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\begin{document}

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\noindent
% {\bf H-UM \& JS: version of \today} \\[.3em] 
Submitted to the 30th International Conference on 
High-Energy Physics ICHEP2000, \\ 
Osaka, Japan, July 2000


\vspace*{3cm}

\begin{center}
  \Large
  {\bf Measurement of the Deeply Virtual Compton Scattering \\
         at HERA \\}
  \vspace*{1cm}
    {\Large H1 Collaboration} 
\end{center}

\begin{abstract}

\noindent
A measurement is presented of Deeply Virtual Compton Scattering 
at HERA. The cross section is measured as a function of $Q^2$ 
and $W$. The data are compared to LO QCD calculations based on 
the two gluon exchange model. 

\end{abstract}


\vfill
\begin{flushleft}
  {\bf Abstract: 966 } \\
  {\bf Parallel session: 02} \\
  {\bf Plenary talk: 12 } 
\end{flushleft}

\end{titlepage}

\pagestyle{plain}

\section{Introduction}

Deeply Virtual Compton Scattering (DVCS) is the hard diffractive 
scattering of a virtual photon
off a proton. The QCD interpretation, based on the two gluon 
exchange model, of this process can be seen in figure 
\ref{dvcsqcd}. The virtual photon emitted by the incoming electron 
is coupling via a quark--loop to the two gluons which are coupling 
to the incoming proton. A real photon is emitted from the quark loop.

\begin{figure}[htb]
 \begin{center}
  \epsfig{figure=H1prelim-00-017.fig1.eps,width=7cm}
  \caption{DVCS diagram in QCD picture.}
  \label{dvcsqcd}
 \end{center}
\end{figure}

DVCS offers a new and 
comparatively clean way to study diffraction at HERA. In comparison 
to vector-meson production it avoids large uncertainties on the     
vector-meson wave-function. The largest interest comes from the 
access it provides to the skewed parton distributions of the proton\cite{rad}. 

DVCS contributes to the reaction 
\mbox{$e^+ p \longrightarrow e^+ \gamma p$}, 
whose total cross section is 
dominated by the purely electromagnetic Bethe--Heitler process. 
The diagrams corresponding to
this process are shown in figure \ref{qedc}. The real photon 
in the final state is either emitted from the incoming or 
outgoing electron line.


\begin{figure}[htb]
 \begin{center}
  \epsfig{figure=H1prelim-00-017.fig2.eps,width=9cm}
  \caption{Diagrams contributing to the Bethe--Heitler process.} 
  \label{qedc}
 \end{center}
\end{figure}


In the presence of a large scale the DVCS process can be  
calculated in perturbative QCD. 
In the present case the scale is given by
the photon virtuality $Q^2$ above a few ${\rm GeV}^2$.
LO QCD calculations exist, based on the two gluon exchange 
model\cite{ffs}. These calculations, including the interference 
between DVCS and Bethe--Heitler processes, are embedded into a MC generator 
used in the analysis.

Since for the DVCS process the virtual photon is scattered 
onto mass shell in the final state it is necessary 
to transfer longitudinal momentum from the proton to the photon. 
In the 
picture of the two gluon exchange the fractional momenta of
the gluons $x_1$ and $x_2$ are therefore not equal which leads to
the concept of the skewed parton distribution, which are
generalised parton distributions.
The DVCS process provides in principle the possibility to extract these 
distributions from experimental data\cite{fre}. 



\section{Event selection}

The analysis is based on data taken in 1997 corresponding to an 
integrated luminosity of $8\,{\rm pb}^{-1}$.
A detailed description of the H1--detector can be found 
elsewhere\cite{h1dect}.
The main components of the detector which are used in this analysis are
the tracking system, the LAr calorimeter which covers the central 
and forward part of the detector, a Spaghetti calorimeter which 
covers the backward part of the detector, the Forward Muon Detector (FMD) 
and the Proton remnant tagger (PRT). 
The forward direction is defined as the direction of the incoming proton.

Since the total  
\mbox{$e^+ p \longrightarrow e^+ \gamma p$} 
cross section is dominated by the Bethe--Heitler 
process the selected phase space has to be chosen in a way that 
the DVCS contribution becomes sizeable; in practice the
photon will be required to be in the forward region.
   
While the proton escapes the main detector through the beam pipe only 
the scattered electron and photon are measured. Therefore the
event selection is based on demanding two electromagnetic clusters.
A cluster with an energy above $15\,{\rm GeV}$ has 
to be found in the backward calorimeter. A second cluster has 
to be in the central part of the LAr calorimeter with a transverse energy 
with respect to
to the incoming proton direction of $p_t > 1\,{\rm GeV}$.
To reject background (incl. inelastic DVCS contributions)
no further clusters with energy above $0.5\,{\rm GeV}$ are allowed.

If a track can be reconstructed it has to be associated 
to one of the clusters and determines the electron candidate. 
If no track is reconstructed the backward cluster is assumed 
to be the electron. If
more than one track is reconstructed, the event is rejected.

%%In the forward direction further detectors 
%%(FMD and PRT) are placed which can detect particles originating 
%%from proton dissociation 
%%processes. These detectors are demanded to show no signal above 
%%the noise level. Furthermore, this requirement strongly suppresses 
%%any contamination from inelastic processes.

In order to reject inelastic and proton dissociation events 
where all additional 
particles escape detection by the LAr calorimeter at 
small polar angles, counters
close to the beam pipe (PRT, FMD) are used as veto.

To reduce the effect of QED radiative corrections a cut on the 
balance of longitudinal momentum is applied; 
$\sum{\left(E-P_z\right)} > 45\,{\rm GeV}$, where the sum runs on
the two selected clusters.

From the selected events two event samples are built:
\begin{itemize}
\item {\bf Control sample:}
The photon candidate is demanded to be in the backward calorimeter. 
The electron candidate has to be found in the central part 
of the detector. 
\item {\bf DVCS candidates:}
The photon candidate is requested to be in the central part of 
the detector and the electron candidate in the backward.

\end{itemize}

\section{Control sample}

\begin{figure}
 \begin{center}
  \epsfig{figure=H1prelim-00-017.fig3.eps,width=18cm}
  \caption{Event distributions (uncorrected) of the control sample. 
The data are 
compared to the sum of the prediction for the Bethe--Heitler process, 
elastic dilepton production and diffractive $\rho$ production.
a) energy of the cluster in the Spaghetti calorimeter (backward) , 
b) energy of the cluster in the LAr calorimeter (central), 
c) polar angle of the cluster in the Spaghetti calorimeter, 
d) polar angle of the cluster in the LAr calorimeter, 
e) coplanarity; difference in the azimuthal angle of the two clusters, 
f) ratio of the energy of the cluster and the momentum measured 
   by the tracking detector for the electron candidate.}
  \label{cont}
 \end{center}
\begin{picture}(0,0)
\put(76,198.0){\bf a)}
\put(150,198.0){\bf b)}
\put(26,148.0){\bf c)}
\put(101,148.0){\bf d)}
\put(26,98.0){\bf e)}
\put(101,98.0){\bf f)}
\end{picture}
\end{figure}

This sample is dominated by the Bethe--Heitler process. Due to 
the large scattering angle of the electron the DVCS process is 
highly suppressed and therefore negligible. Two additional 
background sources can give such a configuration in the 
detector. These are the elastic electro--production of 
$\rho$--mesons 
and the elastic production of electron pairs by photon--photon 
processes. 

In the case of the elastic $\rho$ production 
one of the decay pions is faking an 
electron signature in the calorimeter and the other pion is 
leaving the central detector by the beam pipe. The electron 
originating from this process is found to be in the backward 
detector. Its track is not reconstructed due to the limited acceptance 
of the tracking system. In the case of dilepton production a 
Bethe--Heitler configuration can be faked if two of the 
resulting three leptons are detected and the 
third lepton is leaving the main detector through the beam pipe.
These backgrounds have been studied using a Monte Carlo 
simulation of vector mesons\cite{diffvm} and
two lepton processes\cite{grape}. 
Since these backgrounds involve a charged particle in the central 
part of the detector which is detected by the tracking system, 
these background sources only contribute to the control sample and not 
to the sample of DVCS candidates.

In figure \ref{cont} distributions of the control sample 
are shown. The 
data are compared to  MC predictions which 
include the Bethe--Heitler process, the elastic $\rho$ 
production and the elastic dilepton production.
A good description of the 
data by the sum of the different contributions is achieved showing
that they are well understood and also that the detector response 
is well described by the simulation.

\section{DVCS candidates}

\begin{figure}
\begin{center}
\psfig{figure=H1prelim-00-017.fig4.eps,width=18cm}
\end{center}
\caption{Event distributions (uncorrected) for the DVCS candidates. 
a) energy of the cluster in the Spaghetti calorimeter (backward), 
b) energy of the cluster in the LAr calorimeter (central), 
c) polar angle of the cluster in the Spaghetti calorimeter, 
d) polar angle of the cluster in the LAr calorimeter, 
e) coplanarity; difference in the azimuthal angle of the two clusters.
}
\label{sig}
\begin{picture}(0,0)
\put(76,183){\bf a)}
\put(150,183){\bf b)}
\put(26,133){\bf c)}
\put(101,133){\bf d)}
\put(26,83){\bf e)}
\end{picture}
\end{figure}


\begin{figure}
\begin{center}
\psfig{figure=H1prelim-00-017.fig5.eps,width=15.5cm}
\end{center}
\caption{Event distributions (uncorrected) for the DVCS candidates. 
Distributions of the kinematic variables
a) $Q^2$,
b) $W$,
c) $t$ 
and
d) $x$
 are shown.}

\label{sig2}
\begin{picture}(0,0)
\put(73,116){\bf a)}
\put(100,116){\bf b)}
\put(73,65){\bf c)}
\put(100,65){\bf d)}


\end{picture}
\end{figure}





In this sample where the photon candidate is demanded to be in the 
central part of the detector
the DVCS contribution is the dominating part of 
the cross section. In figures \ref{sig} and \ref{sig2} 
distributions are shown 
where the data are compared to predictions which are based on 
the Bethe--Heitler process only. A large excess of events above 
the prediction is observed. 
The data are different in shape and in absolute normalisation 
in comparison to the Bethe--Heitler simulation.
The coplanarity distribution which is the difference 
in azimuthal angle of the two clusters and which is a measure of the 
$p_t$--balance of the electron--photon system is found to be 
much broader than expected for a pure Bethe--Heitler event sample. 
The Bethe--Heitler process is a pure electromagnetic 
interaction and has a very steep $t$ dependence, where t is the square 
of the four--momentum 
transfer at the proton vertex. The momentum 
transfer to the proton is small and the electron--photon system 
is well balanced in $p_t$. Diffractive events have a flatter $t$ 
dependence than the purely electromagnetic Bethe--Heitler process
which leads to a less $p_t$--balanced
electron--photon system. Such an effect leads  directly to a broader 
coplanarity distribution. The measured coplanarity distributions 
is already a hint for the diffractive nature of the underlying process 
for the excess of events which is observed.

\section{Cross section measurement}

The event kinematics was reconstructed using the polar angle 
of the final state electron and photon (double angle method).
The phase space was restricted to the region 
$2 < Q^2 < 20\,{\rm GeV}^2 $, 
$ |t| < 1\,{\rm GeV}^2$ 
and
$30 < W < 120\,{\rm GeV}$. $W$ is the photon proton 
center of mass energy.  

The data have been corrected for detector effects. The proton 
dissociation background has been estimated to be $10\,\%$ 
and subtracted. 
Data have been corrected for initial state radiation of real 
photons from the electron line. The acceptance has been 
determined by a MC calculation to extract the elastic cross section.

The systematic error has been estimated by varying the energy 
scales of the electromagnetic calorimeters and the measured angle.
Additional errors originate from the noise determination of the 
forward detectors, the luminosity measurement and the uncertainty of 
the proton dissociation background. The mean total systematic error is 
around $15\,\%$. 
The main error source is due to the measurement of the 
scattered electron angle.

In figures \ref{bla3} and \ref{bla4} the differential cross sections
as a function of $Q^2$ and $W$ are shown.
The data
are compared with the Bethe--Heitler prediction alone and with 
the full calculation including Bethe--Heitler, DVCS 
and their interference. The description of the data by 
the calculations is good, both in shape and in absolute normalisation.
The uncertainty in the theoretical prediction for the DVCS visible as 
the band for the prediction is 
dominated 
by the unknown slope of the t-dependence of the DVCS part of 
the cross section, assuming $7 < b < 10\, {\rm GeV}^{-2}$.

\begin{figure}[htb]
\begin{center}
\psfig{figure=H1prelim-00-017.fig6.eps,width=10cm}

\caption{The measured cross sections of the reaction 
$e^+ p \longrightarrow e^+ \gamma p$ as a function of
$Q^2$ is shown and compared to theoretical prediction 
(FFS)\cite{ffs}. 
The uncertainty in the theoretical prediction for the DVCS is 
dominated 
by the unknown slope of the t-dependence of the DVCS part of 
the cross section, assuming $7 < b < 10\, {\rm GeV}^{-2}$.
In addition the prediction for the Bethe--Heitler process (BH) 
alone is shown.}

\label{bla3}
\end{center}
\end{figure}

\begin{figure}[htb]
\begin{center}
\psfig{figure=H1prelim-00-017.fig7a.eps,width=10cm}
\psfig{figure=H1prelim-00-017.fig7b.eps,width=10cm}


\caption{The measured cross section of the reaction
$e^+ p \longrightarrow e^+ \gamma p$ as a function of
$W$ is shown and compared to the theoretical prediction
(FFS)\cite{ffs}. The cross section is measured in the kinematic 
ranges a) $4 < Q^2 < 20\,{\rm GeV}^{2}, |t|<1\,{\rm GeV}^{2} $ 
and b) $2 < Q^2 < 20\,{\rm GeV}^{2}, |t|<1\,{\rm GeV}^{2}$.
The uncertainty in the theoretical prediction for the DVCS is 
dominated 
by the unknown slope of the t-dependence of the DVCS part of 
the cross section, assuming $7 < b < 10\, {\rm GeV}^{-2}$.
In addition the prediction for the Bethe--Heitler process (BH) 
alone is shown.
}

\label{bla4}
\end{center}
\begin{picture}(0,0)
\put(111,208){\bf a)}
\put(111,118){\bf b)}
\end{picture}
\end{figure}

\section{Conclusion}

A clear signal of DVCS is observed at HERA.
Cross sections as a function of $Q^2$ and $W$ have been measured 
for the first time. 
The experimental results are well described in shape by LO QCD 
calculations and in normalisation if the $t$ slope is assumed 
to be between $7$ and $10\,{\rm GeV}^{-2}$.

\section*{Acknowledgments}

We would like to thank M. Diehl and A. Freund for valuable
discussions.
We are grateful to the HERA machine group whose outstanding
efforts have made and continue to make this experiment possible.
We thank
the engineers and technicians for their work in constructing and now
maintaining the H1 detector, our funding agencies for
financial support, the
DESY technical staff for continual assistance,
and the DESY directorate for the
hospitality which they extend to the non DESY
members of the collaboration.



\begin{thebibliography}{99}

\bibitem{rad} A.\,V.\,Radyushkin {\em Phys.\,Rev.\,}D\,{\bf 56}, 5524 (1997).

\bibitem{ffs} L.\,L.\,Frankfurt, A.\,Freund, M.\,Strikman 
{\em Phys.\,Rev.\,}D\,{\bf 58}, 114001 (1998) and 
{\em Phys.\,Rev.\,}D\,{\bf 59}, 119901E (1999).

\bibitem{fre} A.\,Freund, {\em Phys.\,Lett.\,}B\,{\bf 472}, 412 (2000).

\bibitem{h1dect} H1 Collaboration, I.\,Abt et al., 
{\em Nucl.\,Instrum.\,Methods\,}A\,{\bf 386} (1997) 310 and 348.

\bibitem{diffvm} B.\,List, Diploma Thesis, Techn.\,Univ.\,Berlin, 
(1993), unpublished.

\bibitem{grape} T.\,Abe et al., in Proc. 
{\em Monte Carlo Generators for HERA physics}, 
Eds.\, A.\,T.\,Doyle, G.\,Grindhammer, G.\,Ingelman, H.\,Jung, 
DESY-PROC-1999-02, p.\,566.

\end{thebibliography}

\end{document}

