9 December 1999

Ž .Physics Letters B 469 1999 12–18

Expected production of strange baryons and antibaryonsin baryon-poor QGP

Johann Rafelski, Jean LetessierDepartment of Physics, UniÕersity of Arizona, Tucson, AZ 85721, USA

LPTHE, UniÕersite Paris 7, 2 place Jussieu, F–75251 Cedex 05, France´

Received 10 August 1999; received in revised form 7 October 1999; accepted 19 October 1999Editor: W. Haxton

Abstract

In a dynamical model of QGP at RHIC we obtain the temporal evolution of strange phase space occupancy at conditionsexpected to occur in 100q100 A GeV nuclear collisions. We show that the sudden QGP break up model developed todescribe the SPS experimental results implies dominance of both baryon and antibaryon abundances by the strange baryonand antibaryon yields. q 1999 Published by Elsevier Science B.V. All rights reserved.

PACS: 12.38.Mh; 25.75.-q

We explore the consequences of high strangenessabundance we expect to be present in the baryon-poor

Ž .quark-gluon plasma QGP environment formed e.g.,in the central rapidity region in Au–Au, maximumenergy 100q100 A GeV collisions at the relativistic

Ž .heavy ion collider RHIC at the Brookhaven Na-tional Laboratory, Upton, New York. About 10–20%of hadrons produced in these reactions will bestrange, and since mesons dominate hadron abun-dance, there is much more strangeness than baryonnumber. During the break-up of the color chargedeconfined QGP phase there is considerable advan-tage for strangeness to stick to baryons given that theenergy balance for the same flavor content favors

Ž Žproduction of strange baryons over kaons, E Lq. Ž ..p -E NqK . When QGP is formed, we there-

fore expect to find hyperon dominance of baryondistribution i.e. most baryons and antibaryons pro-duced at RHIC will be strange. A similar argument

could be made for reactions leading to the confinedphase, the main difference arises from the observa-tion that the required high abundance of strangenessper participating nucleon can be produced in the

w xdeconfined QGP 1–4 . This qualitative argumentwill be quantitatively elaborated here, in view of theconsiderable effort that has been committed by theSTAR collaboration at RHIC to enhance the capabil-

Ž .ity to measure multi-strange anti baryon productionŽ . w xusing a silicon strip detector SSD 5 .

In the first part of this report we show that thechemical strangeness flavor abundance equilibriumis established at the time of QGP breakup by thedominant process which is gluon fusion, GG™ss.In QGP this reaction overcomes the current quarkmass threshold 2m for strangeness formation fors

temperature T,m )200 MeV. In the second parts

of this report we use the computed chemical condi-tion of strangeness, and employ the knowledge gained

0370-2693r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved.Ž .PII: S0370-2693 99 01238-1

( )J. Rafelski, J. LetessierrPhysics Letters B 469 1999 12–18 13

w xin our analysis of the SPS results 6 , to obtain thestrange baryon and antibaryon abundances expectedat RHIC.

In some key aspects the methods we employdiffer from those obtained in other studies of chemi-cal equilibration of quark flavor for RHIC conditionsw x7–9 . We study the dynamics of the phase spaceoccupancy rather than particle density, and we elimi-nate most of the dynamical flow effects by consider-ing entropy conserving evolution. Moreover, we use

Žrunning QCD parameters both coupling and strange.quark mass to describe strangeness production, with

strong coupling constant a as determined at thes

M 0 energy scale. We will make two assumptions ofZ

relevance for the results we obtain:Ž . Ž .a the kinetic momentum distribution equilibrium

Ž .is reached faster than the chemical abundancew xequilibrium 10,11 ;

Ž .b gluons equilibrate chemically significantly fasterw xthan strangeness 12 .

The first assumption allows to study only the chemi-cal abundances, rather than the full momentum dis-tribution, which simplifies greatly the structure of themaster equations; the second assumption allows tofocus after an initial time t has passed on the0

evolution of strangeness population: t is the time0

required for the development to near chemical equi-librium of the gluon population.

We now formulate the dynamical equation for theevolution of the phase space occupancy g of stranges

quarks in the expanding QGP: the phase space distri-bution f can be characterized by a local temperaturesŽ . Ž . `T x,t of a Boltzmann equilibrium distribution f ,s

with normalization set by a phase space occupancyfactor:

f p , x ;t ,g T f ` p ;T . 1Ž . . Ž . Ž . Ž .s s s

Ž .Eq. 1 invokes in the momentum independence of gs

our first assumption. More generally, the factor g , ii

sg,q,s,c allows a local density of gluons, lightquarks, strange quarks and charmed quarks, respec-tively not to be determined by the local momentumshape, but to evolve independently.

Ž .With variables t, x referring to an observer inthe laboratory frame, the chemical evolution can bedescribed by the strange quark current non-conserva-

tion arising from strange quark pair production de-scribed by a Boltzmann collision term:

Er E zrs smE j ' qm s E t E xg g™ ss1 2 ² :s r t s ÕŽ . Tg2

qq™ ss² :qr t r t s ÕŽ . Ž . Tq q

ss™ g g ,qq² :yr t r t s Õ . 2Ž . Ž . Ž .Ts s

The factor 1r2 avoids double counting of gluonpairs. The implicit sums over spin, color and anyother discreet quantum numbers are combined in theparticle density rsÝ Hd3p f , and we have alsos,c, . . .

introduced the momentum averaged productionrannihilation thermal reactivities:

d3p d3p s Õ f p ,T f p ,TŽ . Ž .H H1 2 12 12 1 2

² :s Õ ' .Trel3 3d p d p f p ,T f p ,TŽ . Ž .H H1 2 1 2

3Ž .

Ž .f p ,T are the relativistic BoltzmannrJuttner distri-¨i

butions of two colliding particles is1,2 of momen-tum p .i

The current conservation can also be written withw xreference to the individual particle dynamics 13 :

consider r as the inverse of the small volumes

available to each particle. Such a volume is definedin the local frame of reference for which the local

Ž . <flow vector vanishes z x,t s0. The consideredlocal

volume d V being occupied by small number oflŽ .particles dN e.g., dNs1 , we have:

dN 'r d V . 4Ž .s s l

Ž . Ž .The left hand side LHS of Eq. 2 can be nowwritten as:

Er E zr 1 ddN dr 1 dd Vs s s s lq ' s qr .sE t E x d V dt dt d V dtl l

5Ž .

Ž .Since dN and d V dt are L orentz -invariant, thel

actual choice of the frame of reference in which theŽ . Ž .right hand side RHS of Eq. 5 is studied is irrele-

vant and we drop henceforth the subscript l.

( )J. Rafelski, J. LetessierrPhysics Letters B 469 1999 12–1814

Ž .We can further adapt Eq. 5 to the dynamics we`Ž . Ž .pursue: we introduce r T as the local chemicals

equilibrium abundance of strange quarks, thus rsg r`. We evaluate the equilibrium abundance dN`

s s s`Ž .sd Vr T integrating the Boltzmann distribution:s

3 ms` 3 2w xdN s d VT z K z , zs , 6Ž . Ž .s 22 Tp

where K is the modified Bessel function of order n ;n

w n Ž .x nwe will below use: d z K z rdzsyz K . Then ny1Ž .first factor on the RHS in Eq. 6 is a constant in

time should the evolution of matter after the initialpre-thermal time period t be entropy conserving0w x 3 314 , and thus d VT sd V T s Const. . We now0 0

Ž .substitute in Eq. 5 and obtain

Er E zr dg g K zŽ .s s s s 1`˙q sTr q z , 7Ž .s ž /E t E x dT T K zŽ .2

˙ Ž .where TsdTrdt. Note that in Eq. 7 only a part ofthe usual flow-dilution term is left, since we imple-mented the adiabatic volume expansion, and studythe evolution of the phase space occupancy in lieu ofparticle density. The dynamics of the local tempera-ture is the only quantity we need to model.

We now return to study the collision terms seenŽ .on the RHS of Eq. 2 . A related quantity is the

Ž . 12™ 34L-invariant production rate A of particles perunit time and space, defined usually with respect tochemically equilibrated distributions:

112™ 3412™ 34 ` `² :A ' r r s Õ . 8Ž .T1 2 s 121qd1,2

Ž .The factor 1r 1qd is introduced to compensate1,2

double-counting of identical particle pairs. In termsŽ . Ž . Ž .of the L-invariant A, Eq. 2 and the Eq. 7 , Eq. 2

takes the form:

dg g K zŽ .s s 1`Tr q zs ž /dT T K zŽ .2

2 g g™ ss qq™ sssg t A qg t g t AŽ . Ž . Ž .g q q

ss™ g g ss™ qqyg t g t A qA . 9Ž . Ž . Ž .Ž .s s

Only weak interactions convert quark flavors, thus,Ž . Ž .on hadronic time scale, we have g t sg t .s,q s,q

Moreover, detailed balance, arising from the timereversal symmetry of the microscopic reactions, as-sures that the invariant rates for forwardrbackwardreactions are the same, specifically

A12™ 34 sA34™12 , 10Ž .

and thus:

dg g K zŽ .s s 1`Tr q zs ž /dT T K zŽ .2

2g tŽ .s2 g g™ sssg t A 1yŽ .g 2g tŽ .g

2g tŽ .s2 qq™ ssqg t A 1y . 11Ž . Ž .q 2g tŽ .q

When all g™1, the Boltzmann collision term van-i

ishes, we have reached equilibrium.As discussed, the gluon chemical equilibrium is

thought to be reached at high temperatures wellbefore the strangeness equilibrates chemically, andthus we assume this in what follows, and the initialconditions we will study refer to the time at whichgluons are chemically equilibrated. Setting l s1gŽand without a significant further consequence forwhat follows, since gluons dominate the production

.rate, also l s1 we obtain after a straightforwardq

manipulation the dynamical equation describing theevolution of the local phase space occupancy ofstrangeness:

dg g K zŽ .s s 1 2˙2t T q z s1yg . 12Ž .s sž /dT T K zŽ .2

Here, we defined the relaxation time t of chemicalsŽ .strangeness equilibration as the ratio of the equilib-rium density that is being approached, with the rateat which this occurs:

1 r`

st ' . 13Ž .s g g™ ss qq™ ss2 A qA q . . .Ž .

( )J. Rafelski, J. LetessierrPhysics Letters B 469 1999 12–18 15

The factor 1r2 is introduced by convention in orderfor the quantity t to describe the exponential ap-s

proach to equilibrium.Ž .Eq. 12 is our final analytical result describing

the evolution of phase space occupancy. Since onegenerally expects that g™1 in a monotonic fashions

as function of time, it is important to appreciate thatthis equation allows g )1: when T drops below m ,s s

Žand 1rt becomes small, the dilution term 2nd terms. Ž .on LHS in Eq. 12 dominates the evolution of g .s

In simple terms, the high abundance of strangenessproduced at high temperature over-populates theavailable phase space at lower temperature, when theequilibration rate cannot keep up with the expansioncooling. This behavior of g has been shown in Fig.s

w x2 of Ref. 15 for the SPS conditions with fasttransverse expansion. Since we assume that the dy-namics of transverse expansion of QGP is similar atRHIC as at SPS, we will obtain a rather similarbehavior for g . We note that yet a faster transverses

expansion than considered here could enhance thechemical strangeness anomaly.

Ž . Ž .t T , Eq. 13 , has been evaluated using pQCDsŽcross section and employing NLO next to leading

.order running of both the strange quark mass andw xQCD-coupling constant a 16 . We believe that thiss

method produces a result for a that can be trusteds

down to 1 GeV energy scale which is here relevant.Ž .0We employ results obtained with a M s0.118s Z

Ž .and m 1 GeV s220 MeV, a somewhat conserva-sŽ .tive high choice for m , which should under-pre-s

dict strangeness production. There is some system-atic uncertainty due to the appearance of the strangequark mass as a fixed rather than running value inboth, the chemical equilibrium density r` in Eq.sŽ . Ž .13 , and in the dilution term in Eq. 12 . We use the

Ž .value m 1 GeV , with the energy scale chosen tos

correspond to typical interaction scale in the QGP.Ž .Numerical study of Eq. 12 becomes possible as

soon as we define the temporal evolution of thetemperature for RHIC conditions. We expect that aglobal cylindrical expansion should describe the dy-namics: aside of the longitudinal flow, we allow thecylinder surface to expand given the internal thermalpressure. SPS experience suggests that the transversematter flow will not exceed the sound velocity of

'relativistic matter Õ ,cr 3 . We recall that forHpure longitudinal expansion local entropy density

3 w xscales as SAT A1rt , 14 . It is likely that thetransverse flow of matter will accelerate the drop inentropy density. We thus consider the followingtemporal evolution function of the temperature:

1r31

T t sT .Ž . 0 21qt 2crd 1qt Õ rRŽ . Ž .H H

14Ž .

We take the thickness of the initial collision regionŽ .at T s0.5 GeV to be d T s0.5 r2s0.75 fm, and0 0

the transverse dimension in nearly central Au–Aucollisions to be R s4.5 fm. The time at whichHthermal initial conditions are reached is assumed tobe t s1 fmrc. When we vary T , the temperature0 0

at which the gluon equilibrium is reached, we alsoscale the longitudinal dimension according to:

3d T s 0.5 GeVrT 1.5 fm . 15Ž . Ž . Ž .0 0

This assures that when comparing the different evo-lutions of g we are looking at an initial system thats

has the same entropy content. The reason we varythe initial temperature T down to 300 MeV, main-0

taining the initial entropy content is to understandhow the assumption about the chemical equilibriumof gluons, reached by definition at T , impacts our0

result.Ž .The numerical integration of Eq. 12 is started at

t , and a range of initial temperatures 300FT F0 0

600, varying in steps of 50 MeV. The high limit ofthe temperature we explore exceeds somewhat the

w x‘‘hot glue scenario’’ 10 , while the lower limit of T0

corresponds to the more conservative estimates ofw xpossible initial conditions 14 . Since the initial p–p

collisions also produce strangeness, we take as anestimate of initial abundance a common initial valueŽ .g T s0.2. The time evolution in the plasma phases 0

is followed up to the break-up of QGP. This condi-tion we establish in view of our analysis of the SPSresults. We recall that SPS-analysis showed that thesystem dependent baryon and antibaryon m -slopesHof particle spectra are result of differences in collec-tive flow in the deconfined QGP source at freeze-outw x6 . There is a universality of physical properties ofhadron chemical freeze-out between different SPS

( )J. Rafelski, J. LetessierrPhysics Letters B 469 1999 12–1816

systems, and in our analysis a practical coincidenceof the kinetic freeze-out conditions with the chemicalfreeze-out. We thus expect extrapolating the phaseboundary curve to the small baryochemical poten-tials that the QGP break-up temperature T SPS ,145f

"5 MeV will see just a minor upward change to thevalue T RHIC ,150"5 MeV.f

With the freeze-out condition fixed, one wouldthink that the major uncertainty in our approachcomes from the initial gluon equilibration tempera-ture T , and we now study how different values of0

T influence the final state phase space occupancy.0Ž .We integrate numerically Eq. 12 and present g ass

function of both time t in Fig. 1a, and temperature Tin Fig. 1b, up to the expected QGP breakup atT RHIC ,150"5 MeV. We see that:f

ŽØ widely different initial conditions with similar.initial entropy content lead to rather similar

chemical conditions at chemical freeze-out ofstrangeness

Fig. 1. Evolution of QGP-phase strangeness phase space occu-Ž . Ž .pancy g a as function of time and b as function of tempera-s

ture, see text for details.

Ø despite a series of conservative assumptions wefind not only that strangeness equilibrates, butindeed that the dilution effect allows an overpop-ulation of the strange quark phase space.

For a wide range of initial conditions we obtain aŽ .narrow band 1.18)g T )0.95. We will in thes f

following study of strange baryon and antibaryonabundances adopt what we believe to be the most

Ž .likely value g T s1.15.s f

We now consider how this relatively large valueof g , characteristic for the underlying QGP forma-s

tion and evolution of strangeness, impacts the strangebaryon and anti-baryon observable emerging inhadronization. Remembering that major changescompared to SPS should occur in rapidity spectra ofmesons, baryons and antibaryons, we will apply thesame hadronization model that worked in the analy-

w xsis of the SPS data 6 :1. the QGP freeze-outrbreak-up occurs without a

Ž .significant transient hadronic gas epoch;2. the deconfined QGP state evaporates over a few

fmrc, during which time it remains near to thefreeze-out temperature, with energy lost due toparticle evaporation and work done against thevacuum balanced by the internal energy flows.

This reaction picture can be falsified easily, sincewe expect, based and compared to the Pb–Pb 158 AGeV results:Ž .a shape identity of RHIC m and y spectra ofH

antibaryons p, L, J , since in our approachthere is no difference in their production mecha-nism, and the form of the spectra is determinedin a similar way by the local temperature andflow velocity vector;

Ž .b the m -slopes of these antibaryons should beHvery similar to the result we have from Pb–Pb158 A GeV since only a slight increase in thefreeze-out temperature occurs, and no increase incollective transverse flow is expected.

The abundances of particles produced from QGPwithin this sudden freeze-out model are controlledby several further chemical parameters: the lightquark fugacity 1-l -1.1, value is limited by theq

expected small ratio between baryons and mesonsŽ .baryon-poor plasma when the energy per baryon isabove 100 GeV, strangeness fugacity l ,1 whichs

² :value for locally neutral plasma assures that syss0; the light quark phase space occupancy g ,1.5,q

( )J. Rafelski, J. LetessierrPhysics Letters B 469 1999 12–18 17

Table 1For g s1.15, l s1 and g , l as shown: Top portion:s s q q

w xstrangeness per baryon sr b, energy per baryon Er b GeV andentropy per baryon Sr b. Bottom portion: sample of hadron ratiosexpected at RHIC

g 1.25 1.5 1.5 1.5 1.60q

l 1.03 1.025 1.03 1.035 1.03q

w xEr b GeV 117 133 111 96 110sr b 17 15 12 11 11Sr b 623 693 579 497 567

pr p 1.19 1.15 1.19 1.22 1.19Lr p 1.61 1.35 1.35 1.34 1.25

Lr p 1.71 1.41 1.42 1.43 1.33

LrL 0.89 0.91 0.89 0.87 0.89J rL 0.17 0.146 0.145 0.145 0.13

J rL 0.18 0.15 0.15 0.15 0.14

J rJ 0.94 0.95 0.94 0.93 0.94V rJ 0.135 0.114 0.113 0.112 0.106

V rJ 0.144 0.119 0.120 0.121 0.113

V rV 1 1. 1. 1. 1.

Ž . Ž .V q V r J q J 0.14 0.12 0.12 0.12 0.11

Ž . Ž .J q J r Lq L 0.18 0.15 0.15 0.15 0.14q yK rK 1.05 1.04 1.05 1.06 1.05

overabundance value due to gluon fragmentation.Given these narrow ranges of chemical parametersand the freeze-out temperature T s150 MeV, wef

compute the expected particle production at break-up.In general we cannot expect that the absolute num-bers of particles we find are correct, as we have notmodeled the important effect of flow in the labora-tory frame of reference. However, ratios of hadrons

Ž .subject to similar flow effects compatible hadronscan be independent of the detailed final state dynam-

w xics, as the results seen at SPS suggest 6 , and wewill look at such ratios more closely.

Taking g s1.25, 1.5, 1.6 we choose the value ofq

l , see the header of Table 1, for which the energyq

Ž .per baryon Erb is similar to the collision conditionŽ .100 GeV , which leads here to the range l s1.03q

"0.005. We evaluate for these examples aside ofErb, the strangeness per baryon srb and entropyper baryon Srb as shown in the top section of the

² :Table 1. We do not enforce sys s0 exactly, butsince baryon asymmetry is small, strangeness is bal-anced to better than 2% in the parameter rangeconsidered. In the bottom portion of Table 1 wepresent the compatible particle abundance ratios,computed according to the procedure developed in

w xRef. 6 . We have presented aside of the baryon andantibaryon relative yields also the relative kaon yield,which is also well determined within our approach.

The meaning of these results can be better appre-ciated when we assume in an example the central

<rapidity density of protons is dprdy s25. Incentral

Ž .Table 2 we present the resulting anti baryon abun-dances. We see that the net baryon density dbrdy,15"2, there is baryon number transparency. We see

Ž .that anti hyperons are indeed more abundant thanŽ .non-strange anti baryons. It is important when quot-

ing results from Table 2 to recall that:1. we have chosen arbitrarily the overall normaliza-

tion in Table 2, only particle ratios were com-puted, and

2. the rapidity baryon density relation to rapidityproton density is a consequence of the assumedvalue of l , which we chose to get Erb,q

100 GeV per participant.However, we firmly believe that our key result

seen in Table 2, the hyperon-dominance of the baryonyields, does not depend on these hypothesis. Indeed,we have explored another set of parameters in our

w xfirst and preliminary report on this matter 17 , find-ing the same primary conclusion explained in theintroduction. Another related notable result, seen inTable 1, is that strangeness yield per participant is

Table 2< <dNrdy assuming in this example dprdy s25central central

0 0 " "g , l b p p LqS LqS S S J J VsVq q

)1.25, 1.03 16 25 21 40 36 28 25 14 13 0.9)1.5, 1.025 13 25 22 34 31 24 21 11 9.4 0.6)1.5, 1.03 15 25 21 34 30 24 21 9.8 9.2 0.6)1.5, 1.035 17 25 21 33 29 23 20 9.6 9.0 0.5)1.60, 1.03 14 25 21 31 28 22 19 8.6 8.0 0.5

( )J. Rafelski, J. LetessierrPhysics Letters B 469 1999 12–1818

13–23 times greater than seen at present at SPSenergies, where we have 0.75 strange quark pairs perbaryon. As seen in Table 2 the baryon rapiditydensity is in our examples similar to the protonrapidity density.

In summary, we have shown that one can expectstrangeness chemical equilibration in nuclear colli-sions at RHIC if the deconfined QGP is formed, witha probable overpopulation effect associated with theearly strangeness abundance freeze-out beforehadronization. We studied the physical conditions at

Ž .QGP breakup and have shown that anti hyperonsŽ .dominate anti baryon abundance.

Acknowledgements

This work was supported in part by a grant fromthe U.S. Department of Energy, DE-FG03-95OR40937. LPTHE, Univ. Paris 6 et 7 is: Unitemixte de Recherche du CNRS, UMR7589.

References

w x Ž .1 J. Rafelski, B. Muller, Phys. Rev. Lett. 48 1982 1066; 56¨Ž .1986 2334E; P. Koch, B. Muller, J. Rafelski, Z. Phys. A¨

Ž .324 1986 453.w x2 T. Matsui, B. Svetitsky, L.D. McLerran, Phys. Rev. D 34

Ž .1986 783, 2047.w x3 N. Bilic, J. Cleymans, I. Dadic, D. Hislop, Phys. Rev. C 52

Ž .1995 401.

w x4 J. Rafelski, J. Letessier, A. Tounsi, Acta Phys. Pol. B 27Ž .1996 1037.

w x5 Proposal for a Silicon Strip Detector for STAR a SUBAT-ECH-Nantes, France led STAR project. Compare also STARcollaboration web page: http:rrwww.star.bnl.govrstarrstarlibr docrwwwrhtmlrstrange_lrstrange.html.

w x6 J. Rafelski, J. Letessier, Hadrons from Pb–Pb collisions at158 A GeV, nucl-thr9903018; J. Letessier, J. Rafelski, Phys.

Ž . Ž .Rev. C 59 1999 947; Acta Phys. Pol. B 30 1999 153; J.Ž .Phys. G 25 1999 295.

w x7 T.S. Biro, E. van Doorn, B. Muller, M.H. Thoma, X.-N.´ ¨Ž .Wang, Phys. Rev. C 48 1993 1275.

w x Ž . Ž .8 S.M.H. Wong, Phys. Rev. C 54 1996 2588; C 56 19961075, and references therein.

w x9 D.K. Srivastava, M.G. Mustafa, B. Muller, Phys. Lett. B 396¨Ž . Ž .1997 45; Phys. Rev. C 56 1997 1054.

w x Ž .10 E. Shuryak, Phys. Rev. Lett. 68 1992 3270.w x Ž .11 J.-e Alam, S. Raha, B. Sinha, Phys. Rev. Lett. 73 1994

1895; P. Roy, J.-e Alam, S. Sarkar, B. Sinha, S. Raha, Nucl.Ž .Phys. A 624 1997 687.

w x Ž .12 S.M.H. Wong, Phys. Rev. C 56 1997 1075.w x13 The conventional Eulerian formulation of Hydrodynamics

and its relation to the Lagrangian description here required isdiscussed in older texts such as: H. Lamb, Hydrodynamics,Dover Publications, New York, reprint of Cambridge Univer-sity Press 6th edition, 1932.

w x Ž .14 J.D. Bjorken, Phys. Rev. D 27 1983 140.w x Ž .15 J. Letessier, A. Tounsi, J. Rafelski, Phys. Lett. B 390 1997

363.w x16 J. Rafelski, J. Letessier, A. Tounsi, APH N.S., Heavy Ion

Ž .Physics 4 1996 181; J. Letessier, J. Rafelski, A. Tounsi,Ž .Phys. Lett. B 389 1996 586.

w x17 http:rrwww.qm99.to.infn.itrprogramrqmprogram.htmlPresentation on Friday, May 24, 1999 at 11:25AM by J.Rafelski; to appear in proceedings of Quark Matter 1999,Torino, Italy, within a group report Last call for RHICpredictions; S. Bass et al., nucl-thr9907090.