PHYSICAL REVIEW C, VOLUME 64, 054903

Transverse energy distributions andJÕc production in Pb¿Pb collisions

A. K. Chaudhuri*Variable Energy Cyclotron Centre, 1/AF, Bidhan Nagar, Calcutta - 700 064, India

~Received 7 February 2001; published 1 October 2001!

We have analyzed the latest NA50 data on transverse energy distributions andJ/c suppression in Pb1Pbcollisions. The transverse energy distribution was analyzed in the geometric model ofAA collisions. In thegeometric model, fluctuations in the number ofNN collisions at a fixed impact parameter are taken intoaccount. The transverse energy dependence ofJ/c suppression was obtained following the model of Blaizotet al., where charmonium suppression is assumed to be 100% effective above a threshold density. Whenfluctuations in the number ofNN collisions are taken into account, the NA50 data onJ/c suppression can bewell fitted with a single parameter, the threshold density.

DOI: 10.1103/PhysRevC.64.054903 PACS number~s!: 25.75.Dw

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In relativistic heavy ion collisionsJ/c suppression hasbeen recognized as an important tool to identify the possphase transition to quark-gluon plasma. Because of the l

mass of the charm quarks,cc̄ pairs are produced on a shotime scale. Their tight binding also makes them immunefinal state interactions. Their evolution probes the statematter in the early stage of the collisions. Matsui and S@1# predicted that in presence of quark-gluon plasma~QGP!,

binding ofcc̄ pairs into aJ/c meson will be hindered, leading to the so calledJ/c suppression in heavy ion collision@1#. Over the years several groups have measured theJ/cyield in heavy ion collisions~for a review of the data and thinterpretations, see Refs.@2,3#!. In brief, experimental datado show suppression. However, this could be attributedthe conventional nuclear absorption, also present inpA col-lisions.

The latest data obtained by the NA50 Collaboration@4# onJ/c production in Pb1Pb collisions at 158AGeV give thefirst indication of the anomalous mechanism of charmonisuppression, which goes beyond the conventional suppsion in a nuclear environment. The ratio ofJ/c yield to thatof Drell-Yan pairs decreases faster withET in the most cen-tral collisions than in the less central ones. It has been sgested that the resulting pattern can be understood in aconfinement scenario in terms of successive meltingcharmonium bound states@4#.

In a recent paper Blaizotet al. @5# showed that the datacan be understood as an effect of transverse energy fluctions in central heavy ion collisions. Introducing a factor«5ET /ET(b), assuming that the suppression is 100% abovthreshold density~a parameter in the model!, and smearingthe threshold density~at the expense of another paramet!the best fit to the data was obtained. Capellaet al. @6# ana-lyzed the data in the comover approach. There also, themover density has to be modified by the factor«. Introduc-tion of thisad hocfactor« can be justified in a model baseon excited nucleons represented by strings@7#.

At a fixed impact parameter, the transverse energy asas the number ofNN collisions fluctuate. The fluctuations i

*Email address: akc@veccal.ernet.in

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the number ofNN collisions were not taken into account ithe calculations of Blaizotet al. @5# or in the calculations ofCapellaet al. @6#. Here, we present a calculation, followinthe model of Blaizotet al. @5#, including these fluctuationsAs will be shown below, if the fluctuations in the numberNN collisions are taken into account, a good descriptionthe NA50 data can be obtained without smearing the threold density. The smearing effect is generated by the flucttions.

A geometric model has been quite successful in explaing the transverse energy production as well as multiplicdistributions inAA collisions @8,9#. In this model, it is as-sumed that at an impact parameterb, the numbern of NNcollisions is Poisson distributed with average^nb&. In theGlauber approximation̂nb& is written as

^nb&5sNNE d2sTA~s!TB~s2b!, ~1!

wheresNN is the inelasticNN cross section, assumed to b32 mb. All the nuclear information is contained in thnuclear thickness functionTA,B(s)5*dzrA,B(s,z). Presently,we have used the following parametric form forrA(r ) @5#:

rA~r !5r0

11expS r 2r 0

a D ~2!

with a50.53 fm,r 051.1A1/3. The central density is obtainefrom *rA(r )d3r 5A.

In the geometric model, the probability to obtainET at animpact parameterb, in n number ofNN collisions, is writtenas

Pn~b,ET!5e2^nb&^nb&

n

G~n11!Q$n} ~ET!, ~3!

whereQ$n%(ET) is then-fold convolution ofET distributionresulting from elementaryNN collisions and is given by

©2001 The American Physical Society03-1

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A. K. CHAUDHURI PHYSICAL REVIEW C 64 054903

Q$n%~ET!5E dET1•••dET

ng~ET1!•••g~ET

n!

3d~ET2ET1•••2ET

n!, ~4!

whereg(ET) is the normalizedET distribution forNN col-lisions. Most of the observedET distributions inNN colli-sions can be well approximated by the gamma distributio

g~ET!5ab

G~b!e2aETET

b21 ~5!

with a andb as parameters. For the gamma distribution,average and the variance are

^ET&NN5b/a, ~6a!

^ET2&/^ET&22151/b. ~6b!

The gamma distribution has an elegant convolution prerty which greatly facilitates computation.n-fold convolu-tion of a gamma distribution is again a gamma distributiowith parametersa85a andb85nb. Thus,

Q$n%~ET!5anb

G~nb!e2aETET

nb21 . ~7!

The final transverse energy distribution is then obtained frEq. ~3! by summing it overn ~from 1 to `) and averagingover the impact parameterb.

The geometric model has been quite successful inplaining theET distributions in heavy ion collisions witha;2 and b;2 @9#. We have fitted theET distribution inPb1Pb collisions varying the parametersa and b. TheNA50 collaboration did not correct theET spectra for theefficiency of the target identification algorithm, whichlower than unity forET lower than 60 GeV. To obtain theparametersa andb, we have fitted the purely inclusive paof theET spectra (ET.60 GeV). A very good fit to the datais obtained witha53.466.19 andb50.37960.021. In Fig.1, experimental data are shown along with the fit~solid line!.

As mentioned in the beginning, we have followed tmodel of Blaizotet al. @5# to analyze theET dependence ocharmonium suppression. The charmonium production csection at an impact parameterb is written as

d2sJ/c/d2b5sJ/cE d2sTAe f f~s!TB

e f f~s2b!S~b,s!, ~8!

whereTA,Be f f is the effective nuclear thickness function,

Te f f~s!5E2`

`

dzr~s,z!expS 2sabsEz

`

dz8r~s,z8! D ~9!

with sabs as the cross section forJ/c absorption by nucle-ons. The exponential factor is the nuclear absorption survprobability, the probability for thecc̄ pair to avoid nuclearabsorption and form aJ/c. S(b,s) is the anomalous part othe suppression. Blaizotet al. @5# assumed thatJ/c suppres-

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sion is 100% effective above a threshold density (nc), a pa-rameter in the model. Accordingly, the anomalous supprsion part was written as

S~b,s!5Q@nc2np~b,s!#, ~10!

wherenp is the density of participant nucleons in the impaparameter space,

np~b,s!5TA~s!@12e2sNNTB(b2s)#1@TA↔TB#. ~11!

Recognizing that the end point behavior of charmoniusuppressions are due to transverse energy fluctuatiBlaizot et al. @5# modified the density of participant nucleonby a factor «5ET /ET(b). This modification makes sensonly whennp is assumed to be proportional to the enerdensity. Implicitly, it was also assumed that theET fluctua-tions are strongly correlated in different rapidity gaps. Tassumption was essential as the NA50 Collaboration msuredET in the 1.1–2.3 pseudorapidity window while thJ/c ’s were measured in the rapidity window 2.92,y,3.92@4#. In the geometric model, strong correlation betweenETfluctuations in different rapidity windows is readily obtaineAt a fixed impact parameter, fluctuations inET can be calcu-lated as@9#

^ET2&AA2^ET&AA

2

^ET&AA2

5^N2&2^N&2

^N&21

1

^N&

^ET2&NN2^ET&NN

2

^ET&NN2

.

~12!

The ET fluctuations have two parts,~i! geometric in na-ture which remains the same irrespective of rapidity windoand~ii ! which depends on fluctuations in theET distributionsin NN collisions. The second part changes with rapidity wdow but its effect is less as it is weighted by the factor 1/^N&.Fluctuations ofET in different rapidity windows are thusstrongly correlated.

We calculate theJ/c production as a function of transverse energy, at an impact parameterb as

FIG. 1. Experimental transverse energy distribution in Pb1Pbcollisions ~filled circles! and the fit to it in the geometric mode~solid line!.

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TRANSVERSE ENERGY DISTRIBUTIONS AND . . . PHYSICAL REVIEW C64 054903

dsJ/c/dET5 (n51

`

Pn~b,ET!P~cuET ,b!, ~13!

wherePn(b,ET) is the probability to obtainET in n numberof NN collisions @Eq. ~3!# and P(cuET ,b) @Eq. ~8!# is theprobability to produce a charmonium with transverse eneET . The anomalous suppression part is modified accordto

S~b,s!5QS nc2ET

nb/anp~b,s! D , ~14!

where we have replacedET(b) by nb/a appropriate in thegeometric model. This modification takes into accountfluctuations in the number ofNN collisions at a fixed impacparameterb.

The Drell-Yan production was calculated similarly, rplacingP(cuET ,b) in Eq. ~13! by the Drell-Yan productioncross section,

FIG. 2. Transverse energy dependence ofJ/c to Drell-Yan ratioin Pb1Pb collisions measured by the NA50 Collaboration in 19~open circles! and in 1998~solid circles!. The solid and dashed lineare fit to the data obtained in the present model withsabs

56.4 mb, nc53.8 fm22 and sabs54.0 mb, nc53.44 fm22, re-spectively.

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d2sDY/d2b5sDYE d2sTA~s!TB~s2b!. ~15!

In Fig. 2, we have compared the theoretical charmoniproduction cross section with NA50 experimental data. Tnormalization factorsJ/c/sDY was taken to be 53.5. Thsolid curve is obtained withsabs56.4 mb, and nc

53.8 fm22. A very good description of the data from 4GeV onward is obtained. It may be noted that if the fluctutions in theNN collisions were neglected, an equivalent dscription is obtained with threshold densitync53.75 fm2,with smearing of theQ function at the expense of anotheparameter. It is evident that in this model, the smearing efis obtained from the fluctuations in the number ofNN colli-sions at a fixed impact parameter. Theoretical calculatipredict more suppression below 40 GeV, a feature evidenother models also. It is possible to fit the entireET range byreducing theJ/c-nucleon absorption cross section. Recedata@10# on theJ/c cross section inpA collisions point to asmaller value ofsabs;4 to 5 mb. The dashed line in Fig.corresponds tosabs54 mb andnc53.44 fm22.

To summarize, we have analyzed the latest NA50 dataET dependence ofJ/c suppression in Pb1Pb collisions. Thetransverse energy distribution was analyzed in the geomemodel. The charmonium production data was analyzedlowing the model of Blaizotet al. @5#, including the effect offluctuations in the number ofNN collisions at a fixed impactparameter. The experimental data from 40 GeV onwacould very well be fitted withsabs56.4 mb and a thresholddensity of 3.8 fm22. Neglecting the fluctuations in the number ofNN collisions, an equivalent fit could only be obtaineby smearing theQ function at the expense of an added prameter. Data in the entireET range could be fitted by reducing the J/c-nucleon absorption cross section tosabs54 mb. The threshold density is then reduced3.44 fm22. The melting of charmoniums above a threshodensity suggests that in Pb1Pb collisions, a QGP-like envi-ronment is produced.

The author would like to thank Dr. K. Krishan for readinthe manuscript and offering various suggestions.

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