arXiv:hep-ph/0009170v1 14 Sep 2000

1

T he Little Bang: Searching for quark-gluon m atterin relativistic heavy-ion collisions U lrich H einz T heoreticalPhysics D ivision,C ER N ,C H -1211 G eneva 23,Sw itzerland Ireview the status ofthe search for quark-gluon plasm a in relativistic heavy-ion collisions. T he available data provide strong evidence forthe "three pillarsofthe Little Bang m odel":strong radialexpansion ofthe collision reballw ith H ubble-like scaling,therm al hadron em ission and prim ordialhadrosynthesis. It is argued that the initialstate ofthe reaction zone exhibits features w hich cannot be understood w ith conventionalhadronic dynam ics,but are consistent w ith the form ation ofdecon ned quark-gluon m atter. 1. P R O LO G U E O n Feb. 10, 2000, C ER N announced o cially [1] that (I paraphrase) \com pelling evidence now existsfortheform ation ofa new stateofm atteratenergy densitiesabout20 tim eslargerthan thatin thecenterofatom icnucleiand tem peraturesabout100000 tim es higher than in the center ofthe sun. T his state exhibits characteristic properties w hich cannot be understood w ith conventionalhadronic dynam ics but w hich are qualitatively consistent w ith expectationsfrom the form ation ofa state ofm atterin w hich quarks and gluonsno longerfeeltheconstraintsofcolorcon nem ent." Iw illhereexplain thescienti c argum ents [2]w hich led to this conclusion. T he announcem ent was not triggered by a single experim entaldiscovery w hich had just happened,but em erged from a painstaking analysis of m any di erent sets of data collected during 15 years of heavy-ion collision experim ents at the C ER N SPS,especially ofresults obtained during the last ve years w ith the 158A G eV /c 207Pb beam and reported over the last 24 m onths [3]. It happened at a tim e w hen the R elativistic H eavy Ion C ollider R H IC at BN L was about to turn on and C ER N wastaking stock ofw hathad been achieved so farw ith the up to then highest energy heavy-ion beam s available. T he announcem ent gave credit to the achievem ents of an internationalcom m unity ofalm ost 500 enthusiastic physicists from allover the world w ho had initiated and driven to successthe heavy-ion program atC ER N ,participating in seven large and severalsm aller experim ents w ith com plem entary goals in orderto search for the creation ofthe theoretically predicted \quark-gluon plasm a" (Q G P) in heavy-ion collisions. T he reaction ofthe internationalpress to this announcem ent was very strong but the reports were not always accurate. Severalstated that C ER N had claim ed the \discovery ofquark-gluon plasm a". T hiswasnottrue:T he C ER N pressrelease [1]and the scienti c O n leavefrom InstitutfurT heoretischePhysik,U niversitatR egensburg,D -93040 R egensburg,G erm any. W ork supported in part by D FG ,G SI,and B M B F.Em ailaddress: [email protected]

2 docum ent on w hich it was based [2] had been form ulated very carefully and m ade a clear and conscious distinction between \evidence for a new state ofm atter" (w hich we claim ed) and \discovery ofQ G P" (w hich we didn’t). Iw illalso report on the rem aining open questions,trying to pointout(asIdid in m y talk on Feb. 10 [4])w hatis needed to turn the present evidence into incontrovertible proof. Severalcrucialissues can only be resolved by heavy-ion experim ents at the higher energies provided by R H IC and LH C .

2. T H E Q U A R K -H A D R O N T R A N SIT IO N

temperature T [MeV]

T he Q C D phase diagram [5]features a transition from a gas of hadronic resonances (H G ) at low energy densities to a quark-gluon plasm a (Q G P) at high energy densities. T he criticalenergy density c is ofthe order of1G eV /fm 3 . It can be reached by either heating m atter at zero net baryon density to a tem perature ofabout Tc 170M eV ,or by com pressing cold nuclear m atter to baryon densities ofabout c 3 10 0 (w here 3 is the equilibrium density),or by com binations thereof. A sim ple version 0 = 0:15fm ofthe phase diagram is show n in Figure1. Figure 1. Sketch ofthe Q C D phase diagram , tem perature T vs. the early universe baryon chem ical potential B assoLHC ciated w ith net baryon density B . quark-gluon RHIC plasma T he cross-hatched region indicates the expected phase transition and 250 its present theoretical uncertainty, w ith the dashed line representing its m ost likely location. Lines w ith ar200 SPS row s indicate expansion trajectories chemical freeze-out oftherm alized m attercreated in dif150 AGS ferent environm ents. (T he lines ladeconfinement belled \R H IC ", \LH C " and \early 100 chiral restoration universe" should be m uch closer to SIS thermal freeze-out thetem peratureaxisbutwould then 50 have been di cult to draw .) For a hadron gas atomic discussion ofthe chem icaland therneutron stars nuclei m alfreeze-outlinesand the location 0.2 0.4 0.6 0.8 1 1.2 1.4 ofthe data points see text. baryonic chemical potential µ [GeV] B

By colliding heavy ions at high energies, one hopes to heat and com press hadronic m atter to energy densities above c. A t lower beam energies (SIS @ 1A G eV /c), the nuclei are stopped and the nuclear m atter is com pressed and m oderately heated. A t higherbeam energiesonereacheshighertem peratures,butsincethecolliding nucleiareno longercom pletely stopped,the baryon chem icalpotentialofthe m attercreated atrestin the center-of-m om entum system decr p SPS @ 160A G eV /c). p eases(A G S @ 10A G eV /cand A t the heavy ion colliders R H IC ( s = 200A G eV ) and LH C ( s = 5500A G eV ) the baryon chem icalpotentialofthe reaction reballisso sm allthatone essentially sim ulates baryon-free hadronic m atter,very m uch like the expanding early universe. Ifthe m atter

3 therm alizes quickly at energy densities above c,it w illpass through the quark-hadron phase transition as the collision reballexpands and cools. A long the tem perature axis at B = 0 our know ledge of the Q C D phase diagram is based on hard theory (lattice Q C D ), but for nonzero baryon density we m ust rely on m odels interpolating between low -density hadronic m atter, described by low -energy e ective theories,and high-density quark-gluon plasm a,described by perturbative Q C D . T he theoreticaluncertainties at high-baryon densities are thus di cult to quantify and relatively large (typically O (30 50% )). A t zero baryon density,the situation is m uch cleaner:num ericalsim ulationsofQ C D w ith 3 dynam icallightquark avorson the lattice are now available,and the system atic errors due to lattice discretization and continuum extrapolation are controllable and beginning to getsm all[6].T he criticaltem perature Tc for real-life Q C D is predicted as Tc 170M eV 15% [6,7]. N ear Tc the energy density in units of T 4 changes dram atically by m ore than a factor of 10 w ithin a very narrow tem perature interval(see Figure 2). A bove T ’ 1:2Tc, =T4 appears to settle at about 80% ofthe Stefan-Boltzm ann value foran idealgasofnon-interacting quarksand gluons. T (MeV) 170 210 250

340

510

16

680

εSB / T4

14

ε / T4

12

6.3 4.3 2.9 1.8

10

RHIC

LHC

8 0.6 GeV / fm3 = εc

6 4 2 0

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Figure 2. Energy density in units of T 4 for Q C D w ith 3 dynam icallight quark avors, extrapolated to zero quark m ass and to the continuum [7]. For two m assless light and one m assive strange quark avor the energy density decreasesby 15% [7]. T helowerhorizontalaxisgivesT=Tc, theupperoneconvertsT to M eV using Tc = 170M eV .For various values ofT absolute values for the energy density in G eV /fm3 are indicated,using the sam e Tc.

T / Tc

A ccording to Figure2 only about 600 M eV /fm 3 ofenergy density are needed to m ake the transition to decon ned quark-gluon m atter. It is,however,very expensive to reach tem peratures well above Tc: an initial tem perature of 220 M eV , about 30% above Tc, already requires an initialenergy density ’ 3:5G eV /fm3 , about 6 tim es the critical value.W e w illsee thatthisseverely lim itsthe reach ofthe C ER N SPS into the new Q G P phase: only the region at and slightly above Tc can be probed. W e are \living at the edge" (W .Zajc)! To really penetrate deep into the new phase requires the m uch higher energy densities w hich becom e accessible w ith the heavy-ion colliders R H IC and LH C . A t Tc two phenom ena happen sim ultaneously [8]: color con nem ent is broken, i.e. colored degrees offreedom can propagate over distances m uch larger than the size ofa hadron,and the approxim ate chiralsym m etry of Q C D ,w hich is spontaneously broken at low tem peratures and densities,gets restored. Both e ects are im portant since they signi cantly accelerate particle production: the liberation of gluons in large densities opens up new gluonic production channels, and the threshold for quark-antiquark pair

4 production islowered sincethequarksshed a largefraction oftheirconstituentm assw hich is dynam ically generated by their interaction w ith the quark condensate characterizing the spontaneously broken chiralsym m etry at low densities. M uch less im portant for the dynam ics of heavy-ion collisions is the actual order of the phase transition: depending on the value ofthe strange quark m ass,existing lattice calculations allow for anything between a sm ooth crossover, sim ilar to the one seen in Figure 2, and a weakly rst order transition w ith a latent heat w hich is sm all on the vertical scale of Figure 2. T he resulting di erences in the dynam ical evolution of the expanding reballarealm ostcertainly unm easurable,exceptifthephasediagram features a criticalpoint and the experim ents pass close to it [5]. 3. R E C O N ST R U C T IN G T H E LIT T LE B A N G A s the two nuclei hit each other w ith fullspeed, a superposition of nucleon-nucleon (N N ) collisions occurs. W hat is di erent com pared to individual N N collisions is that (i) each nucleon m ay scatter severaltim es,and (ii) the liberated partons from di erent N N collisions rescatter w ith each other even before hadronization,as do the secondary hadrons produced in di erent N N collision. Both features change the particle production per participating nucleon.But only the rescattering processes can lead to a state oflocal therm alequilibrium ,by redistributing the energy lost by the beam s into the statistically m ostprobablecon guration.T heserescatteringsresultin therm odynam icpressure acting againstthe outside vacuum w hich causesthereaction zone to expand collectively. T he expansion coolsand dilutesthe reballbelow the criticalenergy density ofthe quark-hadron transition,atw hich pointhadronsareform ed from thequarksand gluons(hadronization). Furtherinteractions between these hadronscease once theiraverage distance exceeds the range ofthe strong interactions: the hadrons \freeze out". T he strong interactions am ong the partons and hadrons before freeze-out w ipe out m ost inform ation about their originalproduction processes. T he extraction ofinform ation about the interesting hot and dense early collision stage thus requires to exploit features w hich are either established early and not changed by the rescattering and collective expansion orcan be reliably back-extrapolated. C orrespondingly one classi es the observables into two classes,early and late signatures. (A com prehensive review ofQ G P signatures w ith a com plete list ofreferences can be found in [9].) T he conceptually cleanest early signatures are the directly produced realand virtual photons(i.e. notthose resulting from hadron decays afterfreeze-out)since photonsshow no strong interaction and directly escape from the reball(virtualphotonsm aterialize as e+ e or + pairs).T hey are em itted throughoutthe expansion,buttheirproduction is expected to be strongly weighted towardsthe hotand dense initialstages. U nfortunately, direct photons are rare,and the experim entalbackground from hadronic decay photons after freeze-out is enorm ous. A notherearly signature arehadronsm ade ofcharm ed quarks. A tSPS energies,ccpairs can only becreated in theprim ary N N collisions,becausethesecondary scatteringsarenot energetic enough to overcom e the cc threshold. T he only thing that can happen to them is a redistribution in phase-space,changing the relative am ounts ofm esons w ith hidden (cc charm onium ) and open charm (cq and qc). Itwas show n thatsuch a redistribution is

5 m uch easierin the color-decon ned Q G P phase than by reinteraction ofcharm ed particles w ith otherhadrons;in thisway charm -redistribution becom esalso an early signature.But also charm production is a very rare process at SPS energies and below . H adronsm ade ofup,dow n and strange quarks,w hich can be relatively easily produced and destroyed in allstages ofthe reballexpansion (I’llslightly qualify this statem ent further below w ith regard to strange hadrons), are late signatures. T hey provide only indirectinform ation aboutthe early collision stages.Butthey arevery abundant,form ing m orethan 99.99% ofallem itted particles,and can thusbem easured very accurately.W e’ll thus use these late signals to reconstruct the Little Bang and then check the consistency ofthe resulting picture w ith the less detailed direct inform ation from the early signals. I would like to note that this procedure is quite analogous to the reconstruction of the cosm ologicalBig Bang from observations. T he three observationalpillars ofthe Big Bang theory are the H ubble expansion (w hich goeson untiltoday),the cosm ic m icrowave background oftherm alphotons (w hich decoupled w hen our universe was about 300,000 yearsold),and the m easured abundancesoflightatom ic nuclei(w hich re ectthe prim ordialnucleosynthesis untilabout3 m inutes afterthe Big Bang).A lm osteverything before thattim e is based on a theoreticalback-extrapolation using Einstein’s equations and the Standard M odelofparticle physicsand noton directastrophysicalobservations.T heonly exception is the observed baryon num ber asym m etry w hich was presum ably established very early but w hich is stillnot entirely understood. 4. IN IT IA L C O N D IT IO N S Before starting to analyze the nalfreeze-outstage ofthe collision using the late signatures,it is usefulto get an idea aboutthe globalconditions ofthe reballform ed shortly after im pact. Follow ing Bjorken [10]it is possible to estim ate the initially produced energy density by m easuring the totaltransverse energy E T (excluding the fraction due to m otion along the beam direction) and putting it into an estim ated initialvolum e ofthe reaction zone. A ssum ing boost-invariant longitudinal expansion (w hich is expected to hold athigh energies [10]and forw hich evidence exists in the m idrapidity region even at SPS energies [11]) we can identify the space-tim e rapidity = 0:5ln[(t+ z)=(t z)]w ith the m om entum -space rapidity y = 0:5ln[(E + pz)=(E pz)]and w rite [10] B j( 0)=

1 1 dE T : 2 R rm s 2 0 dy

(1)

2 2 Inserting R rm s = 63fm for the overlap area oftwo Pb nucleicolliding at zero im pact param eter,choosing 0 = 1fm /cto evaluatethelength 2 dy = 2 d ofa sliceofa cylinder ofw idth d at m idrapidity y = = 0,and using dET =dy(y = 0) 400G eV for central Pb+ Pb collisions [12](\very" centralcollisions even give up to 10% m ore) one obtains P b+ P b (1fm Bj

=c)= 3:2

0:3G eV =fm 3 :

(2)

A s Q G P searchers we thus play in the right ball-park; if the m atter were already therm alized after1fm /c(w hich atthispointwe don’tknow yet),Figure2 tellsusthatthe initialtem perature would have been T0 ’ 210 220M eV .Sim ilar initialenergy densities are obtained from a detailed phase-space analysis ofthe hadronic freeze-out state after

6 back-extrapolation to the tim e before the onset of transverse expansion [13]. Perhaps m ore im portantly,initialenergy densities between 2 and 10G eV /fm 3 during the rst 1-2 fm /c are obtained [14] even in approaches w hich avoid quarks and gluons as relevant degrees of freedom , like the U RQ M D code w hich uses hadronic strings and resonances to describe particle production and rescattering and is tuned to N N data. Indeed, for Pb+ Pb collisionsatthe SPS,U RQ M D predictsthatthe prehadronic com ponent(strings) dom inatesoverthe produced hadronsfornearly 8 fm /c [14]!T hisfurtherstrengthensour expectation to see new physics at the SPS. 5. T H E R M A L F R E E ZE -O U T :A N E X P LO D IN G T H E R M A L F IR E B A LL T he m easured hadron spectra contain two pieces of inform ation: (i) T heir norm alization, i.e. the yields and abundance ratios, provides the chem ical com position of the reballat the \chem icalfreeze-out" point (i.e. w hen the hadron abundances freeze out); this yields inform ation in particular about the degree of chem ical equilibration, to be discussed in Section 7. (ii) T he hadronic m om entum spectra provide inform ation about therm alization ofthe m om entum distributionsand collective ow .T he latteriscaused by therm odynam ic pressure (resulting from intense rescattering am ong the consituents) and thus re ects,in a tim e-integrated way,the equation ofstate ofthe reballm atter. T he expansion rate at \therm alfreeze-out" (i.e. along the last-scattering hypersurface w hich m arks the decoupling ofthe m om enta) provides the Little Bang analogue ofthe H ubble constant for the Big Bang,w hile the corresponding freeze-out tem perature parallels the tem perature ofthe cosm ic m icrowave background at the point ofphoton decoupling. A s in cosm ology,w here the photon tem perature is a ected by the H ubble expansion and red-shifted from originally 3000 K to 2.7 K today,the hadronic m om entum spectra are a ected by the collective expansion of the collision reball. O nly in this case the expansion occursin threedim ensions,and the reballisobserved from outside,resulting in a blue-shiftoftheapparenttem peratureofthespectra.Sincethelongitudinalexpansion is am biguousin thatitisdi cultto assessw hich fraction ofthe nally observed longitudinal ow is generated by hydrodynam ic pressure and how m uch is a result of incom plete stopping oftqhe two nuclei,we concentrate on transverse ow ,re ected in the transverse m ass (m ? = m 2+ p2? ) spectra. T his type of ow is only created after im pact. R oughly,ifrescattering am ong the reballconstituents results in therm alization and collective ow , the shapes ofallhadronic m ? -spectra can be characterized by just two num bers: the tem perature Tf and the m ean transverse ow velocity hv? i at freeze-out. M oreexactly,thisisonly trueifallhadronsdecouplesim ultaneously (i.e.theirrescattering cross sections are sim ilar),and the form in w hich the spectra are characterized by hv? i m ay depend on the ow velocity and density pro les. For this presentation Iw illneglect the latter subtlety;the form er can be checked experim entally. In the relativistic region,i.e. for m ? > 2m 0,the rest m asses can be neglected,and the e ect of ow on the spectra is given by the sim ple blue-shift form ula [15] v u u t

Tslope = Tf

1 + hv? i : 1 hv? i

(3)

A t large m ? allhadron spectra should have the sam e inverse slope Tslope (this tests ther-

7 m alization) but m easuring it does not allow to separate therm alfrom collective m otion. In the nonrelativistic region m ? < 2m 0,on the other, ow doescouple to the restm ass: for a linear transverse ow velocity pro le and a G aussian transverse density pro le one nds exactly [16,17] Tslope = Tf + 21 m 0hv? i2 :

(4)

T (GeV)

Such an approxim ately linearrestm assdependence isindeed observed. Figure 3 show s clearly that the spectra contain a collective ow com ponent;inverse slopes of300 M eV or m ore as seen e.g. for the protons can obviously not be interpreted as hadronic tem peratures (see Figures 1 and 2). T here is som e scatter between the data from di erent experim ents, partly due to di erent kinem atic regions for tting the slope. T he pion spectra are particularly troublesom e due to the strong deform ation at low m ? from resonance decay contributions and C oulom b e ects. Strictly speaking,the pions should not be included in this plot since they are never non-relativistic in the accessible region. 0.5 NA 49 NA 44 0.4

φ

0.3

p 

p

+

K

0.2

π

0.1

0

+

π

-

Figure 3. Inverse slopes T Tslope of the m easured m ? -distributions from 158 A G eV /c Pb+ Pb collisions for various hadron species, plotted against their rest m ass [18]. R esults from di erent experim ents are labelled by di erent sym bols. T he line is described in [18].

d

WA 97

Λ

Ξ

-



Λ

+

Ξ

+

Ω +Ω -

0 KS -

K

0.5

1

1.5

2

2

m (GeV/c )

T he deuterons don’t really belong here either: they are too fragile to be considered partofthe equilibrium ensem ble. In the therm alstate they are continually broken up by collisions,re-form ing only atfreeze-outby coalescence ofprotonsand neutrons.T hatthey tinto the system aticsofFigure 3 israthera testofthe coalescence m echanism by w hich the deuterons inherit the tem perature and ow from their parent nucleons [17]. In fact, the way they tm akesan im portantstatem entaboutthe transverse pro le ofthe reball at freeze-out: for a G aussian density distribution the deuteron slope should be identical to thatoftheparentnucleons,w hereasthe observed largerinverse deuteron sloperequires a m ore box-like density distribution,w ith m ore weight at larger ow velocities [17,19]. A n interesting exception to thetrend isprovided by the :it’sspectrum isconsiderably steeper.T hisre ectstheirearlierkineticfreeze-out,dueto an absence ofstrong scattering resonances w ith the dom inating pion uid [20] w hich are essential for the kinetic reequilibration ofthe other hadron species. A fter allthese caveats it is clear that a very accurate determ ination ofhv? i from the slopein Figure3 aloneisnotpossible.Buttransverse ow also a ectsotherobservables,in particulartwo-particlecorrelationsin m om entum space,likethequantum statisticalBoseEinstein (H anbury Brow n-T w iss)correlationsbetween identicalbosons,orthecorrelations

8 due to \soft" nalstate interactionsam ong the particlesaftertheirlast\hard" scattering w hich e.g.causethecoalescenceoftwo nucleonsinto a deuteron.In both casescorrelations occur only between particles w hich are close in phase-space;by m easuring the w idth of the correlation in m om entum space one can thus estim ate the size ofthe em itting source in coordinate space. C ollective expansion tends to reduce the size ofthe regions w ithin w hich partiqcles can develop such correlations;therm alm otion,controlled by the therm al velocity T=M ? ,sm ears out the ow velocity gradients and thus acts in the opposite direction. T his leads to a characteristic dependence ofthe size ofthe e ective em ission region for correlated pairs on their transverse m ass M ? ;its transverse size is controlled by the transverse ow velocity,hv? i as show n by the approxim ate form ula [21,16,17] R ?2

1+

R2 : hv? i2(M ? =Tf)

(5)

H ere = O (1)isa m odel-dependentfactorw hich dependson the ow velocity and density pro les,and R characterizes the geom etric transverse size ofthe reballat freeze-out. T he form ula (5) predicts that the e ective radius R ? extracted from the correlations scales only w ith the transverse m ass M ? of the particle pair, irrespective of the rest m asses ofthe individualparticles. T his isborne outby experim ent,see Figure4. Sim ilar results, consistent w ith those show n in Figure 4, were obtained by the N A 49 [11]and N A 52 collaborations [22]. PbPb Radii versus Transverse Mass 2

HBT (RS RL) 2 p /d Rg pp HBT Rg

7

ππ

5

ππ

2

p /d

4 3

kk

2

kk R=3.7/mT.29±.04 2 χ /ndf=4.4/5

1 0

pp

NA44 Preliminary

Radius Parameter (fm)

6

1/3

0

0.2

M. Murray QM 99

0.4

0.6

0.8

1

mT (GeV/c)

1.2

1.4

1.6

Figure 4. E ective radius R e of theem ission region extracted from and K K Bose-Einstein (H BT ) correlations,from pp nalstateinteraction correlations and from the deuteron coalescence probability d=p2, as a function ofthetransverse m assM T M ? of the particle pair. T he H BT correlations were analyzed in 3 dim ensions,and R e wasde ned by the geom etric m ean ofthe two transverse and the longitudinalsize param eters, R e = (R ?2 R k)1=3 (R s2R L )1=3. (Figure taken from [23].)

W hile Eq.(5)does notperm it to separate Tf from hv? ieither,the correlation between the two param etersin (5)isexactly opposite to thatprovided by the spectralslopesin (3) and (4). C om bining them in a sim ultaneous analysis ofspectra and correlations [11,24] (see Figure 5) allow s for a rather accurate separation ofdirected collective and random therm alm otion,yielding Tf 100M eV and hv? i 0:55c. T he corresponding therm al energy density is only about f 0:05G eV /fm 3 . Even w hen the kinetic ow energy is added this stillim plies an expansion ofthe reballvolum e by a factor 40 from 0 to f. H BT m easurem ents show that the transverse area grow s by a factor4{5,consistent w ith

9 the large transverse expansion velocity hv? i[24];the rem aing factor8{10 m ustcom e from longitudinalgrow th. 0.8

90%

0.6

0.7 set b1 ✛

0.6 0.5

50 % 90% %

99

l

ηf

0.5 set b2 ✛

0.4 v⊥

set b3 ✛

0.4 50%

0.3 %

%

90

50

0.3

99

%

0.2

BOX 0.08

10%

0.1

5%

0.12 T (GeV)

0.14

0.16

0.2

2 Figure 5. contours for the t of the m easured H BT radius param eters from Bose-Einstein correlations [11] (w idely spaced contours) and ofthe negative particle spectrum [25](narrow ly spaced contours)in the rapidity w indow 3:9 < Ylab < 4:4 from 158 A G eV /c Pb+ Pb collisions. T he best ts require freeze-out tem peratures slightly below 100M eV and average transverse expansion velocities ofabout 0.55c.Fordetails the reader should referto [24]from w herethis gure was taken.

6. T H E M ISSIN G R H O :O B SE R V IN G T H E R M A LIZA T IO N A T W O R K W ith strong experim entalevidencethattheLittleBang started outatan energy density above3G eV /fm 3 ,butonly decoupled atabout50M eV /fm 3,wem ay ask:how can we nd outw hathappened in between? H ere the m eson can provide a rstanswer:itcan decay into e+ e or + pairs w hich escape from the reballw ithout further interactions,and this -decay clock ticks at a rate of1.3fm /c,the naturallifetim e ofthe . W hat Im ean by this is that after one generation of ’s has decayed, a second generation is created by resonant scattering, w hich can again decay into dileptons, etc. T he num ber of extra dileptons w ith the invariant m ass ofthe is thus a m easure for the tim e in w hich the reballconsistsofstrongly interacting hadrons[26].O bviously, m esonsdo notexist beforehadronsappearin the reball,so they won’ttellusanything abouta possible Q G P phase in its initialstages. But they stillallow us to look inside the strongly interacting hadronic reballat a later stage,stilllong before the hadrons decouple. T he experim entalcheck ofthis conjecture yields a surprise: w hen the C ER ES/N A 45 collaboration looked at the e+ e spectrum in 158A G eV /c Pb+ A u collisions (see Figure 6),they could not nd the atall!Sure,there were extra e+ e pairsin the m assregion of the and below (about2.5{3 tim esasm any asexpected),butinstead ofa nice -peak at m = 770M eV one ndsonly a broad sm ear[27].M any explanationsoftheC ER ES-e ect have been proposed,but the sim plest one consistent w ith the data (for a review see [28]) is collision broadening: there is strong rescattering of the pions, not only am ong each other,but also w ith the baryons in the hadronic resonance gas,and this m odi es their spectraldensities and,asa consequence,leadsto a sm earing ofthe -resonance in the scattering cross section. T hisdem onstratesthat,after rstbeing form ed in the hadronization process,the pions (them ostabundantspeciesattheSPS)undergo intenserescattering before nally freezing out. A nd this again is the m echanism w hich allow s the reballto reach and m aintain a

10

10

10

-5

CERES/NA45

Pb-Au 158 A GeV

95 data

σtrig/σtot ~ 30 / 35 %

96 data

p⊥ > 200 MeV/c Θee > 35 mrad

-6

2.1 < η < 2.65 〈Nch〉 = 250 / 220

η→ eeγ

-7

ω→

ρ/ω → ee

10

eeπ o

10

-8

πo → eeγ

10

η ,→

φ → ee

2

(d Nee /dηdmee) / (dNch /dη) (100 MeV/c )

2 -1

state ofapproxim ate localtherm alequilibrium ,to build up therm odynam ic pressure and to collectively explode,as seen from the above analysis ofthe freeze-out stage. T hat the dileptons from collision-broadened ’s outnum ber those from the decay ofunm odi ed ’s em itted attherm alfreeze-out(w hich should show up asa norm al -peak)show s thatthe hadronic rescattering stage m ust have lasted several lifetim es.

eeγ

-9

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2

mee (GeV/c )

Figure 6. Invariant m ass spectrum of e+ e pairs from 158A G eV /c Pb+ A u collisions [27]. T he solid line is the expected spectrum (the sum ofthe m any show n contributions) from the decays ofhadrons produced in pp and pA collisions (w here it was experim entally con rm ed [27]),properly scaled to the Pb+ A u case. T wo sets of data w ith di erentanalysesare show n. N ote that the -peak reappearsifonly e+ e pairs w ith p? > 500M eV /c are selected [27]; such fast ’s escape quickly from the reballand are notasstrongly a ected by collision broadening.

7. SE E IN G T H E Q U A R K -H A D R O N T R A N SIT IO N In the rest ofthis talk I w illconcentrate on observables w hich in heavy-ion collisions were found to be drastically di erentfrom N N collisionsbutw hich we now believe cannot be changed quickly enough by hadronic rescattering during the tim e available between hadronization and kinetic freeze-out. O bservables for w hich this last property can be rm ly established yield insightsaboutw here heavy-ion collisionsdi erfrom N N collisions already before or during hadronization,irrespective w hether ornotthe hadrons rescatter w ith each other after being form ed. O fcourse,the form ation ofa quark-gluon plasm a isone possibility how the early stage ofa heavy-ion collision m ay di er from that in a N N collision. It is thus im portant to review a few key Q G P predictions and check how they fare in com parison w ith the data. In the present Section Idiscuss strangeness enhancem entas a Q G P signature,returning to two further Q G P predictions in the follow ing two Sections. Strangeness enhancem ent and chem icalequilibration was one ofthe earliest predicted Q G P signatures [29]. T he idea is sim ple: color decon nem ent leads to a large gluon density w hich can create ss pairsby gluon fusion,and chiralsym m etry restoration m akes thestrangequarksrelatively light,thusreducing theproduction threshold (notto m ention thatin theQ G P strangequarkscan becreated w ithouttheneed foradditionallightquarks to m ake a hadron). T he two e ects together should cause a signi cant reduction ofthe tim e scale for strangeness saturation and chem icalequilibration, com pared to hadronic rescattering processes after hadronization w here the production ofstrange hadron pairs w ith oppositestrangenessissuppressed by largethresholdsand sm allcrosssections. Since

11 the production ofstrange hadrons in N N and e+ e collisions is know n to be signi cantly suppressed relative to the expectation from sim ple statisticalphase-space considerations [30],this should lead to a relative enhancem ent ofstrangeness production in heavy-ion collisions. K inetic sim ulations,based on know n hadronic propertiesand interaction crosssections, have now convincingly show n thatitisnotpossible to create a state ofhadronic chem ical equilibrium and a signi cantam ountofstrangenessenhancem entoutofa non-equilibrium initialstate by purely hadronic rescattering (for a recent review see [31]). Ifyou want to get those features out,you have to put them in at the beginning ofthe sim ulation. T herem ay bem any di erentwaysofdoing so.H owever,them oste cientway ofcreating a state of(relative orabsolute)hadronic chem icalequilibrium appearsto be provided by the hadronization process itself: due to color-con nem ent,the coalescence ofcolored quarksinto hadronsisa processw ith very large crosssections,allow ing form any di erent arrangem ents am ong the quarks w ith essentially equalprobability. Ifbefore hadronization the quarks and gluons are essentially uncorrelated (like in a Q G P),then the m ost likely outcom e of the hadronization process is a statistical occupation of the hadronic phase-space,i.e. a state ofm axim um entropy,subjectonly to the constraintsofconservation ofenergy,baryon num ber,net strangeness,and (sic!) the totalnum ber ofavailable ss pairs. T hus, if (as predicted for the Q G P [29]) the num ber of ss-pairs is enhanced before the onsetofhadronization,orby the fragm entation ofgluonsduring hadronization, theirstatisticaldistribution overthe available hadronic channelsw illnaturally lead to an apparenthadronic chem icalequilibrium state (w ith the appropriate enhancem ent of,say, the ) even ifnone ofthe hadrons ever scattered with each other after being form ed.

Figure7.A com pilation ofm easured particle ratios from 158A G eV /c Pb+ Pb collisions, com pared w ith a hadron resonance gas in com plete chem ical equilibrium (full strangeness saturation) at Tchem = 168M eV and B = 266M eV [32].

Such a state of\apparent" or \pre-established" chem icalequilibrium is indeed seen in theexperim ents:Figure7 show ssom e18 hadronicparticleratiosm easured in 158A G eV /c Pb+ Pb collisions,com pared w ith a chem icalequilibrium reballm odelatTchem = 168M eV and B = 266M eV [32]. T he agreem ent between the data is at least as good as between di erentexperim ents. T he value ofT chem isinteresting: in the m axim um entropy sense it characterizesthe energy density atw hich hadronization occurs(about0.5G eV /fm 3 )and coincides w ithin errors w ith the criticaltem perature forcolor decon nem ent from lattice Q C D .Ifthe hadrons were form ed by hadronization ofa prehadronic state at the critical energy density c and their abundances froze out at Tchem = 168M eV ,there was indeed

12 no tim e to achieve this equilibrium con guration by hadronic rescattering; the hadrons m ust have been \born" into chem icalequilibrium [33,34]. λS

0.6

Figure 8. T he strangeness suppression factor of produced strange vs. nonstrange valence quarks, s = 2hssi=huu + ddijproduced , in elem entary particleand heavyion collisions p as a function of s [35]. T he two points each for pp collisions re ect the inclusion (exclusion) of the initialvalence quarks.

pp collisions – pp collisions + e e collisions A+B collisions

0.5

0.4

0.3

0.2

0.1

0 10

2

10

3

√ s (GeV)

Enhancement E

But this only halfthe story. N am ely,a sim ilar picture ofstatisticalhadronization at the criticalenergy density c arises even from an analysis ofe+ e ,pp and pp collisions [30].W hatisreally dram atically di erentin heavy-ion collisionsisthelevelofstrangeness saturation re ected in the apparent chem icalequilibrium state: Figure8 show s that the overall fraction of strange particles is about tw ice as high in heavy-ion collisions as in elem entary particle collisions! Essentially the strangeness suppression observed in N N collisions has disappeared in A A collisions. A ccording to the preceding paragraph,this extra strangeness cannot have been produced by nalstate rescattering;it thus re ects the properties ofthe prehadronic state before hadronization. T his points to a new ,fast strangeness production m echanism before hadronization,as predicted for Q G P [29].

Figure 9. Enhancem ent factor for the m idrapidity yields per participating nucleon in 158A G eV /c Pb+ Pb relative to p+ Pb collisions for various strange and non-strange hadron species [36].

10

1

h

KS Λ 0

Ξ

Λ

–

Ξ

0

1

2

1

2

-

–

–

Ω+Ω 3 Strangeness |S|

A very striking way ofplotting these ndingsisshow n in Figure9 [36]:relative to p+ Pb collisions,the num ber ofproduced strange hadrons perparticipating nucleon is the m ore strongly enhanced the m ore strange (anti)quarks for its form ation are required. For and thisenhancem entfactorisabout15!T he tendency show n in Figure9 iscom pletely counterintuitive for hadronic rescattering m echanism s,w here m ultistrange (anti)baryons are suppressed by higherthresholdsthan kaonsand ’s;butitisperfectly consistentw ith a statisticalhadronization picture [37]w here m ulti-strange particlespro tm ore from the globalstrangeness enhancem ent than singly strange hadrons. K inetic codes like U RQ M D [38]tend to lose (anti)baryons (and thus a fraction ofthe

13 initial enhancem ent of m ulti-strange (anti)baryons) by baryon-antibaryon annihilation during the rescattering stage. It was recently show n [39]that this is to a large extent a m anifestation ofthe lack ofdetailed balance in the codes w hich include processes like pp ! n (w ith n = 5 6)butnottheirinverse. R app and Shuryak [39]argue that,asthe system coolsbelow Tchem ,pionsand kaonsdon’tannihilate butinstead build up a positive chem icalpotentialw hich enhances the probability for the inverse reaction and strongly reduces the net annihilation of antibaryons. T his is really fortunate,because it is this lack ofabundance-changing processes during the hadronic expansion stage w hich allow s us to glim pse the hadronization process itself through the nal hadronic abundances, in spite ofintense, resonance-m ediated elastic rescattering am ong the hadrons between hadronization at Tchem 170M eV and kinetic freeze-out at Tf 100M eV . 8. J= SU P P R E SSIO N A N D C O LO R D E C O N F IN E M E N T T he observation ofhadronicchem icalequilibrium abundanceshastaken usfrom kinetic freeze-out allthe way back to the hadronization transition. T he observed strangeness enhancem entgivesindirectinform ation aboutthe state thatexisted before hadronization. It is consistent w ith the hypothesis that this state consisted ofcolor-decon ned quarkgluon m atterand thatintense rescattering am ong the quarksand gluons,before orduring the hadronization process,produced the extra strangeness. Butthism ay notbe the only explanation. C an one nd other,perhaps m ore direct indications for m atter containing decon ned gluons in the early collision stages? T his brings us to the second key prediction for Q G P form ation: M atsui and Satz suggested [40] that the high gluon density resulting from color decon nem ent should D ebye-screen the color interaction potential between a c and a c quark pair produced during the initial im pact of the two nuclei and thus prevent them from binding into charm onium states(J= , c, ’).Instead,they would eventually nd lightquark partners to m ake hadrons w ith open charm . T his would lead to a suppression of charm onium production in heavy-ion collisions,and the screening m echanism should lead to a speci c suppression pattern w hich,asa function ofenergy density achieved, rsta ectstheloosely bound ’and c states and then the strongly bound J= ground state [41]. T here is an expected background to this charm onium suppression w hich already exists in pA collisions and can be studied there in order to extrapolate it to A A : if you put yourselfin the C M fram e,a cc pair created in a hard pp collision (i.e. after 1=(2m c) < 0:1fm /c)w illbe a ected by interactions w ith othernucleons from the restofthe nucleus w hich isstillsweeping overit.T his\norm alsuppression" hasby now been wellstudied [41] and is indicated by the straight lines in Figure 10. It follow s an exponentialattenuation w ith the length L of cold nuclear m atter of density 0 sweeping over the cc-pair,w ith an absorption cross section of about 6m b for both the weakly bound ’ and the tightly bound J= ! T he equalabsorption is understood as an e ect on the pre-resonant cc state atearly tim es,before the bound charm onium statesactually form (w hich atSPS energies and above happens only after the w hole nucleus has passed over the pair). Figure10 show s that a deviation from this \norm al" absorption occurs in heavy-ion collisionsonce the nuclearoverlap volum e (related to the variable L)becom essu ciently large. T he weakly bound ’su ers \anom alous absorption" rst,at around L = 5 fm ,

14

p (200 GeV/c) - A (A = p, d) p (450 GeV/c) - A (A = W, U) S (32 × 200 GeV/c) - U Pb (208 × 158 GeV/c) - Pb

1 A e - ρ0 σabs L with σabs = 5.8 mb

Bµµσ (J/ Ψ) / σ(Drell-Yan)

Bµµ σ ( Ψ’) / σ (Drell-Yan)

w hile forthe J= and/orthe c (w hich in pA collisionsisknow n to contribute about30% to the m easured J= yield via itsradiative decay c ! J= )the anom alousabsorption does not set in untilabout L = 7:5fm . 70 60 50

p (200 GeV/c) - A (A = W, U) S (32 × 200 GeV/c) - U

40

Pb (208 × 158 GeV/c) - Pb

30 20

0.1

p (450 GeV/c) - A (A = p, d)

Bµµσ (J/ Ψ) / σ(DY) = A e- ρ0 σabsL σabs = 5.8 +/- 0.6 mb ρ0 = 0.17 fm -3

10

0.01 0

2.5

5

7.5

10 L (fm)

0

2.5

5

7.5

10 L (fm)

Bσ(J/ψ) / σ(DY)2.9-4.5

Measured / Expected J/ψ suppression

Figure10. N A 38/N A 50 data on 0=D Y and (J= )=D Y [42],plotted as a function ofthe nuclear thickness param eter L (see text). 1.4 1.2 1 0.8

40 Pb - Pb 1996

35

Pb - Pb 1996 with Minimum Bias Pb - Pb 1998 with Minimum Bias

30 25 20

0.6

15

0.4

10

Pb - Pb 1998 with Minimum Bias Pb - Pb 1996 with Minimum Bias Pb - Pb 1996 S - U NA38 p - A NA38 p - p(d) NA51

0.2

5

0

0 0

0.5

1

1.5

2

2.5

3 3.5 3 ε (GeV/fm )

0

20

40

60

80

100

120 140 ET (GeV)

Figure11. Left: \A nom alous J= suppression" (see text) as a function ofinitialenergy density [43].R ight:T he ratio (J= )/D rell-Yan production,asa function ofthe m easured transverse energy E T ,com pared to di erent hadronic com over m odels [43]. T he J= suppression hasin the m eantim e been studied in m uch greaterdetailasshow n in Figure11. T he left part show s the \anom alous suppression" (w ith the norm al preresonant absorption on the incom ing nucleidivided out) as a function ofenergy density [43]. T he latter is com puted from the m easured transverse energy E T via Bjorken’s form ula (1),w here the e ective overlap area in the denom inatorisrelated to E T via a geom etric m odeland G lauber theory [43]. T he observed suppression pattern is interesting: it occurs in two \waves", w ith an interm ediate attening after about 30% of suppression (w hich one m ight be tem pted to associate w ith the com plete suppression ofthe c com ponent) followed by a stronger suppression at energy densities above 3G eV /fm 3 .

15 T he real origin of this \wavy" structure is not yet clear; on a super cial level it is qualitatively consistent w ith a suppression hierarchy 0 ! c ! J= as expected from theQ G P color-screening scenario.In any case,therightpartofFigure11 show sthatitcan notbe reproduced by conventionalhadronic nalstate interactions(collision dissociation) between the charm onium and the produced hadrons. Such \hadronic com over m odels" m ust be tuned to relatively large inelastic J= -com over scattering cross sections to even reproduce the average suppression in Pb+ Pb collisions, at the expense of som etim es overpredicting the e ectin S+ U collisions. Even then m ostofthe destructive interactions happen at very early tim es w here the com over densities are so high that a hadronic description should really not yet apply. M ost im portantly,however,they allconsistently failto reproduce the strong suppression at very high E T . Itwasrecently noted thatthe apparentonsetofthe second,strongersuppression above = 3G eV /fm3 coincides roughly w ith the \knee" in the E T -distribution,i.e. w ith the pointoffullnuclear overlap above w hich one enters the region ofE T uctuations [44,45]. T hese uctuations tend to increase the J= suppression even in the com over m odels, but the e ect is not strong enough to reproduce the data [44]. O n the other hand, if one associates them w ith uctuations ofthe energy density in the Q G P D ebye-screening approach the uctuation e ects are m uch stronger and the data can be reproduced [45]. Itwould be im portantto clarify thisissue,e.g. by perform ing U + U collisions w here,due to the deform ation ofthe uranium nucleus,in the tip-on-tip con guration sim ilar energy densities can be reached w ithout having to exploit E T uctuations. 9. T H E R M A L E LE C T R O M A G N E T IC R A D IA T IO N T he third (and earliest) key prediction for Q G P form ation was therm alradiation of (realand virtual) photons from the therm alized quarks in the Q G P [46]. T hey are conceptually clean direct probes of the Q G P phase itself, but experim entally di cult due to large backgrounds. N onetheless,experim ents at the SPS have searched for this type ofradiation. A n excess yield in the photon spectrum above about 1.5 G eV w hich is attributed to direct em ission was found by W A 98 [47]and discussed by T h. Peitzm ann at this m eeting. It is,Ithink,fair to say that the relation ofthis signalw ith therm alQ G P radiation is presently unclear. T he N A 50 C ollaboration found an excess in the dim uon spectrum between the and J= peaks w hich was interpreted by them as an excess in open charm production [48]but w hich m ay also be due to therm alQ G P radiation [49]. A gain,the true origin isnotclear. T he situation issuch that,forthe initialtem peratures reachable atthe SPS,the theoreticalpredictionsfora therm alradiation signalare so low thatitisnotobviousthatitcan be dug outfrom the experim entalbackground. Since the therm alradiation rate goes w ith T 4,the higher initialtem peratures reachable at R H IC and LH C ,com bined w ith the longerlifetim e ofthe plasm a phase,should help a lotto see the plasm a \shine" and thus con rm this prediction experim entally. 10. C O N C LU SIO N S R elativistic heavy-ion collisions at the C ER N SPS have taken us into new and unprecedented regionsofenergy density: in Pb+ Pb collisions at158A G eV /c initialenergy densitiesofabout3.5G eV /fm 3 (i.e.m ore than 20 tim esthe energy density ofcold nuclear

16 m atter) have been created over large volum es. Ifthe m atterwas approxim ately therm alized even at this early stage (for w hich we do not yet have convincing direct evidence, although data on elliptic ow [50,51],w hich I had no tim e and space to discuss, point in this direction),the initialtem perature was around 210{220 M eV ,i.e. 30% above the criticaltem perature for color decon nem ent. W e have strong and direct experim entalevidence for a large degree oftherm alization and strong collective behaviourin the late stagesofthe collision,driven by intense rescattering am ong the reballconstituents w hich is directly visible in the low -m ass dilepton spectra. A t kinetic freeze-out the reballradiates hadrons w ith a tem perature ofabout 100 M eV ,atthe sam e tim e undergoing collective explosion w ith m ore than halfthe light velocity (the \Little Bang"). Extensive theoreticalsim ulationshave show n thatconventionalhadronic processesduring thehadronicrescattering phase lead m ostly to elastic collisionsand arevery ine cient in changing the nalhadron abundances. T he observed hadronic particle ratios thus reect the \prim ordial hadrosynthesis" in the Little Bang and provide a direct glim pse of the hadron form ation stage. T he data show that the hadrons are born into a state of\pre-established chem icalequilibrium " at a tem perature ofabout 170M eV w hich coincides w ith the decon nem ent tem perature predicted by lattice Q C D .T his is the rst observation oftherm alequilibrium m atteratsuch a high tem perature and energy density. T he phenom enon ism osteasily understood in term sofstatisticalhadronzation ofa Q G P, although other m echanism s w ith sim ilar statisticalfeatures cannot be excluded. T he experim entally determ ined \chem ical" and \therm al" freeze-outpointscan be connected by an isentropic expansion trajectory as indicated in Figure1. (N ote that the part of the sam e trajectory w hich runs through the Q G P phase is so far speculative.) Strangeness enhancem ent and charm onium suppression have been predicted as Q G P signatures and are indeed found to characterize the prehadronic state from w hich the observed hadrons appear during hadronization. T hese features cannot be understood in term s ofconventionalhadronic nalstate rescattering e ects after hadronization. T hey are consistent w ith Q G P expectations,although otherexplanationsm ay stillbe possible. T he inability to understand these propertiesin term sofknow n hadronic physicswarrants the characterization ofthis prehadronic state as a \new state ofm atter" [1]. So what is m issing to claim \discovery" of the quark-gluon plasm a? First, on the theoreticalside,we only know thatw ith know n hadronic physics we can notdescribe the data,butithasnotyetbeen show n thata fully dynam icaltheory w hich beginsw ith Q G P and follow sthe system untilfreeze-outactually can describe allobservations. O ne reason isthata description ofstrongly interacting m atterand itsdynam ics in the neighborhood ofthe phase transition is an exceedingly di cult problem ,and that at the SPS we are neverfaraway from thephasetransition.T histask m ay thusbecom eeasieratR H IC /LH C than at the SPS.Furtherm ore,the evolution ofthe \late signatures" from pp via pA to A A collisions,to establish a clearline between \conventionalhadronic physics" and \new physics" has so far not received enough careful theoretical attention. T his should be rem edied,but it requires m uch im proved pp and pA data at the sam e energy,w ith m ore di erentialexperim entalinform ation. Such data can (only) be obtained at the SPS. Further im portant experim entalquestions w hich can be answered at the SPS (and in a few cases only there) are: A ssum ing that we have seen quark decon nem ent,w here is

17 its energy threshold? H ow big does the collision system have to be to establish approxim ate therm alequilibrium and strangeness saturation and to exhibit collective ow ? If charm onia are suppressed,w hat happens w ith open charm { is D rell-Yan production of dileptons (w hich depends on the quark structure functions in the colliding nuclei) really the appropriate norm alization forJ= suppression (w hich is sensitive to the gluon structure functions since cc pairs are m ade from gluons)? Som e answers w illbe provided by data already collected atlowerbeam energiesand w ith sm allernucleiand m oreperipheral collisions. A search foropen charm at the SPS was proposed [52]and recently approved. But other questions are stillwaiting for proposals to be m ade. Still, w ith the SPS we w ill never be able to get \away from the edge". A detailed characterization ofthe \new state ofm atter" w illonly be possible w hen the largerinitial energy densities and resulting longer plasm a lifetim es before hadronization provided by R H IC and LH C becom eavailable.T he higherinitialtem peraturesareexpected to give an observabletherm alradiation signal,thusallow ing to m easurethetherm al\Q G P structure functions". T he higher collision energies allow for the creation ofhigh-pt jets w hich can then be used as probes of the Q G P, by their interactions w ith the plasm a w hen they penetrate it. A nd last not least, the fact that R H IC is a dedicated heavy-ion m achine at w hich experim ents can be run for a large fraction of each year is conducive to the system atic studies that w illbe required to eventually obtain a com plete and consistent picture ofquark-gluon plasm a dynam ics. R E FE R E N C E S 1. C ER N Press R elease Feb.10,2000: http://cern.web.cern.ch/CERN/Announcements/2000/NewStateMatter/ 2. U .H einz and M .Jacob,nucl-th/0002042. 3. Proceedings of \Q uark M atter ’97", T . H atsuda et al. (Eds.), N ucl. Phys. A 638 (1998); of \Strangeness in Q uark M atter 1998",M .M orando (Ed.), J.Phys. G 25 (1999);and of\Q uark M atter’99",L.R iccatietal.(Eds.),N ucl.Phys.A 661 (1999). 4. http://webcast.cern.ch/Archive/2000/2000-02-10. 5. For a recent discussion of detailed features of the Q C D phase diagram see K .R ajagopal,C om m ents on M odern Physics (Part A :C om m .N ucl.Part.Phys.) 2 (2000), in press (hep-ph/0009058). 6. F.K arsch,N ucl.Phys.B (Proc.Suppl.) 83-84 (2000)14. 7. F.K arsch,private com m unication,based on work presented in F.K arsch,E.Laerm ann,and A .Peikert,N ucl.Phys.B (Proc.Suppl.) 83-84 (2000) 390;Phys.Lett.B 478 (2000) 447;and in A .Peikert’s PhD thesis (unpublished). 8. F.K arsch and E.Laerm ann,Phys.R ev.D 50 (1994)6954. 9. S.A .Bass,M .G yulassy,H .Stocker,and W .G reiner,J.Phys.G 25 (1999)R 1. 10.J.D .Bjorken,Phys.R ev.D 27 (1983) 140. 11.N A 49 C ollaboration,H .A ppelshauser et al.,Eur.Phys.J.C 2 (1998) 661. 12.N A 49 C ollaboration,T .A lber et al.,Phys.R ev.Lett.75 (1995)3814;W A 98 C ollaboration,M .A ggarwalet al.,N ucl.Phys.A 610 (1996) 200c;and nucl-ex/0008004. 13.U .H einz,nucl-th/9710065. 14.H .W eber et al.,Phys.Lett.B 442 (1998) 443.

18 15.K .S.Lee,U .H einz,and E.Schnederm ann,Z.Phys.C 48 (1990) 525. 16.T .C sorg} o,B.Lorstad,N ucl.Phys.A 590 (1995)465c;Phys.R ev.C 54 (1996) 1390. 17.R .Scheibland U .H einz,Phys.R ev.C 59 (1999)1585. 18.W A 97 C ollaboration,F.A ntinoriet al.,Eur.Phys.J.C 14 (2000) 633. 19.A .Polleri,J.P.Bondorf,and I.N .M ishustin,Phys.Lett.B 419 (1998)19. 20.H .van H ecke,H .Sorge,and N .X u,Phys.R ev.Lett.81 (1998)5764. 21.S.C hapm an,J.R .N ix,and U .H einz,Phys.R ev.C 52 (1995)2694. 22.N A 52 C ollaboration,G .A m brosiniet al.,N ew J.Phys.1 (1999) 22. 23.N A 44 C ollaboration,M .M urray et al.,N ucl.Phys.A 661 (1999) 456c. 24.B.Tom asik,U .A .W iedem ann,and U .H einz,nucl-th/9907096. 25.N A 49 C ollaboration,P.G .Jones et al.,N ucl.Phys.A 610 (1996)188c. 26.U .H einz and K .S.Lee,Phys.Lett.B 259 (1991) 162. 27.C ER ES C ollaboration,B.Lenkeit et al.,N ucl.Phys.A 661 (1999) 23c. 28.R .R app and J.W am bach,hep-ph/9909229,A dv.N ucl.Phys.,in press. 29.J.R afelskiand B.M uller,Phys.R ev.Lett.48 (1982) 1066;P.K och,B.M uller,and J.R afelski,Phys.R ep.142 (1986)167. 30.F.Becattini,Z.Phys.C 69 (1996)485;F.Becattiniand U .H einz,ibid.76 (1997)269. 31.U .H einz,N ucl.Phys.A 661 (1999) 140c. 32.P.Braun-M unzinger,I.H eppe,and J.Stachel,Phys.Lett.B 465 (1999) 15. 33.U .H einz,N ucl.Phys.A 638 (1998)357c;J.Phys.G 25 (1999)263;hep-ph/9902424. 34.R .Stock,Prog.Part.N ucl.Phys.42 (1999) 295;Phys.Lett.B 456 (1999)277. 35.F.Becattini,M .G azdzicki,and J.Sollfrank,Eur.Phys.J.C 5 (1998) 143. 36.W A 97 C ollaboration, R .Lietava et al., J.Phys. G 25 (1999) 181 (see p 460 in the sam e volum e for the correct Fig.7!). 37.J.R afelski,Phys.Lett.B 262 (1991) 333;A .Bialas,Phys.Lett.B 442 (1998) 449. 38.S.A .Bass et al.,Phys.R ev.C 60 (1999)021902. 39.R .R app and E.V .Shuryak,hep-ph/0008326. 40.T .M atsuiand H .Satz,Phys.Lett.B 178 (1986)416. 41.For a recent review see H .Satz,R ep.Prog.Phys.63 (2000)1511. 42.N A 50 C ollaboration,L.R am ello et al.,N ucl.Phys.A 638 (1998) 261c;M .A breu et al.,Phys.Lett.B 450 (1999)456. 43.N A 50 C ollaboration,M .A breu et al.,Phys.Lett.B 477 (2000) 28. 44.A .C apella,E.G .Ferreiro,and A .B.K aidalov,Phys.R ev.Lett.85 (2000) 2080. 45.J.-P.Blaizot,P.M .D inh,and J.-Y .O llitrault,nucl-th/0007020. 46.E.V .Shuryak,Phys.Lett.78 B (1978)150;K .K ajantie and H .I.M iettinen,Z.Phys. C 9 (1981)341. 47.W A 98 C ollaboration,M .M .A ggarwaletal.nucl-ex/0006007 and nucl-ex/0006008. 48.N A 38 and N A 50 C ollaborations,M .C .A breu et al.,Eur.Phys.J.C 14 (2000)443. 49.R .R app and E.V .Shuryak,Phys.Lett.B 473 (2000)13;K .G allm eister,B.K am pfer, and O .P.Pavlenko,ibid.,p.20. 50.N A 49 C ollaboration,H .A ppelshauser et al.,Phys.R ev.Lett.80 (1998) 4136;A .M . Poskanzer,S.A .Voloshin et al.,N ucl.Phys.A 661 (1999) 341c. 51.P.K olb,J.Sollfrank,U .H einz,Phys.Lett.B 459 (1999)667;and hep-ph/0006129. 52.Study of prom pt dim uon and charm production with proton and heavy ion beam s at the C ER N SPS,C ER N /SPSC 2000-010