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%
%========================================================================%
%################################################## titlepage declaration
%
\begin{titlepage}
\pagenumbering{arabic}
\vspace*{-1.5cm}
\begin{tabular*}{15.cm}{lc@{\extracolsep{\fill}}r}
{\bf DELPHI Collaboration} &
\hspace*{1.3cm} \epsfig{figure=/afs/cern.ch/user/d/delnote/tex/dolphin_bw.eps,
width=1.2cm,height=1.2cm}
&
%===================> DELPHI note number =====> To be filled <=====%
DELPHI 2001-000
%========================================================================%
\\
& &
%===================> DELPHI note date =====> To be filled <=====%
%5 February 2001
\today
%========================================================================%
\\
&&\\ \hline
\end{tabular*}
\vspace*{2.cm}
\begin{center}
\Large
{\bf \boldmath
%0
%===================> DELPHI note title =====> To be filled <=====%
\rightline{\Large\bf\fbox{DRAFT \#3}}
\vskip24mm
Inclusive \jpsi\ Production \\
in Two-Photon Collisions at LEP
%========================================================================%
}
\vskip23mm
\normalsize {
%===================> DELPHI note author list =====> To be filled <=====%
{\bf M. Chapkin, S.-U. Chung, P. Gavillet,\\
V. Obraztsov, D. Ryabchikov, A. Sokolov, S. Todorovova}\\
%========================================================================%
}
%\vspace*{2.cm}
\end{center}
\vspace{\fill}
\begin{abstract}
\noindent
%===================> DELPHI note abstract =====> To be filled <=====%
Inclusive \jpsi\ production
in photon-photon collisions has been
observed by the DELPHI collaboration at LEP II beam energies.
A clean signal
from the reaction $\gamma\gamma\to\jpsi+X$ is seen.
The number of observed events $N(\jpsi\rightarrow \mu^+\mu^-)$
is $36\pm7$ for the integrated luminosity of
617 pb$^{-1}$\kern-0.9em,\kern+0.9em yielding a cross section
of $\sigma(\jpsi+X)=45.3\pm18.4$ pb.
Based on a study of the event shapes of different types of $\gamma\gamma$
processes in the PYTHIA program, we conclude that
$(74\pm22)$\% of the observed \jpsi\ events are due to the
`resolved' photons, the dominant contribution of which is evidently
a single color-octet gluon within the photon.
%
%=========================================================================%
\end{abstract}
\vspace{\fill}
\begin{center}
%==========> Proceedings.. presented at ..==> To be filled if needed<=====%
Submitted to Summer Conferences of 2001
%=========================================================================%
\end{center}
\vspace{\fill}
\end{titlepage}
%##################################################################### Text
%==================> DELPHI note text =====> To be filled <======%
%1
\section{Introduction}
An important component of the $e^+e^-$ collisions at LEP II energies
is the two-photon fusion process.
It has been pointed out that two-photon production of inclusive \jpsi's
\bln{jpse}
e^++e^-\to e^++e^-+\gamma_{_1}+\gamma_{_2}
\eln
followed by
\bln{jps0}
\gamma_{_1}+\gamma_{_2}\to\jpsi+X
\eln
is a sensitive channel for investigating
the gluon distribution in the photon~\cite{LEP2}.
There are two important processes leading to inclusive \jpsi\ production.
The corresponding typical diagrams are given in Figs.~\ref{fg01}
and \ref{fg02}. Less important diagrams are not considered here.
Our motivation is to illustrate two major categories of
diagrams which are used to fit the observed $p_{_T}^2(\jpsi)$
distribution in our data.
The first process is undoubtedly attributable to
the vector-meson dominance (VMD) model~\cite{VDM}
\bln{rc1}
\gamma_{_1}\to c+\bar c,
\qquad\gamma_{_2}\to q+\bar q
\qquad{\rm and}\qquad\gamma_{_1}+\gamma_{_2}\to\jpsi+q+\bar q
\eln
as shown in Fig.~\ref{fg01}. The vertices for $\gamma_{_1}$ and
$\gamma_{_2}$ are connected by Pomeron exchange or diffractive
dissociation of photons. The final-state parton pairs $c+\bar c$ and
$q+\bar q$ are both in the state of $J^{PC}=1^{--}$, which means
that the latter is dominated by the low-mass vector mesons $\rho^0$,
$\omega$ and $\phi$ but a more general inclusive hadronization of the
partons may also be important.
%f1
\begin{figure}[ht]\vskip12mm
\begin{center}\strut\hskip6mm
\mbox{\epsfig{file=vdm0.eps,width=8cm}}
\end{center}
\vskip 3mm
\caption{Inclusive \jpsi\ production in $\gamma\gamma$ processes
through vector-meson dominance.}
\label{fg01}
\vskip8mm\end{figure}
\noindent
The second process is due to the color-octet model~\cite{CSM}.
It proceeds through the so-called `resolved' contribution of the
photons, in which the intermediate photons are `resolved' into
their constituent partons.
\bln{rc2}
\gamma_{_1}+g_{_\gamma}\to c+\bar c,\qquad
\gamma_{_2}+g_{_\gamma}\to q+\bar q,\qquad{\rm and}\qquad
\gamma_{_1}+\gamma_{_2}\to\jpsi+q+\bar q
\eln
as shown in Fig.~\ref{fg02}.
%f2
\begin{figure}[ht]\vskip12mm
\begin{center}\strut\hskip6mm
\mbox{\epsfig{file=oct0.eps,width=8cm}}
\end{center}
\vskip 3mm
\caption{Inclusive \jpsi\ production in $\gamma\gamma$ processes
via gluon content of the photon, i.e. `resolved' contributions.
Presence of additional soft gluon(s) is required for color
neutralization.}
\label{fg02}
\vskip8mm\end{figure}\noindent
It is seen that this process requires
production of a `resolved' gluon ($g_{_\gamma}$) from both photons.
Thus, this production mechanism provides a sensitive probe of
the gluon content of the photon.
The purpose of this letter is to report observation of inclusive
\jpsi\ production from the two-photon fusion process; to give
its production characteristics along with the cross section; and finally
to assess the relative importance of the
production processes discussed above.
%2
\section{Experimental Procedure}
The analysis presented here is based on the data taken with the DELPHI
detector~\cite{DELPHI1,DELPHI2} during the years 1996--2000 for which
$\sqrt{s}$ for LEP ranged from 161 to 207 \gevcc,
excluding the part of the data collected in the last period of 2000
when one of the TPC sectors was not in operation.
The total integrated luminosity
used in the analysis is 617 pb$^{-1}$\kern-0.84em.
%The energies of ${e}^+{e}^-$ collisions,
%and the corresponding integrated luminosities $L$
%are presented in the Table I.
%%t1
%\vskip5mm
%\def\arraystretch{1.5}
%\begin{table}[ht]
%\begin{center}
%\tbhead{I}{DELPHI Data Sample for LEP II}
%\begin{tabular}{|c|c|c|c|c|c|c|}
% \hline\hline
% Year & 1996 & 1997 & 1998 & 1999 & 2000 & $\Sigma$ \\
% \hline
% $\sqrt{s}$, \gevcc & 161 -- 172 & 183 & 189 & 192 -- 204 & 207 & \\
% \hline
% $\int L\,{\rm d}t \,( {\rm pb}^{-1}\,)$
% & 20.4 & 54.1 & 157.6 & 226.3 & 235.6 & 694.0 \\
% \hline\hline
%\end{tabular}
%\end{center}
%\end{table}
%\def\arraystretch{1.0}
%\vskip5mm
The charged particle tracks were measured in the 1.2--T magnetic field by a
set of tracking detectors including the TPC and the forward/backward chambers
FCA and FCB. The following criteria were applied:
\begin{list}{}{\setlength{\leftmargin}{42pt}
\setlength{\topsep}{0pt}
\setlength{\itemsep}{0pt}
\setlength{\parsep}{0pt}}
\item[($a$)] particle momentum $p \ >$ 200 \mevc;
\item[($b$)] relative error of a track momentum $\Delta p/p \ <$ 100\%;
\item[($c$)] impact parameter of a track, transverse to the beam axis
$\Delta_{xy} \ <$ 3 cm;
\item[($d$)] impact parameter of a track, along the beam axis
$\Delta_{z} \ <$ 7 cm;
\item[($e$)] polar angle of a track, with respect to the beam axis
$10^{\circ} < \theta < 170^{\circ}$;
\item[($f$)] track length $\ell \ >$ 30 cm.
\end{list}
The neutral particles ($\gamma$, $\pi^0$, ${K}^0_{_L}$, $n$)
were selected by demanding that the calorimetric
information, not associated with charged particle tracks,
satisfy the following cuts:
\begin{list}{}{\setlength{\leftmargin}{42pt}
\setlength{\topsep}{0pt}
\setlength{\itemsep}{0pt}
\setlength{\parsep}{0pt}}
\item[($g$)] $E(\rm neutral)>0.2$ GeV for the electromagnetic showers
unambiguously identified as photons;
\item[($h$)] $E(\rm neutral)>0.5$ GeV for all the other showers;
\item[($i$)] polar angle of a neutral track, with respect to the beam axis
$10^{\circ} < \theta < 170^{\circ}$.
\end{list}
In order to ensure a very high trigger efficiency,
the selected events were required to satisfy at least
{\em one} of a set of the four following criteria:
\begin{list}{}{\setlength{\leftmargin}{42pt}
\setlength{\topsep}{0pt}
\setlength{\itemsep}{0pt}
\setlength{\parsep}{0pt}}
\item[($j_1$)] one or more charged tracks in the barrel region
($40^{\circ} < \theta < 140^{\circ}$) with $p_{t}>1.2\,\gevc$,
is found;
\item[($j_2$)] one or more neutral tracks in the the Forward Electromagnetic
Calorimeter (FEMC) ( $10^{\circ} < \theta < 36^{\circ}$ and
$144^{\circ} < \theta < 170^{\circ}$)
with energy greater than 10 GeV\kern-0.1em, \kern+0.1em is found;
\item[($j_3$)] the sum of the number of charged tracks in barrel
with $p_{t} > 1\,\gevc$ and charged tracks in forward region
($10^{\circ} < \theta < 40^{\circ}$ or
$140^{\circ} < \theta < 170^{\circ}$)
with $p_{t} > 2\,\gevc$ and neutrals in the forward electromagnetic
calorimeter (FEMC) with $E > 7$ GeV is greater than one;
\item[($j_4$)] the sum of the number of charged tracks
in barrel with $p_{t}>0.5 \,\gevc$
and charged tracks in forward with $p_{t} > 1\,\gevc$ and
neutral tracks in FEMC with $E > 5$ GeV is greater than four.
\end{list}
The trigger efficiency for the events which passed
the above requirements is bigger than 98\%.
The hadronic two-photon events are characterized by low track multiplicity
and low visible invariant mass.
Consequently, the following additional cuts were applied:
\begin{list}{}{\setlength{\leftmargin}{42pt}
\setlength{\topsep}{0pt}
\setlength{\itemsep}{0pt}
\setlength{\parsep}{0pt}}
\item[($k$)] the visible invariant mass, $W_{\rm vis}$,
calculated from the four-momentum vectors of the
measured charged and neutral tracks, is less than 35 \gevcc;
\item[($l$)] the number of charged tracks $N$ satisfies
$4 \ \leq \ N_{\rm ch} \ \leq \ 30$;
\item[($m$)] the sum of the transverse energy components with respect
to the beam direction for all charged
particles ($\sum{E^{\rm vis}_{_T}}$) is greater than 3 GeV.
\end{list}
The comparison of the $W_{\rm vis}$ distributions---after
the cuts $N_{\rm ch} \geq 4$ and
$\sum{E^{\rm vis}_{_T}} > 3$ \gevcc---both for the data and
the events simulated by PYTHIA
(Fig.~\ref{fg04}) shows that the cut
$W_{\rm vis} \ \leq$ 35 \gevcc\
rejects major part of the non-two-photon events.
%f3
\begin{figure}[ht]\vskip12mm
\begin{center}\mbox{
\epsfig{file=wvis.eps,width=10cm}
}\end{center}
\vskip 3mm
\caption{$W_{\rm vis}$ distributions for the data
and for the simulated $\gamma\gamma\rightarrow \ {\rm hadrons}$,
${e}^+{e}^-\rightarrow {Z}^0 \gamma$,
${e}^+{e}^-\rightarrow {W}^+ {W}^-$ and
the sum of all above Monte-Carlo contributions}
\label{fg04}
\vskip8mm
\end{figure}
A total of 274 510 events
remain in the data sample after applying all these cuts.
The main background comes from the process
${e}^+{e}^-\rightarrow {Z}^0 \gamma$
and amounts to $\sim$1.2\% of the selected $\gamma\gamma$ events.
The backgrounds from the ${e}^+{e}^-\rightarrow {W}^+{W}^-$ and
other processes are negligible, as seen in Fig.~\ref{fg04}.
J/$\psi$ candidates have been selected
using the $\mu^+\mu^-$ decay channel.
For the muon selection the following criteria were imposed:
\begin{list}{}{\setlength{\leftmargin}{42pt}
\setlength{\topsep}{0pt}
\setlength{\itemsep}{0pt}
\setlength{\parsep}{0pt}}
\item[($n$)] the track should satisfy the standard DELPHI
muon-tagging algorithm~\cite{DELPHI2}
or be identified as a muon by the hadronic calorimeter~\cite{ECTANA};
\item[($o$)] the track should not come from any reconstructed secondary vertex
or be identified as a kaon, proton or electron by standard DELPHI
identification packages;
\item[($p$)] at least two charged particles with zero net charge
should be identified as muons.
\end{list}
%3
\section{Inclusive \jpsi\ Production}
We give in Fig.~\ref{fg05} the invariant mass distribution for $\mu^+\mu^-$
from the DELPHI data selected as outlined in the previous section.
It is seen that the \jpsi\ is produced over little background.
A fit to the $M(\mu^+\mu^-)$ distribution with a Gaussian
for the signal and a polynomial for the background
gives the following results:
\vskip8pt\begin{center}\begin{tabular}{lc@{$\ =\ $}r@{$\pm$}ll}
\jpsi\ mass:&$M$&3119&8&\mevcc\\
\jpsi\ width:&$\Gamma({\rm obs})$&35&7&\mevcc
\end{tabular}\end{center}\vskip8pt
%f4
\begin{figure}[ht]\vskip2mm
\begin{center}\mbox{
\epsfig{file=jpsi.eps,width=8.0cm}
}\end{center}
\vskip 3mm
\caption{$M(\mu^+\mu^-)$ distribution from the DELPHI data.
The solid curve corresponds to a Gaussian fit over a polynomial
backgraound.}
\label{fg05}
\vskip2mm
\end{figure}
The observed width of the peak is consistent within error with
the invariant mass resolution of the pair of charged tracks in the
mass region around 3\,\gevcc. The number of observed events
is $N(\jpsi)=36\pm7$ from the fit. If we take the L3 result\cite{L3} on beauty
cross section from $\gamma\gamma$ events and the PDG value\cite{PDG}
for the branching ratio of beauty hadrons to \jpsi, the expected number of
$\jpsi\to\mu^+\mu^-$ from beauty hadrons is $2.1\pm0.6$. The backgrounds
from the processes $\gamma+\gamma\to Z+\gamma\to\jpsi+X$ and
$\gamma+\gamma\to \chi_{c2}\to\jpsi+\pi^++\pi^-+\pi^0$ are less than
0.20 and 0.30, respectively.
For efficiency estimation we used the PYTHIA 6156 generator~\cite{PYTHIA}.
The generated events were passed through the simulation package of
the DELPHI detector~\cite{DELSIM} and then processed with the same
reconstruction and analysis programs as the real data.
There is a substantial fraction of PYTHIA events where $\jpsi$'s are produced
just as a simple fusion of two photons because there is not enough
phase space to produce additional particles. We checked that all such
events are produced when both the colliding photons are direct or
one photon is anomalous and the other one is DIS (we use here the
PYTHIA notation, for the details see~\cite{PYTHIA}). That is why
for the efficiency estimation we did not use the events with
direct-direct or DIS-anomalous photons. Among the rest of the PYTHIA
events about 93\% of the $\jpsi$'s are produced when at least one photon
is a VDM photon.
Fig.~\ref{fg06a} shows the $p_{_T}^2(\jpsi)$ distribution.
%f5
\begin{figure}[ht]\vskip-6mm
\begin{center}
\mbox{\epsfig{file=spectr.eps,width=8.0cm}}
\end{center}
\vskip-3mm
\caption{
$p_{_T}^2(\jpsi)$ distribution from the DELPHI data, shown as
points with error bars. The histogram is a composite of the renormalized
`resolved' and `diffractive' processes from PYTHIA (see text).}
\label{fg06a}
\end{figure}
As expected, the PYTHIA prediction for
the $p_{_T}^2(\jpsi)$ distribution is sharply peaked
near zero for the diffractive MC events (see Fig.\ref{fg01}),
while the `resolved' MC events (see Fig.\ref{fg02})
are very much spread out. We fitted the experimental $p_{_T}^2(\jpsi)$
distribution as a function of the two categories of MC events
\bln{pta}
{{\rm d}N\over{\rm d}p_{_T}^2}%\Biggm\vert
=f\cdot\left.{{\rm d}N\over{\rm d}p_{_T}^2}\right|_{\rm Diffractive}
+(1-f)\cdot\left.{{\rm d}N\over{\rm d}p_{_T}^2}\right|_{\rm Resolved}
\eln
which gives $f=(26.0\pm22.0)\%$. The PYTHIA study tells us that
the experimental efficiencies are very different for the two
categories:
\bln{ptb}
\epsilon({\rm diffractive})&=(0.94\pm0.04)\%\cr
\epsilon({\rm resolved})&=(3.87\pm0.09)\%
\eln
According to PYTHIA, about one-half of all the $\gamma\gamma$ events with
$\psi\to\mu^+\mu^-$ are produced with the charged tracks at polar
angles below 10 degrees, so that they are `invisible to the DELPHI detector.
The individual efficiencies as a function of $p_{_T}^2$ are given
in Fig.~\ref{fg06}. One gains some insight into these efficiencies,
if they are broken down into products of two factors, as follows:
\bln{ptc}
\epsilon({\rm diffractive})
&=\epsilon_{\gamma\,\gamma}({\rm diffractive})
\times\epsilon_{\jpsi\to\mu^+\mu^-}({\rm diffractive})\cr
\epsilon({\rm resolved})
&=\epsilon_{\gamma\,\gamma}({\rm resolved})
\times\epsilon_{\jpsi\to\mu^+\mu^-}({\rm resolved})
\eln
where $\epsilon_{\gamma\,\gamma}$ is the efficiency for
the process $\gamma\,\gamma\to\jpsi+X$ and $\epsilon_{\jpsi\to\mu^+\mu^-}$
is that for $\jpsi\to\mu^+\mu^-$. As expected, the latter is relatively
process-independent
\bln{ptd}
\epsilon_{\jpsi\to\mu^+\mu^-}({\rm diffractive})
&=(37.0\pm1.5)\%\cr
\epsilon_{\jpsi\to\mu^+\mu^-}({\rm resolved})
&=(32.1\pm0.7)\%
\eln
It is clear, therefore, that the difference in efficiency in \eqn{ptb}
is mostly due to $\epsilon_{\gamma\,\gamma}$---this is highly
process-dependent and hence model-dependent.
The overall experimental efficiency is
\bln{ef0}
{1\over\epsilon}={f\over\epsilon({\rm diffractive})}
+{1-f\over\epsilon({\rm resolved})}
\quad \cases{00,\ \epsilon({\rm resolved})>0}
\eln
which gives $\epsilon=(3.93\pmth{}{2.18}{1.03})$\%.
%f6
\begin{figure}[ht]\vskip-6mm
\begin{center}
\mbox{\epsfig{file=eff.eps,width=8.0cm}}
\end{center}
\vskip-3mm
\caption{
Efficiencies for resolved and diffractive processes
as functions of $p_{_T}^2$.
}
\label{fg06}
\end{figure}
Under the assumption that PYTHIA captures the kinematical
features of the resolved and diffractive processes---but not
their absolute cross sections---the cross section
for inclusive $\jpsi$ production is
\bln{sg0}
\sigma=N(\psi)\cdot(Br\cdot {\cal L}\cdot\epsilon)^{-1}
= 45.3\pm18.4\ {\rm pb}
\eln
where $Br=(5.88\pm0.10)\%$ is the branching ratio
for $\jpsi\to\mu^+\mu^-$~\cite{PDG} and
${\cal L}=617\,{\rm pb}^{-1}$ is the total integrated luminosity.
The quoted error reflects only that associated with the visible
part of the spectra; in particular, it does not include the
uncertainties inherent in the PYTHIA program.
Because of the model-dependent aspect of this analysis
(see, for example, the efficiencies given in \eqn{ptb}),
it may be of interest to quote the `visible' cross section.
Substituting $\epsilon_{\jpsi\to\mu^+\mu^-}({\rm diffractive})$
and $\epsilon_{\jpsi\to\mu^+\mu^-}({\rm resolved})$ for
$\epsilon({\rm diffractive})$ and
$\epsilon({\rm resolved})$---respectively---in \eqn{ef0},
the `visible' cross section can be calculated;
it is
\bln{sg1}
\sigma_{\rm vis}=2.98\pm0.58\ {\rm pb}
\eln
Following the same line of philosophy,
we also give the `visible' production rate $\bra n\ket$
for $\jpsi$ production
\bln{rt0}
\bra n\ket
=N(\psi)\cdot
\left(N_t\cdot Br\cdot\epsilon_{\jpsi\to\mu^+\mu^-}\right)^{-1}
=(6.7\pm1.3)\times10^{-3}
\eln
where $N_t$ is the data sample for the $\gamma\gamma$ selection
as given in the previous section, i.e. $N_t=274\,510$.
The rapidity distribution for the \jpsi\ is shown
in Fig.~\ref{fg07}. The PYTHIA MC events have been combined
using the same fraction $f$ found in \eqn{pta} and then
normalized to the observed number of events in $0<|y|<2.0$.
%f7
\begin{figure}[ht]\vskip-6mm
\begin{center}
\mbox{\epsfig{file=y0.eps,width=8.0cm}}
\end{center}
\vskip-3mm
\caption{
$|y|$ distribution for the \jpsi\ from the DELPHI data, shown as
points with error bars. The histogram is a composite of
the renormalized `resolved' and `diffractive' processes from PYTHIA (see text).}
\label{fg07}
\end{figure}
It is seen that the MC events are in fair agreement with the
experimental rapidity distribution, although the data tend
to have some deficiency below $|y|=0.4$ (but not statistically
significant).
The same techniques have been used to compare the experimental
distributions of $M(X_{\rm vis})$, $M(\jpsi+X_{\rm vis})$,
the total and charged multiplicities [$N_{\rm tot}(X_{\rm vis})$ and
$N_{\rm ch}(X_{\rm vis})$], in Figs.~\ref{fg08a},\ \ref{fg08b},\
\ref{fg08c} and \ref{fg08d}. There is fair agreement
between the shape of our measured distributions
and the PYTHIA predictions (using the best fit for the relative content
of diffractive and resolved events and renormalizing the PYTHIA
prediction to the number of observed events).
%f8a
\begin{figure}[ht]\vskip-6mm
\begin{center}
\mbox{\epsfig{file=mx.eps,width=8.0cm}}
\end{center}
\vskip-3mm
\caption{
$M(X_{\rm vis})$distribution
for the $\jpsi+X_{\rm vis}$ from the DELPHI data, shown as
points with error bars. The histogram is a composite of
the renormalized `resolved' and `diffractive' processes from PYTHIA (see text).}
\label{fg08a}
\end{figure}
%f8b
\begin{figure}[ht]\vskip-6mm
\begin{center}
\mbox{\epsfig{file=mjpsix.eps,width=8.0cm}}
\end{center}
\vskip-3mm
\caption{
$M(\jpsi+X_{\rm vis})$ distribution from the DELPHI data, shown as
points with error bars. The histogram is a composite of
the renormalized `resolved' and `diffractive' processes from PYTHIA (see text).}
\label{fg08b}
\end{figure}
%f8c
\begin{figure}[ht]\vskip-6mm
\begin{center}
\mbox{\epsfig{file=cmult.eps,width=8.0cm}}
\end{center}
\vskip-3mm
\caption{
Total multiplicity [$N_{\rm tot}(X_{\rm vis})$] distribution
for the $\jpsi+X_{\rm vis}$ from the DELPHI data, shown as
points with error bars. The histogram is a composite of
the renormalized `resolved' and `diffractive' processes from PYTHIA (see text).}
\label{fg08c}
\end{figure}
%f8d
\begin{figure}[ht]\vskip-6mm
\begin{center}
\mbox{\epsfig{file=mult.eps,width=8.0cm}}
\end{center}
\vskip-3mm
\caption{
Charged multiplicity [$N_{\rm ch}(X_{\rm vis})$] distribution
for the $\jpsi+X_{\rm vis}$ from the DELPHI data, shown as
points with error bars. The histogram is a composite of
the renormalized `resolved' and `diffractive' processes from PYTHIA (see text).}
\label{fg08d}
\end{figure}
In figs.\ref{fg08e} (a--c) are shown the acceptance-corrected distributions
in $\cos\theta$ where $\theta$ is the helicity angle of $\mu^+$
in the rest frame of $\psi\to\mu^+\mu^-$, along with the results of a fit
to the form $1+a\,\cos^2\theta$. The fitted parameters are
$a=-0.93\pm0.57$ for the total sample (a), $a=-1.76\pm0.53$ for
$p_{_T}^2(\jpsi)<1.0$ \gevc\ (b) and $a=0.71\pm1.33$ for
$p_{_T}^2(\jpsi)>1.0$ \gevc\ (c). These results demonstrate that the \jpsi's
are produced with little polarization at high $p_{_T}^2(\jpsi)$, where the
main contribution comes from the resolved processes.
%f8e
\begin{figure}[ht]\vskip-6mm
\begin{center}
\mbox{\epsfig{file=cth.eps,width=12.0cm}}
\end{center}
\vskip-3mm
\caption{
Acceptance-corrected distributions in $\cos\theta$ where $\theta$
is the helicity angle of $\mu^+$ in the rest frame of $\psi\to\mu^+\mu^-$.
The figures (a--c) correspond to the total sample (a),
those with $p_{_T}^2(\jpsi)<1.0$ \gevc\ (b)
and $p_{_T}^2(\jpsi)>1.0$ \gevc\ (c).}
\label{fg08e}
\end{figure}
\clearpage
%4
\section{Conclusions}
We have studied the inclusive \jpsi\ production from $\gamma\gamma$
collisions. The data have been taken by the DELPHI collaboration
during the LEP II phase, i.e. $\sqrt{s}$ of the LEP machine
ranged from 161 to 207 \gevcc. A clean signal
from the reaction $\gamma\gamma\to\jpsi+X$ is seen.
The inclusive cross section is estimated to be
$\sigma(\jpsi+X)=25.2\pm10.2$ pb.
Based on a study of the event shapes of different types of $\gamma\gamma$
processes in the PYTHIA program, we conclude that
some $74\pm22\,$\% of the observed \jpsi\ events are due to the
`resolved' photons, the dominant contribution of which is
evidently derived from
a single color-octet gluon within the photon~\cite{CSM}.
The distributions in $p_{_T}^2(\jpsi)$, $y$ and $\cos\theta$
(for $\mu^+$ in the rest frame of $\jpsi\to\mu^+\mu^-$) are presented.
In addition, a study is given of the characteristics of the
visible $X$ and its multiplicities.
It is clear that theoretical models are still in the state of flux
for the inclusive production of {\jpsi}'s in two-photon fusion processes.
Thus we anticipate an extended period
of close collaboration between experimentalists and theorists,
before emergence of a clear understanding of the nature of the
processes involved and---with it---a more reliable estimate
of the cross sections. We have made the first attempt at extracting
the relative importance of the processes involved by fitting
the observed $p_{_T}^2(\jpsi)$ distribution as a supperposition
of the same distributions from diffractive and resolved processes
predicted by PYTHIA. We look forward to a further refinement of our
analysis both with a future version of PYTHIA and other programs
on the same topic.
%a
\section*{Acknowledgements}
We are indebted to Dr. T. Sj\"ostrand for his help with
the diagrams included in this paper and for his comments on PYTHIA.
We thank M. Klasen for his help with the diagrams important
for inclusive \jpsi\ production.
S.-U. Chung is grateful for the warm hospitality extended to him
by the CERN staff during his sabbatical year in the EP Division.
%=========================================================================%
%r
%\newpage
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\end{document}