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\pagestyle{empty}
\begin{titlepage}

\noindent
Submitted to the 30th International Conference on 
High Energy Physics ICHEP2000, \\
Osaka, Japan, July 2000

\vspace*{3cm}

\begin{center}
  \begin{Large}

  {\bf 
  Inelastic Photoproduction of \boldJPSI Mesons at low {\boldmath $z$}}

  \vspace*{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{2cm}

\begin{abstract}
\noindent
A measurement of the inelastic \JPSI photoproduction cross section for
$z<0.45$ via the decay $\JPSI \rightarrow \mu^+ \mu^-$ is presented. 
In this domain, the contribution of resolved photon processes is
expected to dominate. 
The photoproduction cross section is measured as a function of 
$W_{\gamma p}$ and differential cross sections are extracted as functions of 
$p_{t,\psi}^2$ and $z$. The kinematic region covered 
is $Q^{2} < 1$~GeV$^{2}$, $130<W_{\gamma p}<250$~GeV and 
$p_{t,\psi}^2>1$~GeV$^{2}$. A QCD calculation involving colour singlet and 
colour octet contributions is compared with the measurements.
\end{abstract}

\vspace{1.5cm}

\begin{flushleft}
 {\bf Abstract: 988, 989 } \\
 {\bf Parallel sessions: 3, 7 } \\
 {\bf Plenary talks:  11, 3 } \\ 
\end{flushleft}

\end{titlepage}

%\newpage
\pagestyle{plain}

\section*{Introduction}
The inelastic production of \JPSI mesons at HERA, $ep\rightarrow e\JPSI X$, 
is dominated by photon
gluon fusion. Calculations for the direct process in the colour singlet 
model~\cite{csm} are available in next to leading order
(NLO)~\cite{kraemer} 
and are found to describe the data well in an intermediate $z$-region: 
$0.3<z<0.9$. On the basis of results from CDF, large additional colour
octet contributions were predicted for the highest 
values of $z$, the energy of the \JPSI meson relative to the exchanged
photon in the proton rest system.
Such contributions could not be confirmed 
experimentally at HERA~\cite{jpsipho,zeusjpsi}.  
Since these predictions were based on the theoretically very 
attractive non--relativistic QCD approach, many subsequent theoretical 
investigations have tried
to find a reason for this discrepancy\footnote{For an overview see
e.g. ref.~\cite{beneke}}. Discussions have included
smaller octet matrix elements~\cite{kniehl},
transverse momentum effects~\cite{sridhar} or resummations of higher
orders leading to shape functions~\cite{beneke}. Alternatively,
solutions 
without any colour octet contributions have been proposed~\cite{hagler}.\\ 
\\ 
\noindent
The present analysis addresses lower $z$ values\footnote{Strictly 
speaking $z=0$ is not accessible; the kinematical limit for $z$ is of the order
of $10^{-3}$.}: $0<z<0.45$, where
significant contributions from resolved photon processes are 
expected. This region is interesting in view of the large contributions from 
colour octet processes expected in this domain~\cite{kniehl,kraemer_co}.
Due to the limited acceptance of the H1 tracking detectors the analysis of 
\JPSI mesons at lower $z$ values implies a shifted region of the photon proton center
of mass energy $W_{\gamma p}$: $130<W_{\gamma p}<250\,$GeV.
%
\section*{Data Analysis and Results}
Data collected with the H1 detector in 1996 and 1997, when HERA collided 
27.6 GeV positrons with 820 GeV
protons, with an integrated luminosity of ${\cal L} = 24.1$~pb$^{-1}$ are used 
for this analysis. The data selection proceeds in close analogy to previous H1 
analyses~\cite{jpsipho}. 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 decays into
muons in the central tracking chambers of the H1 detector (polar angles 
$20^{\degree} \leq \theta \leq 140^{\degree}$)\footnote{The coordinate 
system of H1 defines the positive $z$ axis to be in the direction of the
incident proton beam. The polar angle $\theta$ is then defined with respect to
the positive $z$ axis.}. Both tracks have to be 
identified as muons, at least one of them in the muon detector and the other 
one either in the liquid argon calorimeter of the H1 detector or in the muon 
detector. Inelastic \JPSI events are selected by requiring in addition to the 
decay leptons at least one more charged particle originating from the 
interaction vertex.
In addition, the inelasticity $z$ of the \JPSI meson is used. It is 
defined as $z=\frac{P_p \cdot P_{\psi}}{P_p \cdot q}$
where $P_p$, $P_{\psi}$ and $q$ are the four vectors of the proton, 
the \JPSI meson and the photon.\\
\\
\noindent
The resulting mass distribution of the muon pairs in the range 
$z<0.45$, $130<W_{\gamma p}<250$~GeV and $p_{t,\psi}^2>1$~GeV$^{2}$ is shown 
in figure~\ref{masspeak}. The unlike sign muon pairs are fitted
with the sum of a Gauss distribution and a linear function to parametrize 
the background.
The number of \JPSI signal events is obtained for each analysis bin by
repeating this fit,  
counting the number of muon pairs in the mass window 
$2.9 < M_{\mu \mu} < 3.3$~GeV, and
subtracting the non--resonant background obtained from the linear fit.
%
\begin{figure}[ht]
\begin{center}
\unitlength1.0cm
\begin{picture}(10,10)
\put(0,0){\epsfig{file=H1prelim-00-072.fig1.eps,width=10cm}}
\end{picture}
\caption{Mass distribution of the selected muon pairs in the range 
$z<0.45$, $130<W_{\gamma p}<250$~GeV and $p_{t,\psi}^2>1$~GeV$^{2}$.
The unlike sign muon pairs are fitted with the sum of a Gauss 
distribution and a linear function to parametrize 
the background.}
\label{masspeak}
\end{center}
\end{figure}
\\
The measurement of the cross section proceeds as in ref.~\cite{jpsipho}. 
After correcting the observed number of events for detector acceptance  
and efficiencies, the $ep$ cross section is obtained. It is converted into a 
$\gamma p$ cross section assuming factorisation of 
the $ep$ reaction into emission of photons described by 
a photon flux and the $\gamma p$ interaction.\\
\\
\noindent
The correction of the data is performed using the Monte Carlo program 
EPJPSI\footnote{The following parameters 
were used: $\alpha_s=0.3$, \JPSI wave function calculated from the measured 
leptonic decay width $\Gamma_{ee}$ including QCD corrections, MRSA'~\cite{mrsa}
for the gluon density in the proton, GRV-LO~\cite{grvg} for the photon, 
the scale in both cases is $M_{J/\psi}^2$.}~\cite{epjpsi}, generating both 
direct and resolved 
processes. The resolved process is dominated by gluon gluon fusion; 
quark initiated processes are neglected as are contributions from cascade 
decays via $\chi_c$ states. For the direct boson gluon fusion process
the $p_{t,\psi}^2$ distribution is reweighted according to an exponential 
which was determined from the data for $0.3<z<0.9$, 
$p_{t,\psi}^2 > 1\gevsq$ and $60<W_{\gamma p}<180\,$GeV. In this kinematic 
region,
the normalization factor of the direct boson gluon fusion MC is determined.
The resolved part is 
added to match the total number of \JPSI mesons for $z<0.45$.\\ 
\\
\noindent
All efficiencies are determined using this Monte Carlo mixture. The efficiency 
of the lepton identification
and the trigger was checked and adjusted to data using independent
subtriggers. The remaining differences between data and MC are used as 
systematic errors.
The background, originating from proton dissociative production of \JPSI and 
\PSIP\ and from the decays of $B$ mesons, is found to be negligible.
The total systematic error is of the order of $20\%$.
In the lowest $z$ bin, where the background is highest, the
error was enlarged to cover possible fluctuations.\\
\\
\noindent
The cross sections are presented in figure~\ref{plot} as functions 
of $W_{\gamma p}$, $p_{t,\psi}^{2}$ and $z$.
For comparison the prediction of the colour singlet model, as calculated in 
leading order in the Monte Carlo generator EPJPSI in the corresponding
ditributions, is shown. 
The $W_{\gamma p}$ distribution~(fig.~\ref{plot}a) shows that, with a 
$k$-factor of 2, the direct boson gluon fusion MC still lies below the data. The
difference can be explained by resolved processes which mainly contribute at
$z<0.15$~(fig.~\ref{plot}c). The dependence of the cross section on 
$p_{t,\psi}^{2}$ (fig.~\ref{plot}b) agrees within errors with 
the power law obtained from the medium $z$ data (see insert).
In fig.~\ref{plot}d the $z$ dependence is compared with a theoretical 
calculation~\cite{kniehl}
including colour singlet (CSM) and colour octet (COM) contributions and taking 
into account higher order corrections approximately for the colour octet matrix 
elements. 
A $k$-factor of 3 as suggested by the authors was applied. Within errors the
data are compatible with the sum of the terms as well as with the colour singlet
contribution alone.\\
%
\begin{figure}[ht]
\begin{center}
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\put(-0.2,8.5){\epsfig{file=H1prelim-00-072.fig2a.eps,width=8.5cm}}
\put(8.3,8.5){\epsfig{file=H1prelim-00-072.fig2b.eps,width=8.5cm,clip=}}
\put(-0.2,0){\epsfig{file=H1prelim-00-072.fig2c.eps,width=8.5cm,clip=}}
\put(8.3,0){\epsfig{file=H1prelim-00-072.fig2d.eps,width=8.5cm,clip=}}
\put(11.9,5.73){\sf $\Bigg\}$ }
\put(6.9,16.4){\small \sf a) }
\put(15.2,16.4){\small \sf b) }
\put(6.9,7.9){\small \sf c) }
\put(15.2,7.9){\small \sf d) }
\end{picture}
\caption{a) Total photoproduction cross section for inelastic \JPSI 
production for $z<0.45$ and $p_{t,\psi}^2>1\gevsq$. The inner error bars are
statistical, the outer include statistical and systematic uncertainties added 
in quadrature. The histograms represent results from the LO Monte Carlo program
EPJPSI (a $k$-factor of 2 was applied to all distributions).
b) Differential cross section
${\rm d}\sigma_{\gamma p}/{\rm d}p_{t,\psi}^2$ with $z<0.45$ 
integrated over $130< W <250\gev$. For comparison a fit to the
distribution in the range $0.3<z<0.9$ (see insert) is shown.
c) ${\rm d}\sigma_{\gamma p}/{\rm d}z$ with a cut $p_{t,\psi}^2> 1\gevsq$.
d) ${\rm d}\sigma_{\gamma p}/{\rm d}z$ compared with a theoretical 
prediction~\cite{kniehl}  
including colour singlet (CSM) and colour octet (COM) contributions and taking 
into account higher order corrections approximately for the colour octet matrix 
elements. A $k$-factor of 3 as suggested by the authors was applied.}
\label{plot}
\end{center}
\end{figure}
%
\section*{Conclusion}
Photoproduction of \JPSI\ mesons has been measured in extremely inelastic
events: $z<0.45$. The measured cross section is larger than the contribution
expected from direct processes alone. The data can however be explained by
contributions from resolved and direct processes. Experimental and
theoretical uncertainties do not yet allow a firm conclusion concerning the 
presence of colour octet contributions.
%
\section*{Acknowledgements}
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{csm} 
E.L. Berger, D. Jones, \Journal{\PRD}{23}{1981}{1521}\\
R. Baier, R. R\"uckl, \Journal{\NPB}{201}{1982}{1}
\bibitem{kraemer}
M.~Kr\"amer, \Journal{\NPB}{459}{1996}{3}
\bibitem{jpsipho}
H1 Collaboration, S.~Aid et. al., \Journal{\NPB}{472}{1996}{3}\\
H1 Collaboration, C.~Adloff et. al., {\em 
Inelastic Photoproduction of \JPSI\ and \PSIP}, contributed paper 157aj to
EPS99, Tampere 
\bibitem{zeusjpsi} ZEUS Collaboration, J.~Breitweg et al., {\em Measurement of 
Inelastic $J/\psi$ Photoproduction at HERA}, contributed paper 814 to ICHEP98, 
Vancouver 
\bibitem{beneke}
M.~Beneke, G.A.~Schuler, S.~Wolf, \Journal{\PRD}{62}{2000}{034004}
\bibitem{kniehl} 
B.~Kniehl and G.~Kramer, \Journal{\EJC}{6}{1999}{493} 
\bibitem{sridhar}
K.~Sridhar, A.D.~Martin, W.J.~Sterling, \Journal{\PLB}{438}{1998}{211}
\bibitem{hagler} 
P.~Hagler, R.~Kirschner, A.~Schafer, L.~Szymanowski, O.~V.~Teryaev,
hep-ph/0004263
\bibitem{kraemer_co}
M. Beneke, M. Kr\"amer, M. V\"anttinen, \Journal{\PRD}{57}{1998}{4258}
\bibitem{epjpsi} 
H.~Jung, 'Monte Carlo Generator EPJPSI for \JPSI\ mesons in high energy 
$\gamma p$, $ep$, $\mu p$, $p \bar{p}$ and $pp$ collisions',
http://www-h1.desy.de/\~ \protect{jung}/epjpsi.html;\\
Proceedings 'Physics at HERA', Eds. W.~Buchm\"uller, G.~Ingelman, 1488 (1991)
\bibitem{mrsa} A.D.~Martin, R.G.~Roberts, W.J.~Stirling,
\Journal{\PLB}{354}{1995}{155}
\bibitem{grvg} 
M. Gl\"uck, E. Reya, A. Vogt, \Journal{\PRD}{46}{1992}{1973},
\Journal{\PRD}{45}{1992}{3986}
\end{thebibliography}

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