\documentstyle[preprint,psfig,aps]{revtex}
%\documentstyle[twocolumn,prl,aps,psfig]{revtex}
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\begin{document}
\title{$J/\psi$ suppression in heavy ion collisions --
interplay of hard and soft QCD processes}
\author{C.~Spieles$^1$\footnote{Supported by the 
Alexander v.~Humboldt Foundation}\footnote{Email: cspieles@lbl.gov },
R.~Vogt$^{1,2}$, L.~Gerland$^3$, S.A.~Bass$^4{}^*$, M.~Bleicher$^3$, 
L.~Frankfurt$^{3,5}{}^*$, M.~Strikman$^6$, H.~St\"ocker$^3$, W.~Greiner$^3$}

\address{$^1$~Nuclear Science Division,
Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA}
\address{$^2$~Physics Department,
University of California at Davis, 
Davis, CA 95616, USA}
\address{$^3$~Institut f\"ur
Theoretische Physik,  J.~W.~Goethe-Universit\"at,
D-60054 Frankfurt a.M., Germany}
\address{$^4$~Department of Physics, Duke University,
Durham, N.C. 27708-0305, USA}
\address{$^5$~School of Physics and Astronomy, Tel Aviv University, 69978
Ramat Aviv, Tel Aviv, Israel}
\address{$^6$~Department of Physics, Pennsylvania State University,
University Park, PA 16802, USA}
\maketitle

\begin{abstract}
We study $J/\psi$ suppression in $AB$ collisions assuming that the
charmonium states evolve from small, color transparent configurations.
Their interaction with nucleons and nonequilibrated, 
secondary hadrons is simulated using the microscopic model UrQMD.
The Drell-Yan lepton pair yield and the $J/\psi/$Drell-Yan ratio
are calculated as a function of the neutral transverse energy 
in Pb+Pb collisions at 160~GeV and found to be in reasonable 
agreement with existing data.
\end{abstract}

\pagebreak

\section{Introduction}
Experimental data on the $AB$ and $E_T$ dependence of $J/\psi$-meson
production
from the CERN SPS
\cite{baglin,gonin,abreu,romana} 
exhibit tantalizing evidence for $J/\psi$ suppression when compared to hard
QCD production.
Do the $J/\psi$ data in Pb+Pb-collisions indicate the creation of a
deconfined phase of strongly interacting matter, {\it i.e.}  a quark-gluon
plasma (QGP) \cite{kharzeev,wong}?
Such QGP scenarios generally rely on the experimental observation of
deviations from the predictions of models of hadronic suppression.
Simple analytical models of $J/\psi$ suppression have used nuclear 
absorption alone
\cite{kharzeev} or absorption by nucleons and comoving secondaries
\cite{vogtplb98} to fit all but the Pb+Pb data. 
These models
generally assume a single, fixed nucleon absorption cross section for all charmonium
states and that the comover interaction rate, assuming a Bjorken scaling
expansion, is essentially thermal.
(For theoretical reviews, see
Refs.~\cite{reviewvogt,reviewkharzeev,reviewmuller}.)\footnote{Recently, there have been several attempts to build models of
charmonium production and absorption by means of microscopic 
hadronic transport simulations \cite{cassing,cassing2,geiss,kahana}. 
%In Refs.~\cite{cassing,cassing2} $c\bar c$ production was implemented
%as a possible subchannel of the total $NN$ cross section into the 
%hadronic transport code. 
%In Refs.~\cite{geiss,kahana}, on the 
%other hand, the space-time production points are 
%obtained from hard processes in each event before the hadronic 
%background simulation. 
%Only in  \cite{kahana},
%feeddown from $\psi'$ and $\chi$ mesons was also included. 
%In contrast to the present work, in Refs.~\cite{cassing2,geiss,kahana}, 
%charmonium precursor states can be immediately dissociated by nucleons 
%with constant cross sections larger than $5$~mb. 
Based on rather different model treatments of the charmonium dynamics and the 
interconnection of hard and soft processes it is claimed in all these 
studies that conventional hadronic scenarios are consistent with the Pb+Pb
data.}

%The present study
%accounts for the fact that $\approx 40\%$ of the produced $J/\psi$'s 
%result from decays of $\chi$ and $\psi'$ states
%with significantly larger nucleon absorption cross sections 
%than that of the $J/\psi$ \cite{gerland}. 
%%
%%%Another reason for suppression of $J/psi$ production is large cross
%%%section of dissociation  with  any comovers except pions. Actually
%%%threshold cross section is infinity.(Famous $1/v$ law for inelastic
%%%nearthreshold processes when sum of masses of colliding particles is
%%%larger than that for the final particles.)
%%  

Charmonium final state interactions with mesons and
baryons are simulated using the Ultrarelativistic Quantum Molecular Dynamics, 
UrQMD \cite{bigpaper}, a microscopic hadronic transport model.
The charmonium nucleon cross sections employed here are calculated in a 
nonrelativistic potential model \cite{gerland} since
at SPS energies, charmonium-nucleon interactions are predominantly
nonperturbative. 
The charmonium precursors are not
eigenstates of the QCD Hamiltonian, therefore their effective sizes and
interaction cross sections may vary from their production to the final state
formation \cite{gerland}. 
Thus the charmonium absorption cross sections are assumed to
expand linearly with time until their asymptotic value is reached.
Since the produced particles in the collision have a non-thermal
distribution \cite{mycollspec}, comover interactions can rather effectively
dissociate the $J/\psi$. Because of abundant high mass resonances,
most of the meson induced $J/\psi$ dissociation processes are exothermic
\cite{mycollspec}. They account for an important fraction of the observed
suppression, larger in Pb+Pb collisions than the nuclear absorption
alone. 

% WE NEED KIND OF DISCUSSION BELOW TO OUTLINE REGION OF
%APPLICABILITY AND THE DIFFERENCE FROM TEVATRON,LHC PHYSICS.
%THIS IS BECAUSE PHYSICS AT RHIC AND LHCMAY BE AND WILL BE DIFFERENT.
%DIFFERENT KINEMATICS, DIFFERENT PHYSICAL PROCESSES. SO UNCLEAR
%WHETHER WE ARE STRUGLING WITH PQCD SCENARIO IN GENERAL AS SOUNDS NOW
%OR FOR RESCTRICTED KIEMATICAL REGION.
%%%Our calculations are applicable for fixed target energy range where 
%%%color singlet model has no problem to describe data see~\cite{halzen}
%%%and references therein. Possible role of minijet production in collider
%%%physics is beyond the scope of this paper.

\section{The model}

We apply perturbative QCD to the production of charmonium states by 
simulating nucleus-nucleus collisions in the impulse approximation.
The nuclear dependence of parton distribution functions is neglected.
The resulting 
space-time distribution of charmonium production points is inserted into the
evolving hadronic environment calculated with UrQMD \cite{mycollspec}
since the rare quarkonium
production processes are small perturbations on the heavy ion 
%%%new:
collision\footnote{Since we consider only exclusive charmonium production, 
the QCD factorization theorem is inapplicable.}.
Our model is thus designed to account for partonic and hadronic aspects of
the charmonium dynamics. 
%IT IS NECESSARY TO EXPLAIN
%WHETHER OUR DESCRIPTION DOES NOT CONTRADICT TO THE QCD FACTORIZATION THEOREM.
%I WANT TO STRESS THAT IF SUM OVER ALL CHARMED STATES WILL BE 
%PERFORMED THE FINAL STATE
%INTERACTION WILL BE CANCELLED IN THIS SUM. THUS IF THE SAME APPROACH
%TO BE APPLIED TO TOTAL CROSS SECTION OF CHARMED PARTICLE PRODUCTION
%WILL LEAD TO WRONG RESULT. THIS IS BECAUSE EXACT CANCELLATION OF
%DIFFERENT TERMS WILL BE LOST IN THE APPROXIMATE CALCULATION. REMEMBER
%ANALOGY WITH CONSERVATION OF EM CURRENT.
%%%We consider production of certain charmed state but not sum over all
%%%charmed states, so the
%OVERLAP BETWEEN SOFT AND HARD PHYSICS IS HIGHER TWIST EFFECT IN THE
%TOTAL CROSS SECTION OF HARD PROCESSES (SUMMED OVER ALL CHARMED
%PARTICLE PRODUCTION)-THIS IS ESSENCE OF QCD
%FACTORIZATION THEOREM . BUT WE CONSIDER EXCLUSIVE
%CHANNEL WHERE QCD FACTORIZATION THEOREM IS INAPPLICABLE.
%% 
The space-time distributions of hard and soft processes, {\it i.e.} in
particular charmonium production and absorption, 
%cnot just nuclear interactions, also psi-N and psi-comover...
%%%from the interaction between different nucleons
%% THIS IS IMPORTANT. BECAUSE IF WE ASSUMED HARD MECHANISM OF 
%CHARM PRODUCTION IN NN COLLISIONS WE HAVE NO RIGHT TO ACCOUNT FOR THE
%INTERACTION OF CHARM WITH HADRONS PRODUCED IN THE SAME NN COLLISIONS.
may overlap.
%SO CURRENT TEXT SOUNDS UNSATISFACTORY: 
Thus, in our model, a charmonium state produced in a hard process can be
dissociated by the interaction with a comoving hadron before 
this state leaves the nuclear environment and before all other hard
production processes are completed (in contrast to Ref.~\cite{kahana}).
The probability for such an event, however, is reduced due to the 
initially small absorption cross sections and the finite formation times of 
comoving mesons according to the string model (see below).
%new text:
To avoid double counting, interactions of $c \bar c$ states with produced
hadrons in individual $NN$ collisions are excluded. In $AB$
collisions, all hard $NN$ collisions can contribute to the $c\bar c$
production while all soft $NN$ collisions can contribute to the hadronic
environment in which the $c \bar c$ state may be dissociated. The error
imposed by this concept --- inherent to all microscopic and analytical
models of comover absorption --- is estimated to be very small.
%end new

The charmonium states are distributed according to their assumed 
production probability 
times their decay probability to $J/\psi$'s.
Thus 40\% of the final states are $\chi$'s, 55\% are $J/\psi$'s, and 5\% are 
$\psi'$s
%%referenz geaendert (war vorher gerland)
\cite{gavai}. According to the spin degeneracy, 
1/3 of the $\chi$'s are $\chi_{c10}$ states and 2/3 are $\chi_{c11}$ states.
Their momenta are assigned according to the parametrization \cite{ramona},
\[
E\frac{d\sigma}{dMdp^3}\sim(1-x_F)^{3.55} \exp(-p_T\, 2.08\rm \,GeV^{-1})\;
.
\]

The rescattering cross sections for $X(c\bar c)+B$, assuming $B\equiv N$,
are taken from Ref.~\cite{gerland}:
$\sigma(J/\psi N)=3.6$~mb, $\sigma(\psi' N)=20$~mb, 
$\sigma(\chi_{c10} N)=6.8$~mb, and
$\sigma(\chi_{c11} N)=15.
%%8
9
%%
$~mb. Charmonium-meson cross sections 
($X(c \bar c) +\pi$, $X(c \bar c) +\rho$, {\it etc.})
are reduced by a factor of 2/3 from the corresponding baryon values.
All baryon and meson collisions above the respective dissociation 
thresholds are assumed to break up the charmonium state. 
Universal and energy independent cross sections are employed, ignoring any
charmonium-meson resonances, perhaps too 
crude an assumption. 
%%%new:
From phase space arguments one can infer that the $J/\psi$ dissociation cross
sections with $\pi$'s should be suppressed close to threshold while it
should be enhanced for exothermic channels. 
%deleted and changed:
%Calculations within the
%framework of a meson exchange model show that the cross sections for 
%$\pi J/\psi\rightarrow D\bar D^*$ and $\rho J/\psi\rightarrow D \bar D$ 
%are both small close to threshold \cite{reviewmuller}.
However, we have found that, during the initial stage of the $J/\psi$ comover
collisions, the average interaction energy, $<E>\approx 5$~GeV, is far 
above threshold \cite{mycollspec}.
There are no calculations of $J/\psi$ dissociation cross sections with
mesons other than $\pi$'s and $\rho$'s \cite{reviewmuller}.
In a thermal comover scenario the density of heavier mesons is suppressed 
by the Boltzmann factor. According to the UrQMD simulations, however,
these mesons dominate the comover absorption \cite{mycollspec}.
%which give an important contribution to the total
%absorption according to the UrQMD simulations \cite{mycollspec}.
In a forthcoming paper~\cite{paper} the influence of the energy 
dependence of the comover interactions will be studied further.
%%%(averaged according to Veneziano type dual models 
%%%over possible resonances)  SOUND THEORETICAL REASONS FOR THE 
%EXISTENCE OF CHARMED MOLECULES
%WHICH ARE APPROPRIATE RESONANCES IS DISCUSSED MORE THAN 20 YEARS. 
%% CF KOGUT AND SUSSKIND 1975?
%FOR THRESHOLD INTERACTION THIS IS EVEN QUALITATIVELY INCORRECT:
%WE NEED HERE FORMULAE_HOW THIS SUPPRESSION HAS BEEN TAKEN INTO ACCOUNT
%I DONT KNOW WHAT REALLY DO YOU MADE :SO BELOW IS MY GUESS.
%($\sigma=\sigma_0 \Theta(s-4m_D^2)$
%where $\sigma_0\approx $5 mb). In this estimate we use the observation that
%the average cross section of hadron interactions weakly depend 
%on the energy in nonperturbative QCD regime.
%%

The cross sections correspond to the geometrical transverse radii
$r_T^i=\sqrt{\frac{\sigma^i}{\pi}}$ of the
charmonium states. 
We use $\sigma^i$  to estimate the respective 
formation times $\tau_F^i$ of the charmonium states by choosing
$\tau_F^i=r_T^i/c$.  
During these formation times 
the cross sections increase linearly with $t$ \cite{gerland}, 
starting from 0 at $t=0$.

Here it is important that we also take into account the formation 
time of comoving mesons (on average, $\tau_F\approx 1$ fm/c). Particles 
produced by string fragmentation are not allowed to interact with other hadrons --
in particular with a charmonium state -- within their formation time. However,
leading hadrons are allowed to interact with a reduced cross section even
within their formation time. The reduction factor is 1/2 for mesons which
contain a leading constituent quark from an incident nucleon and 2/3 for
baryons which contain a leading diquark.

For this study, we have slightly modified the angular distributions of 
meson-baryon interaction in the UrQMD~1.0 model since their strong forward peak
underpredicts the total produced transverse energy \cite{bleicher}.
%BUT IN THE CALCULATION REALISTIC CROSS SECTION SHOULD BE USED. 
%FORM OF CROSS SECTION CITED BELOW IS FAR FROM REALISTIC ONE.
%Using the ad hoc parametrization: $d\sigma/d\cos\theta\sim \exp(8\cos\theta)$ 
%THIS IS DANGEROUS POINT. CROSS SECTION MAY DEPEND ON COS \TETA IN
%TWO REGIMES. EXTREEMLY LOW ENERGIES OR 90 DEGREE HIGH ENERGY SCATTERING.
%OTHERWISE CROSS SECTION HAS FORWARD OR BACKWARD PEAK. THUS 
%SEMIREALISTIC PARAMETRIZATION IS BADLY NEEDED. SAY EXP Bt    ETC.
%THIS IS ONE OF KEY POINTS IN THE CALCULATION.
%for all inelastic meson-baryon interactions which do not form an $s$-channel
%(baryon-)resonance, 
The model now reproduces the $E_T$ spectra in 
S(200~GeV)+Au and Pb(160~GeV)+Pb collisions measured by NA35 and NA49,
respectively \cite{unpubl}.
Neither the amount of baryon stopping nor the rapidity distribution of 
negatively charged particles 
which have been shown to agree with experimental $pp$ and $AB$ interactions
\cite{bigpaper} are significantly affected by this 
modification. 
%IF SO SEMIREALISTIC PARAMETRIZATION CAN BE EASILY SUGGESTED AND CHECKED. 

%%These observables have been shown to agree with experimental $pp$ and $AB$
%%interactions \cite{bigpaper}.


\section{Results and discussion}

Figure~\ref{hardet} shows the calculated number of Drell-Yan muon pairs, 
proportional to the number of hard collisions, in Pb+Pb collisions
as a function of the produced neutral transverse energy within
$1.1<\eta<2.3$. The NA50 data
\cite{ramello} have been included
with the abscissa rescaled to reflect the latest change in
data \cite{romana} which indicates an $\approx 20$~\% shift in the 
absolute $E_T$ scale from previous publications \cite{abreu,ramello}.
We are aware that the new analysis does not imply a simple
overall rescaling of the old data points. However, in order to reasonably
compare the gross features of the
experimental dimuon $E_T$ spectrum  
with our model calculation, we have multiplied all $E_T$-values of the data
by 0.8.
This factor was obtained by comparing the $E_T-E_{ZDC}$ contour from
Quark Matter '97 \cite{ramello} and the Moriond '98 \cite{romana} proceedings.
The  agreement between the model and the rescaled data
is to be expected since the NA49 $E_T$ distribution \cite{na49} is 
described correctly \cite{unpubl}\footnote{However, the agreement between the 
model and 
the NA38 experiment becomes poor for S+U collisions. 
The UrQMD calculation appears
to overestimate the neutral transverse energy by about 25\%
in the range $1.7<\eta<4.1$ \cite{baglin,borhani}
although the calculated $E_T$ spectrum of the similar
S+Au system agrees well with the NA35 data \cite{na49}. 
The UrQMD calculation thus indicates an inconsistency between the $E_T$
measurements by NA35, NA49 and NA50 on the one hand and NA38 on the other
\cite{unpubl}.}. The additional 
%%`Glauber' 
simulation
is a simple and well understood model of hard scattering 
processes in nucleus-nucleus collisions.

Figure~\ref{sigab} shows the $J/\psi$ production cross section 
according to 
UrQMD calculations for several projectile-target combinations 
($p$(450~GeV)+C, $p$(200~GeV)+Cu, $p$(200~GeV)+W, $p$(200~GeV)+U, 
S(200~GeV)+U, and Pb(160~GeV)+Pb) in comparison to experimental data
\cite{abreu}.
The results of the calculations are normalized to the experimental
cross section in $p$(200~GeV)+$p$ interactions. The 450~GeV and 160~GeV 
simulations are rescaled to $p_{lab}=200$~GeV with the parametrization of 
Ref.~\cite{schuler}, as done by NA50 \cite{gonin,abreu}. 
Considering only nuclear dissociation results in a far smaller $J/\psi$ 
suppression than seen in the data, not only for Pb+Pb collisions but also
for S+U and even $pA$ reactions. Note that the systematics of
nuclear absorption shown in Fig.~\ref{sigab} does not reflect a universal
straight line as in Glauber calculations with constant absorption cross
sections.
By taking the nonequilibrium charmonium-meson interactions into
account, good agreement with the data is obtained. However, a strong 
dependence on parameters such as the charmonium and comover formation 
times and the dissociation cross sections remains to be 
studied in detail \cite{paper}.

%%Figure~\ref{ratab} shows the $\psi'/J/\psi$ ratio in $pA$ interactions 
%%as a function of target mass. UrQMD calculations are compared with the
%%experimental data \protect\cite{lourenco}.
%%The observed weak $A$ dependence of the ratio had led to the hypothesis the
%%formation of a
%%`preresonance' state, e.g.~\cite{kharzeev}. The resulting universal 
%absorption cross section 
%%naturally leads to equal survival probabilities of $J/\psi$ and $\psi'$.
%%In our model prescription, the absorption cross sections for the individual
%%charmonium states evolve linearly with time. Thus, the $\psi'$, the
%%$\chi_{c10}$ and the $\chi_{c11}$ state have the same absorption cross
%%section as the $J/\psi$ as long as $\tau^i < \tau_F^{J/\psi}$. 
%%Only for $\tau^i > \tau_F^{J/\psi}$ the
%%cross sections differ, because then $\sigma(J/\psi N)$ has reached its
%%asymptotic value, while the cross sections of the bigger resonances still
%%increase. The differences in the calculated $J/\psi$ and $\psi'$ survival
%%probabilities for $pA$ reactions, as shown in Fig.~\ref{ratab}, are 
%%therefore mainly due to nuclear dissociation processes at the later stage of the reaction. 
%%Figure~\ref{ratab} also shows the calculated $\psi'/J/\psi$ ratio in S+U and Pb+Pb
%%reactions.
%%Here, dissociation by mesons leads to a significant decrease of 
%%the $\psi'/J/\psi$ ratio which is even stronger than seen in the
%%data \cite{gonin}. 
%%Although the charmonium-comover dissociation cross sections shortly 
%%after the charmonium production are equal for all states, 
%%the kinematic threshold leads to different dissociation probabilities.
%%It will be interesting to learn if introducing more realistic 
%%energy dependent cross sections close to threshold will have a strong
%%influence on the $\psi'/J/\psi$ ratio.

Due to the linear expansion of the charmonium cross sections with 
time, the $J/\psi$ and $\psi'$ cross sections are similar in the very
early stages, leading to a weak $A$-dependence of the $\psi'/J/\psi$
ratio in $pA$ collisions 
at central rapidities, apparently consistent with the data.
However, for a deeper understanding of this ratio quantum interference
effects \cite{lonya} as well as refeeding processes, $\pi J/\psi \rightarrow
\psi' \pi$ \cite{sorge,chen}, must be considered.
The $\psi'/J/\psi$ ratio will be studied further later \cite{paper}.

 
Figure~\ref{psidyet} shows the $J/\psi$ to Drell-Yan ratio 
as a function of $E_T$ for Pb+Pb interactions at 160~GeV compared to 
the NA50 data \protect\cite{romana}.
The normalization of $B_{\mu\mu}\sigma(J/\psi)/\sigma({\rm DY})=46$ in $pp$
interactions at 200~GeV has been 
fit  to S+U data within a geometrical
model \protect\cite{kharzeev}.
The application of this value to our analysis is not arbitrary:
the model of Ref.~\protect\cite{kharzeev} renders 
the identical $E_T$-integrated $J/\psi$ survival probability, $S=0.49$, 
as the UrQMD calculation for this system.
An additional factor of 1.25
\protect\cite{reviewvogt} has been applied to the Pb+Pb calculation
in order to account for the lower energy, 160 GeV, since the
$J/\psi$ and Drell-Yan cross sections have different energy and isospin
dependencies. 
The gross features of the $E_T$ dependence of the $J/\psi$ to Drell-Yan
ratio are reasonably well described by the model calculation. 
No discontinuities in the shape of the ratio as a function of $E_T$ 
are predicted by the
simulation. 

\section{Conclusion}

We have examined charmonium production and absorption processes in
$pA$ and $AB$ collisions at SPS energies.
The microscopic simulation of hard processes in the impulse 
approximation and the hadronic transport description of 
$AB$ collisions with the UrQMD model
simultaneously provide reasonable $E_T$
dependencies of the Drell-Yan rates as well as
baryon and meson rapidity distributions. We have modelled $J/\psi$
absorption according to the scenario described in Ref.~\cite{gerland}.
Cross sections evolving from color transparent small configurations to
asymptotic states derived from quantum diffusion and the 
dynamical $\chi$ polarization (color filtering) are taken into account.

The calculated $J/\psi$ production cross sections for minimum bias $pA$,
S+U and Pb+Pb collisions agree with experiment. Dissociation by
nonequilibrium 
comovers accounts for about half of the total absorption in 
S+U and Pb+Pb reactions.
The contribution of the interaction with comovers
in $pA$ reactions is small but not negligible.
The suppression of charmonium states is sensitive 
to the comover momentum distributions. The effective dissociation by comovers
seems to indicate a nonequilibrated hadronic environment.
%
The observed $E_T$ dependence of the $J/\psi$ to Drell-Yan ratio in Pb+Pb
collisions is reproduced by the model. The calculated result is
smooth, without abrupt discontinuities,
in agreement with new high statistics data~\cite{kluberg}.
%However, the high and low $E_T$ data points 
%require considerable additional experimental effort before definite
%conclusions can be drawn.
We conclude that within our model, the data on charmonium cross 
sections at the SPS can be explained without invoking exotic mechanisms.
%A more detailed discussion of Drell-Yan $E_T$ distributions
%and the $E_T$ dependence of the $J/\psi$ and $\psi'$ to Drell-Yan
%ratios in different 
%systems as well as the dependence of our results on the model parameters 
%will be forthcoming \cite{paper}.

\begin{figure}[b]
\vspace*{\fill}
\centerline{\psfig{figure=fig1.eps,width=12cm}}
\caption{
Number of Drell-Yan pairs in Pb+Pb interactions as a function of the
 neutral transverse energy within $1.1<\eta<2.3$. 
The calculation is normalized to the data.
Shown is the UrQMD result and experimental data from NA50
\protect\cite{ramello} with the
$E_T$ of the data rescaled by $0.8$. The modification is motivated by 
a comparison of the
recently published $E_T-E_{ZDC}$ contour plot \protect\cite{romana}
with the previously published analysis
\protect\cite{abreu,ramello}.
\label{hardet}}
\vspace*{\fill}
\end{figure}

\begin{figure}[b]
\vspace*{\fill}
\centerline{\psfig{figure=fig2.eps,width=12cm}}
\caption{$J/\psi$-production cross sections times dimuon branching ratio
 in the
kinematical domain $0<y_{cm}<1$ and $|\cos\theta_{CS}|<0.5$, and rescaled,
if necessary, to $p_{\rm lab}=200$~GeV as a function of
$AB$. The data (open triangles) are from \protect\cite{abreu}.
Open circles denote the production cross
sections if only nuclear absorption is considered.
\label{sigab}}
\vspace*{\fill}
\end{figure}

\begin{figure}[b]
\vspace*{\fill}
\centerline{\psfig{figure=fig3.eps,width=12cm}}
\caption{The ratio of $J/\psi$ to Drell-Yan production as a function of 
$E_T$ for Pb+Pb at 160~GeV. 
The experimental data are from Ref.~\protect\cite{romana}.
The normalization factor, from $pp$ interactions at 200~GeV, $B_{\mu\mu}\sigma(
J/\psi)/\sigma({\rm DY})=46$ 
is taken from Ref.~\protect\cite{kharzeev}. 
This value, however, has been indirectly determined in the framework 
of a different model. An additional factor of 1.25 
\protect\cite{reviewvogt} has been applied to the Pb+Pb calculation
in order to account for the lower energy. Note that no scaling factor has
been applied to the $x$-axis for either the calculations or the data.
\label{psidyet}}
\vspace*{\fill}
\end{figure}


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\end{document}


