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\begin{titlepage}

\noindent
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      Submitted to & & &
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      \multicolumn{4}{l}{{\bf
          International Europhysics Conference 
          on High Energy Physics, EPS03},
        July~17-23,~2003,~Aachen} \\
      (Abstract {\bf 108} & Parallel Session & {\bf 5}) & \\
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          XXI International Symposium on  
          Lepton and Photon Interactions, LP03},
        August~11-16,~2003,~Fermilab} \\ 
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 & \multicolumn{3}{r}{\footnotesize {\it
     www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
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\begin{center}
  \begin{Large}
    {\bf Elastic Photoproduction of \boldmath\Jpsi Mesons at HERA}\\
    \vspace{2cm}
    H1 Collaboration
  \end{Large}
\end{center}
\vspace{2cm}

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\begin{abstract}
  \noindent
  The elastic \Jpsi photoproduction cross section $\sigma(\gamma p\ra\jpsi
  p)$ is measured in the kinematic region $\qsq\les 1\gevsq$,
  $40\gev\les\wgp\les 150\gev$ and $|t|\les 1.2\gevsq$ using the muon decay
  channel. The analysis is based on an integrated luminosity of
  $\mathcal{L}=54.8\pb^{-1}$. Single and double differential cross sections
  are measured as a function of \wgp and $|t|$ and are compared to
  calculations in perturbative QCD.
\end{abstract}

\end{titlepage}

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\section*{Introduction}

\noindent
Elastic photoproduction of \Jpsi mesons has been studied previously by the H1
and ZEUS experiments at HERA \cite{Adloff:2000vm,Chekanov:2002xi}. Here, we
report on a new measurement with increased statistics, which allows a study
of the dependence of the elastic photoproduction cross section as a function
of \wgp, the photon proton centre-of-mass energy, and of $|t|$, the squared
four-momentum transfer at the proton vertex, with increased precision. The
\wgp and $|t|$ dependences of the cross section are analysed single and
double-differentially.

The preliminary results are compared to calculations in perturbative Quantum
Chromodynamics, where the process of diffractive charmonium production in \gp
scattering is described as follows.  An almost real photon, emitted from the
incoming lepton, fluctuates into a $c\bar{c}$ pair.  The $c\bar{c}$ pair
subsequently interacts with the proton via the exchange of two gluons (or a
gluonic ladder) in a colour-singlet state and then evolves into a \Jpsi
meson.

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\section*{Data Analysis}

\noindent
For this analysis, data collected with the H1 detector in the years 1999 and
2000 are used. During this period, HERA collided $27.6\gev$
positrons\footnote{For the first half of the year 1999, HERA collided
  $27.6\gev$ electrons with $920\gev$ protons. Since this measurement is not
  sensitive to the incoming lepton charge, the term `positrons' will be used
  for both electrons and positrons.} with $920\gev$ protons, with an
integrated luminosity of $\mathcal{L}=54.8\pb^{-1}$ are used. The data
selection is very similar to previous H1 analyses
\cite{Adloff:2000vm,Schmidt:2001}.  Photoproduction events are selected by
rejecting events with electromagnetic energy clusters above $8\gev$ in the
Liquid Argon or the Spacal calorimeters.  This restricts the photon
virtuality to $\qsq<1\gevsq$. \Jpsi mesons are reconstructed via their
leptonic decay into muons. The data selection requires exactly two oppositely
charged tracks in the central region\footnote{The coordinate system of H1
  defines the positive $z$ axis to be in the direction of the outgoing proton
  beam. The polar angle $\theta$ is the defined with respect to the positive
  $z$ axis.} $20\deg\le\theta\le 160\deg$, at least one of which is
identified as a muon either as a minimally ionising particle in the liquid
argon calorimeter or as a highly penetrating particle reaching the
instrumented iron surrounding the calorimetry.

In elastic photoproduction of \Jpsi mesons, both the scattered positron and
the scattered proton are not generally detected. The largest contribution to
the background is events in which the proton dissociates. Most of the events
with proton dissociation are rejected by demanding no deposits in the forward
section of the calorimeter ($\theta<10\deg$), the proton remnant tagger
($0.06\deg<\theta<0.26\deg$) and the forward muon detector
($3\deg<\theta<17\deg$).

The resulting mass distribution of the the muon pairs is shown in
fig.\ref{fig:mpeak} for the range $40\gev<\wgp<150\gev$ and $|t|<1.2\gevsq$.
The remaining non-resonant background is dominated by the process
$\gamma\gamma\ra\mup\mum$, where one of the photons originates from the beam
positron and the other from the beam proton. The number of \Jpsi signal
events is obtained for each analysis bin by fitting the invariant mass
distribution with the sum of a Gaussian and a power law distribution to
parameterise the background.\footnote{A second Gaussian distribution is used
  for the \psip signal.} The systematic error on the fits is obtained by
varying the function used to describe the background and also by counting all
events within a mass window of $2.9\gev < M_{\mup\mum}<3.3\gev$ and
subtracting the fitted background.

The resulting number of signal events is corrected for detector acceptance,
efficiency losses and remaining background from proton dissociation using the
Monte Carlo program DIFFVM \cite{diffvm}. It can be used to generate both
elastic and proton dissociative processes. The correction for proton
dissociation has been checked with the data and is typically 15\%.

The efficiency for muon identification and of the triggers are checked and
adjusted to data where necessary using independent data samples. The
remaining differences between data and MC contribute to the systematic error.
The total systematic error is estimated to be 12\%. The dominant error sources
are the determination of the proton dissociative background (5-10\%) and the
trigger efficiencies (6\%).

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\section*{Results}

\noindent
After correcting the observed number of events in each bin for detector
acceptance and efficiencies, the $ep$ cross section is obtained. It is
converted into a \gp cross section assuming factorisation of the $ep$
reaction into emission of photons described by a photon flux and the \gp
interaction.  The cross section for the full range $|t|<1.2\gevsq$ is
presented in fig.\ref{fig:wxsec1} as a function of \wgp.

A combined fit of the form $\sigma\propto\wgp^\delta$ is performed using
separate normalisation factors for this data set and the $\jpsi\rightarrow
e^+ e^-$ data points\footnote{A correction ranging from +10\% to +14\% was
  applied to the six data points above $\wgp\gre 135\!\gev$ as compared to
  \cite{Adloff:2000vm}. In \cite{Adloff:2000vm} the branching ratio for
  $\jpsi\ra e^+ e^-\gamma$ \cite{Caso:1998tx} was erroneously assumed not to
  be included in that for $\jpsi\ra e^+ e^-$.} \cite{Adloff:2000vm} also
shown in the figure.  The fit yields a value\footnote{The statistical and
  systematic errors are added in quadrature.} of $\delta = 0.70\pm0.08$,
which is in agreement with previous measurements \cite{Adloff:2000vm} and the
latest results from the ZEUS collaboration \cite{Chekanov:2002xi}. In
fig.\ref{fig:wxsec2} the same data are shown, this time in comparison with
results from the ZEUS collaboration and QCD based theoretical calculations
\cite{Lai:1997mg,Martin:1998sq,Lai:1999wy,Caldwell:2001ky}, which describe
the steep rise of the cross section qualitatively.

The fit to the \wgp dependence is repeated for bins of $|t|$, which yields an
effective pomeron trajectory via $\delta = 4\cdot(\ap(t)-1)$. The results for
$\ap(t)$ are shown in fig.\ref{fig:alpha} and compared with ZEUS data
\cite{Chekanov:2002xi}. A linear effective trajectory
($\ap(t)=\alpha_0+\ap'\cdot t\gev^{-2}$) is assumed and fitted yielding
$\ap(t) = (1.20\pm0.02)+(0.15\pm0.06)\cdot t \gev^{-2}$. The effect of
shrinkage is observed with a significance of three standard deviations.

In fig.\ref{fig:txsec} the dependence of the photoproduction cross section of
\Jpsi mesons as a function of $|t|$ is studied in the region of
$40\gev<\wgp<150\gev$.  This dependence is measured averaging over the entire
\wgp range.  Assuming an exponential behaviour $e^{-b|t|}$, a fit yields an
elastic slope parameter $b=4.65\pm0.08$. The procedure is repeated in bins of
\wgp and the resulting $b$ values are shown in fig.\ref{fig:bslope}. Here a
fit of the form $b(\wgp)=b_0+4\alpha'\cdot \ln(\wgp/90\gev)$ has been
performed, yielding $b_0=(4.73\pm 0.12)\gev^{-2}$ and
$\alpha'=(0.19\pm0.08)\gev^{-2}$. Both parameters are in good agreement with
those derived from the fits in fig.\ref{fig:alpha} and~\ref{fig:txsec}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgments}

\noindent
We are grateful to the HERA machine group whose outstanding efforts have made
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 support and for the hospitality which
they extend to the non DESY members of the collaboration.

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\bibliographystyle{h-physrev3}
\bibliography{references}

\begin{figure}[p]
  \includegraphics[width=0.9\textwidth,height=\textheight,keepaspectratio]{h1prelim-03-075.fig1.eps}
  \caption{The dimuon mass spectrum after final data selection. The curve shows
    the result of a fit combining two Gaussian distributions for the \Jpsi
    and \psip signals and a power law parametrisation of the non-resonant
    background. The number of events in the signal are extracted in a mass
    window between $2.9\gev$ and $3.3\gev$.}
  \label{fig:mpeak}
\end{figure}

\begin{figure}[p]
    \includegraphics[width=0.9\textwidth,height=\textheight,keepaspectratio]{h1prelim-03-075.fig2.eps}
    \caption{The elastic cross section $\sigma_{\gp}$ as a function of
      \wgp. The inner (outer) bars give the statistical (total) error. The
      data from the process $\jpsi\ra e^+ e^-$ are from \cite{Adloff:2000vm}.
      The fit is applied to the two data sets, allowing different
      normalisation factors for both.}
    \label{fig:wxsec1}
\end{figure}

\begin{figure}[p]

  \includegraphics[width=0.9\textwidth,height=\textheight,keepaspectratio]{h1prelim-03-075.fig3.eps}
  \caption{The elastic cross section $\sigma_{\gp}$ as a function of
    \wgp. The inner (outer) bars give the statistical (total) error. The
    experimental data \cite{Binkley:1982kv,Denby:1984az,Chekanov:2002xi} are
    compared with pQCD models
    \cite{Lai:1997mg,Martin:1998sq,Lai:1999wy,Caldwell:2001ky}.}
    \label{fig:wxsec2}
\end{figure}

\begin{figure}[p]
    \includegraphics[width=0.9\textwidth,height=\textheight,keepaspectratio]{h1prelim-03-075.fig4.eps}
    \caption{The effective pomeron trajectory as a function of
      $|t|$. The inner (outer) bars give the statistical (total) error. A
      linear form is assumed and fitted to the H1 data. The ZEUS data are
      from \cite{Chekanov:2002xi}. Shrinkage is observed with a significance
      of three standard deviations.}
    \label{fig:alpha}
\end{figure}

\begin{figure}[p]
    \includegraphics[width=0.9\textwidth,height=\textheight,keepaspectratio]{h1prelim-03-075.fig5.eps}
    \caption{The differential cross section $d\sigma/dt$ as a function of
      $|t|$. The inner (outer) bars give the statistical (total) error. The
      result of a fit of the form $d\sigma/dt\propto e^{bt}$ in the range
      $0.07\gev^2 < |t| < 1.2\gev^2$ is shown as the solid line.}
    \label{fig:txsec}
\end{figure}

\begin{figure}[p]
    \includegraphics[width=0.9\textwidth,height=\textheight,keepaspectratio]{h1prelim-03-075.fig6.eps}
    \caption{The slope parameter $b$ derived from a fit to the differential
      cross section $d\sigma/dt\propto e^{bt}$ as a function of \wgp together
      with the ZEUS data \cite{Chekanov:2002xi}. The inner (outer) bars give
      the statistical (total) error. The result of a fit of the form
      $b(\wgp)=b_0+4\alpha'\cdot \ln(\wgp/90\gev)$ in the range
      $40\gev<\wgp<150\gev$ is shown as the solid line.}
    \label{fig:bslope}
  \end{figure}

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