetian {\it et al.}  [HERMES Collaboration],
%``Measurement of the beam spin azimuthal asymmetry associated with
%deeply-virtual Compton scattering,''
Phys.\ Rev.\ Lett.\  {\bf 87} (2001) 182001
[hep-ex/0106068].
%%CITATION = HEP-EX 0106068;%%

\bibitem{rainer} R.\,Stamen, PhD dissertation, Universit\"at Dortmund
and Univ.~Libre de Bruxelles, DESY-THESIS-2001-057, available through:\\
http://www-h1.desy.de/publications/theses\_list.html.

\bibitem {h1dect}
I.~Abt {\it et al.}  [H1 Collaboration],
%``The H1 detector at HERA,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310 and 348.
%%CITATION = NUIMA,A386,310;%%


%%% Factorisation
%%%%%%%%%%%%%%%%%
\bibitem{Radyushkin:1997ki}
A.~V.~Radyushkin,
%``Nonforward parton distributions,''
Phys.\ Rev.\ {\bf D 56} (1997) 5524
[hep-ph/9704207].
%%CITATION = HEP-PH 9704207;%%

\bibitem{Collins:1999be}
J.~C.~Collins and A.~Freund,
%``Proof of factorization for deeply virtual Compton scattering in
%{QCD},''
Phys.\ Rev.\ {\bf D 59} (1999) 074009
[hep-ph/9801262].
%%CITATION = HEP-PH 9801262;%%

\bibitem{Ji:1998xh}
X.~Ji and J.~Osborne,
%``One-loop corrections and all order factorization in deeply virtual
%Compton scattering,''
Phys.\ Rev.\ {\bf D 58} (1998) 094018
[hep-ph/9801260].
%%CITATION = HEP-PH 9801260;%%

%%% GPD
%%%%%%%%%%%%%%%%%%%
\bibitem{Muller:1994fv}
D.~M\"uller, D.~Robaschik, B.~Geyer, F.~M.~Dittes and
J.~Ho\v{r}ej\v{s}i,
%``Wave functions, evolution equations and evolution kernels from
%light-ray operators of {QCD},''
Fortsch.\ Phys.\  {\bf 42} (1994) 101
[hep-ph/9812448].
%%CITATION = HEP-PH 9812448;%%

\bibitem{Ji:1997ek}
X.~Ji,
%``Gauge invariant decomposition of nucleon spin,''
Phys.\ Rev.\ Lett.\  {\bf 78} (1997) 610
[hep-ph/9603249].
%%CITATION = HEP-PH 9603249;%%

%%% QCD Predictions
%%%%%%%%%%%%%%%%%%%
\bibitem{Frankfurt:1998at}
 L.L.~Frankfurt, A.~Freund and M.~Strikman,
 Phys.\ Lett.\ B {\bf 460} (1999) 417, [hep-ph/9806535].

\bibitem{Freund:2001hm}
 A.~Freund and M.~F.~McDermott,
 %``A next-to-leading order analysis of Deeply Virtual Compton
 %Scattering,''
 Phys.\ Rev.\ D {\bf 65} (2002) 091901,
 [hep-ph/0106124].

\bibitem{Freund:2001hd}
 A.~Freund and M.~McDermott,
 % A detailed next-to-leading order QCD analysis of deeply virtual Compton
 % scattering observables
 Eur.Phys.J.C23:651-674,2002,
 [hep-ph/0111472].

%\bibitem{Belitsky:2001gz}
%A.~V.~Belitsky, D.~M\"uller, L.~Niedermeier and A.~Sch\"afer,
%%``Leading twist asymmetries in deeply virtual Compton scattering,''
%Nucl.\ Phys.\ B {\bf 593} (2001) 289
%[hep-ph/0004059].
%%CITATION = HEP-PH 0004059;%%

\bibitem{Freund:2003qs}
A.~Freund,
%``A detailed QCD analysis of twist-3 effects in DVCS observables,''
[hep-ph/0306012].
%%CITATION = HEP-PH 0306012;%%
hep-ph/0306012.

%%% Dipole Models
%%%%%%%%%%%%%%%%%%%
\bibitem{Donnachie:2000px}
A.~Donnachie and H.~G.~Dosch,
%``Diffractive exclusive photon production in deep inelastic
%scattering,''
  Phys.\ Lett.\ B{\bf 502} (2001) 74-78,
[hep-ph/0010227].
%%CITATION = HEP-PH 0010227;%%

\bibitem{Favart:2003cu}
 L.~Favart and M.~V.~Machado,
 %``Deeply virtual Compton scattering and saturation approach,''
 accepted by Eur. Phys. J. C, [hep-ph/0302079].

%\bibitem{McDermott:2001pt}
% M.~McDermott, R.~Sandapen and G.~Shaw,
% %``Colour dipoles and virtual Compton scattering,''
% \EPJ {C22}{2002}{655}, [hep-ph/0107224].

%\bibitem{Sandapen:2002zs}
% R.~Sandapen,
% %``Colour dipoles and deeply virtual Compton scattering,''
% Acta Phys.\ Polon.\ B {\bf 33} (2002) 3567
% [hep-ph/0207021].

% aligned jet model ref
\bibitem{Bjorken:1973gc}
J.~D.~Bjorken and J.~B.~Kogut,
%``Correspondence Arguments For High-Energy Collisions,''
Phys.\ Rev.\ D {\bf 8} (1973) 1341.
%%CITATION = PHRVA,D8,1341;%%

%\cite{Golec-Biernat:1999qd}
\bibitem{Golec-Biernat:1999qd}
K.~Golec-Biernat and M.~Wusthoff,
%``Saturation in diffractive deep inelastic scattering,''
Phys.\ Rev.\ D {\bf 60} (1999) 114023
[hep-ph/9903358].
%%CITATION = HEP-PH 9903358;%%

%\cite{Bartels:2002es}
\bibitem{Bartels:2002es}
J.~Bartels, K.~Golec-Biernat and H.~Kowalski,
%``DGLAP evolution in the saturation model,''
Acta Phys.\ Polon.\ B {\bf 33} (2002) 2853
[hep-ph/0207031].
%%CITATION = HEP-PH 0207031;%%
%%% Monte Carlo
%%%%%%%%%%%%%%%%%%%

\bibitem{diffvm} B.\,List, A.\,Mastroberardino,
{\sl DIFFVM: A Monte Carlo generator for diffractive
processes in ep scattering},
{\em Proceedings of the Monte Carlo Generators for HERA physics},
%Eds.\, A.\,T.\,Doyle, G.\,Grindhammer, G.\,Ingelman, H.\,Jung,
DESY-PROC-1999-02, p.\,396.

\bibitem{grape} T.\,Abe et al.,
{\sl GRAPE-Dilepton},
{\em Proceedings of the Monte Carlo Generators for HERA physics},
%Eds.\, A.\,T.\,Doyle, G.\,Grindhammer, G.\,Ingelman, H.\,Jung,
DESY-PROC-1999-02, p.\,566.



\bibitem{h1_rho}
 C.~Adloff {\it et al.}  [H1 Collaboration],
 %``Elastic electroproduction of rho mesons at HERA,''
 Eur.\ Phys.\ J.\ C {\bf 13} (2000) 371
 [hep-ex/9902019].

\end{thebibliography}


%\clearpage
%\vspace{3cm}

\clearpage
% \input{figures}

%%%%%%%%%%%%%%%%%%% Fig 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
 \begin{center}
  \epsfig{figure=H1prelim-03-017.fig1.eps,width=\textwidth}
  \caption{\sl Diagrams illustrating (a) the DVCS and (b and c)
  the Bethe-Heitler processes.}
  \label{fig:dvcs}
  \label{fig:bh}
 \end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%% Fig 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
 \begin{center}
  \epsfig{file=H1prelim-03-017.fig2.eps,width=\textwidth}
 \end{center}
  \caption{\sl Event distributions of the BH dominated sample,
i.e. in which the cluster in the LAr calorimeter corresponds to
the positron candidate. a) energy of the cluster in the SpaCal, b)
energy of the cluster in the LAr, c) coplanarity, i.e.~difference
of the azimuthal angle of the positron and photon candidates, d)
polar angle of the cluster in the SpaCal, e) polar angle of the
cluster in the LAr, f) ratio of the transverse momentum of the
positron measured with the LAr calorimeter to that determined from
the track curvature. The error bars on the data points are
statistical. The data are compared to the sum of the predictions
for the Bethe-Heitler process, elastic dilepton production and
diffractive $\rho$ production. All predictions are normalised to
the luminosity of the data.}
 \label{fig:bhcont}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%% Fig 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
 \begin{center}
  \epsfig{file=H1prelim-03-017.fig3.eps,width=\textwidth}
 \end{center}
  \caption{\sl Event distributions of the DVCS candidate sample,
i.e. the cluster in the LAr calorimeter corresponds to the photon
candidate. a) energy of the cluster in the SpaCal, b) energy of
the cluster in the LAr, c)  coplanarity, i.e.~difference of the
azimuthal angle of the positron and photon candidates, d) polar
angle of the cluster in the SpaCal, e) polar angle of the cluster
in the LAr. The error bars on the data points are statistical. The
data are compared to the sum of the predictions for the $e^+ p
\rightarrow e^+ \gamma p$ reaction according to FFS, using a fixed
value of $b = 7 $ GeV$^{-2}$ for the DVCS calculation. All
predictions are normalised to the luminosity of the data. }
 \label{fig:dvcscont}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%% Fig 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
 \begin{center}
  \epsfig{file=H1prelim-03-017.fig4.eps,width=\textwidth}
 \end{center}
  \caption{\sl Kinematic variable distributions for the DVCS candidate sample,
a) $Q^2$, b) $W$ c) $t$. The error bars on the data points are
statistical. The data are compared to the sum of the predictions
for the $e^+ p \rightarrow e^+ \gamma p$ reaction according to
FFS, using a fixed value of $b=7$ GeV$^{-2}$ for the DVCS
calculation. All predictions are normalised to the luminosity of
the data.}
 \label{fig:dvcskin}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%% Fig 5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
 \begin{center}
  \epsfig{file=H1prelim-03-017.fig5.eps,width=\textwidth}
 \end{center}
 \caption{\sl The $\gamma^* p \rightarrow \gamma p$
cross section as a function of $Q^2$ (upper plot) for $<W>=82$~GeV
and as a function of $W$ (lower plot) for $<Q^2>=8$~GeV$^2$. The
inner error bars are statistical and the full error bars include
the systematic errors added in quadrature. The measurement is
compared with NLO QCD predictions~\cite{Freund:2001hd} using two
different GPD parameterisations based on MRST2001 and
CTEQ6~\cite{Freund:2003qs} and a $t$ dependence parameterised as
$e^{bt}$, with $b=b_0(1-0.15 \log(Q^2/2))$~GeV$^{-2}$. The bands
correspond to $b_0$ values between 5 and 9\,GeV$^{-2}$.}
\label{fig:gpsig1}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%% Fig 6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
 \begin{center}
  \epsfig{file=H1prelim-03-017.fig6.eps,width=\textwidth}
 \end{center}
 \caption{\sl The $\gamma^* p \rightarrow \gamma p$
 cross section as a function of $Q^2$ (upper plot) for $<W>=82$~GeV
 and as a function of $W$ (lower plot) for $<Q^2>=8$~GeV$^2$.
 The inner error bars are statistical and
 the full error bars include the systematic errors added in quadrature.
 In addition the result of a fit of the form
 $\sigma(W) \sim W^{\delta}$ is shown in the lower plot.
 The measurement is compared with the Colour Dipole models of
 Donnachie and Dosch~\cite{Donnachie:2000px} and Favart and
 Machado~\cite{Favart:2003cu}. The latter is shown both without and
 with DGLAP evolution of the dipole cross section (BGBK).
 In all predictions, a fixed $t$ slope of $b=7.$~GeV$^{-2}$ is used.
 }
 \label{fig:gpsig2}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%% Fig 7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
 \begin{center}
  \epsfig{file=H1prelim-03-017.fig7.eps,width=\textwidth}
 \end{center}
 \caption{\sl The $\gamma^* p \rightarrow \gamma p$ DVCS
 cross section as a function of $Q^2$ (upper plot) for $<W>=82$~GeV
 and as a function of $W$ (lower plot) for $<Q^2>=8$~GeV$^2$.
 The inner error bars are statistical and
 the full error bars include the systematic errors added in quadrature.
 Previous H1 data~\cite{h1-dvcs} and data from the ZEUS
 Collaboration~\cite{zeus-dvcs} are also shown.
 The measurement is compared
 with a NLO QCD prediction~\cite{Freund:2001hd} using a GPD
 parameterisation based on MRST2001~\cite{Freund:2003qs} for
 $b_0=7.$~GeV$^{-2}$ and with the Donnachie and Dosch~\cite{Donnachie:2000px}
 Colour Dipole model prediction using $b=7$~GeV$^{-2}$.
 }
 \label{fig:gpsig3}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
