14
Nuclear Physics A544 (1992) 279c-292c North-Holland, Amsterdam trange an Johann R.afelski hot matter Department of Physics, University of Arizona, Tucson, AZ 55721 Abstract I consider the strangeness degree of freedom in hot nuclear matter and its significance for the observation and identification of a quark-gluon plasma. Particuiar attention is given to the interpretation of new and intriguing results on strange antibaryon produc- tion . ERE ARE THE STRANGE QUARKS COMING YSICS The third (and still rather light) strange s quark flavor is absent in all stable forms of matter known to us today. But, in recent years, we have seen, in collisions of relativistic heavy nuclei, production of strange hadronic particles in abundaaces suggesting that, at least during the fleeting moments when highly excited forms of nuclear matter are produced, we re-establish some significant level of strangeness akirl to that prevailing in the early Universe (or perhaps in dense stars) . The question is how does this happen and what we can learn about the fundamental behavior of nuclear matter under ex- treme conditions from the in-depth studies of strange particle production, in particular, production of (multi-)strange (anti-)baryons? 1 .1 . Models of strangeness production There are several distinct classes of theoretical approaches to strangeness production in high energy nuclear collisions . A simple classification consists of dividing the models into local equilibrium models and kinetic (microscopic) reaction models. Among the local equilibrium descriptions, I distinguish between those based on hadronic gas constituents and those based on quark-gluon matter . Similarly, we can identify two different classes of microscopic models of collision dynamics : hadronic cascades involving reactions between individual hadrons and quark cascades, which may be further differentiated as color string models and parton (cascade) models . No one doubts that such microscopic models are superior in principle, but we all realize that, in practice, they suffer critically from the need to understand all accessible reaction mechanisms . Consequently, it is almost always the case that microscopic models cannot be used to interpret results without, fine tuning the various implicit and explicit assumptions made . By comparison, the 1°eartion dynamics in local equilibrium approaches are usually relatively simple and often allow one to come to model-independent conclusions about ratios of particle yields . The local equilibrium approach to finite systems is compatible with the possible existence of macroscopic flows or spatial and temporal distributions of temperature and chemical potentials as long as the time scale of local equilibration of the considered 0375-9474/92/. .$05 .00 © 1992 - Elsevier Science Publishers B .V . All rights reserved .

Strange and hot matter

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Page 1: Strange and hot matter

Nuclear Physics A544 (1992) 279c-292cNorth-Holland, Amsterdam

trange an

Johann R.afelski

hot matter

Department of Physics, University of Arizona, Tucson, AZ 55721

AbstractI consider the strangeness degree of freedom in hot nuclear matter and its significance

for the observation and identification of a quark-gluon plasma. Particuiar attention isgiven to the interpretation of new and intriguing results on strange antibaryon produc-tion .

ERE ARE THE STRANGE QUARKS COMING

YSICS

The third (and still rather light) strange s quark flavor is absent in all stable forms ofmatter known to us today. But, in recent years, we have seen, in collisions of relativisticheavy nuclei, production of strange hadronic particles in abundaaces suggesting that,at least during the fleeting moments when highly excited forms of nuclear matter areproduced, we re-establish some significant level of strangeness akirl to that prevailing inthe early Universe (or perhaps in dense stars) . The question is how does this happenand what we can learn about the fundamental behavior of nuclear matter under ex-treme conditions from the in-depth studies of strange particle production, in particular,production of (multi-)strange (anti-)baryons?

1 .1 . Models of strangeness productionThere are several distinct classes of theoretical approaches to strangeness production

in high energy nuclear collisions . A simple classification consists of dividing the modelsinto local equilibrium models and kinetic (microscopic) reaction models. Among the localequilibrium descriptions, I distinguish between those based on hadronic gas constituentsand those based on quark-gluon matter . Similarly, we can identify two different classes ofmicroscopic models of collision dynamics : hadronic cascades involving reactions betweenindividual hadrons and quark cascades, which may be further differentiated as colorstring models and parton (cascade) models. No one doubts that such microscopic modelsare superior in principle, but we all realize that, in practice, they suffer critically fromthe need to understand all accessible reaction mechanisms. Consequently, it is almostalways the case that microscopic models cannot be used to interpret results without, finetuning the various implicit and explicit assumptions made. By comparison, the 1°eartiondynamics in local equilibrium approaches are usually relatively simple and often allowone to come to model-independent conclusions about ratios of particle yields .

The local equilibrium approach to finite systems is compatible with the possibleexistence of macroscopic flows or spatial and temporal distributions of temperature andchemical potentials as long as the time scale of local equilibration of the considered

0375-9474/92/..$05 .00 © 1992 - Elsevier Science Publishers B.V . All rights reserved .

Page 2: Strange and hot matter

280c

.1 . Rafelski / Stratige and hot inatter

fractions of the physical system is short compared to the characteristic times of globalchanges . The thermal character of transverse mass particle spectra suggests that localkinetic equilibrium is a good working hypothesis . A different issue is the existenceof local chemical equilibria . We can distinguish two cases : first, absolute chemicalequilibrium which requires that the particles produced fill all available phase space ;secondly, relative chemical equilibrium, where a weaker requirement is satisfied, namelythe redistribution of some prope-.ty (e.g . strange quark flavor) among different carriers(particles) according to the relative phase space size . If we wish to take advantage of thepowerful methods of quantum statistical mechanics, we must consider which quantitiesin our description can be seen in equilibrium and which require a kinetic description .When considering strange hadronic, particles, the absolute saturation of the phase spaceis the object which must be studied with care ; relative chemical equilibrium is muchmore easily attained due to significant strangeness exchange cross-sections .

Local equilibrium models allow one to make detailed abundance predictions, sincethey depend typically on only a few state variables (such as temperature T or chemicalpotential it) which can be obtained from independent observations . In my work, Iwill aim to correlate several observables so that these parameters play a minor (evencompletely insignificant) role. This approach to strangeness flow (the distribution ofstrangeness among different particles) can allow one to distinguish the possible reactionmechanisms : one obtains combinations of observable quantities which differ greatly fordifferent phases, viz . hadronic gas (HG) or quark-gluon plasma (QGP) . This will bethe key point made in this report .

I must emphasize that the view represented here of strangeness production avoidsentirely the a priori assumption of absolute chemical equilibrium which is sometimesmade. This assumption, which has been considered by a number of researchers, hasbeen rejected as physically inadmissible : even in the largest collision systems presentlyavailable, the strange particle yields do not reach absolute chemical equilibrium. Indeed,I believe that one of the important elements for the understanding of particle produc-tion mechanisms, will be the understanding of the approach to chemical equilibrium ofstrangeness abundance as the she of colliding nuclei changes . Therefore, I now brieflysummarize the physics behind the kinetic strangeness enhancement in nuclear collisions .

1 .2 . Kinetics of strangeness productionSince the time scale in a typical nucleus-nucleus coll ;Aon is very short, the strangeness

content of either the quark-gluon phase or the hadranic gas~,,phase cannot be assumedto be in equilibrium : it is necessary to determine explicitly the rate of strangenessproduction in both phases .

The plasma initially contains very few, if any, strange quarks as those produced indirect had,.ron-hadron reactions will generally b , 2 at higher rapidity than the rapidityof the fireball . The angle averaged cross sections for strangeness production for bothglue and quark induced processes in the QGP are found to be of comparable magnitude[I] . However, the statistical factors entering the thermal average will strongly favor thegluon induced processes : there are simply more glue-glue than quark-antiquark collisionsof suitable quantum number in the plasma . Essentially all the 39-pair production istherefore dominated by collisions of the central gluons, which in a first approximationcan be assumed to be in a thermal distribution (I will discuss in next section thelarge gluon abundance) . Because of glue dominance, the time evolution of strangenessduring the production process is a function of temperature but not of the baryo-chemical

Page 3: Strange and hot matter

J. Rafeiski I Strange and hot matter 23îc

potential . Consequently, the detailed baryon number retained in the plasma (stopping) is of no importance for strange particle yield; the actual plasma lifetime,volume an-: temperature (i.e . gluon density) are the critical parameters for the yield.

The strangeness production time constant (chemical equilibrium relaxation time) inthe quark-gluon phase has often been studied [21 and is believed to be of the order of10-23 s for T - 200MeV. The typical time scale for the creation and decay of a fireballcan be estimated as the time to traverse, say, a distance of 15 fm i.e . ^_- 5 x 10-23 s .Consequently, strangeness will nearly saturate the available phase space should a quark-gluon deconfined phase be formed . It is evident that the coincidental similarity of thetime constant of strangeness production with the believed life-span of the QGP has theeffect of making strangeness a quantity very appropriate to the study of the QGP.

Strangeness will not fill the available phase space in a thermal hadronic gas [31 sincethe strangeness production time constant in hadronic gas phase is expected to be consid-erably longer than in the QGP at the same temperature and baryo-chemical potential .(It is also worth remembering that, at the time of hadronization, the ss density is ex-pected to be about half as large as its peak in the QGP, which is about 0.4 strangeparticle pairs per fm3.) A kinetic description of strangeness production involving theusual hadronic particles should result in a strange particle yield significantly below theupper limits resulting from an equilibrium picture of a hadronic gas fireball . The mostaccessible HG reactions for strangeness production are N+ 7r --> A + and direct KRpair production. Cascade models which claim to reproduce strangeness enhancement [4]introduce other potentially numerous but as yet unexplored reactions involving heavynon-strange mesons and pions which may also contribute to strangeness production inthe HG.

Whichever the microscopic mechanism one adopts for computation of the strangeflavor production in the yet unknown form of high density nuclear matter that has beengenerated in these collisions, one can identify the different factors controlling the yield ofthe strangeness production processes in a rather model independent way. Consider twoas yet unidentified constituent parts of centrally interacting nuclei, A and B producingstrangeness in individual collisions . The total number of pairs produced (neglectingpossible strangeness annihilation), leading either to deconfined or bound (confined)strange quarks within individual hadrons, is given by

dN,N' -V- t- (dVdt)

Here V and t describe the 3+1 dimensional volume in which the reactions have takenplace . The rate of production per unit of time and volume is given by

The first factor NANB/n, is rather independent of the form of protomatter : the numberof components in A or B, be they gluons and quarks or be they pions, will alwaysremain of the same magnitude as. the final multiplicity. This is dictated by the nea :

dN, 1 __dV dt ) < QABVAB > PAPB (2)

Since p = NIV, the specific strangeness yield is :

N, NA NB= . . t ' < aABVAB > . (3)n, % V

Page 4: Strange and hot matter

AN

elieved to holf saranqeness Prnormal hadronic

Uvkki / Strange atul hot iiiat:-r

the evolution of the thenmalizet! centralction (as reported by many CERN and BNL

interactions (e.g. p+A interactions) is in view

lume V per particle and/time t and/ork cross sWi

e satisfied in the QGP fireball . Note that the cross section forhas the neneral behavior

where the threshold qh control the low energy behavior and the high energy behavioris governed by the mud Ils form, and a is the strength of the interaction. These

le averaged) cross sections U strangeness production have been studied for manyprocesses involving light quarks, gluons, PiGns and so on. They can be parameter-ized successfully by taking a2 t-- 1, leading to values of about 0.5 mb for processes atVs- = 2.5T+2.5T = 1 GeV. The threshold st h differentiates to some degree the differing;..)ossible processes - in the QGP we expect st ,% = 2m. t--- 350 MeV, while, in hadronicinteractions, this value is considerably greater on the scale of relevance here : 700 MeV

K.n

+Kreactions . Also, in a confined phase, one cannot invoke summation-,r + 7rover color quantum numbers in the final state, reducing cross sections still further.

eeking quark gluon plasmanhancement in the total strangeness abundance alone is not a characteristic signa-

ture of any novel form of matter . It tells us that we deal with a state of matter whichis either den. se or relatively long-lived or in which strangeness production cross sectionsare enhanced or possesses some combination of these three factors . In order to be morespecific about the nature of the dense matter, we must measure individual strange quarkand anti-quark clusters, which are mom sensitive to the environment from which theyemery.

slow, I will discuss the abundance of strange antibaryons as compared to strangebaryons and the relative abundances of (anti) baryons of differing strangeness content.I show that knowledge of these particle abundances can lead to interesting qualitativeconclusions about the nature of the underlying strangeness production mechanisms . Oneimportant input which I use to identify the `OGP' is that -9s pairs are produced withoutinhibition (there is no need to bind them in some hadronic clusters) . Another is thatwe can have high strangeness density. These properties (characteristic of a new state ofmatter) are beginning to emerge from the experimental results. Do they imply that thedense state is a color plasma of deconfined quarks and gluons? The answer is yes onlyif the behavior of the observed abundances follow the pattern predicted as parametersof the experiments such as Vrs-, volume of the dense matter (size of colliding nuclei) andentropy (multiplicity) are changed. It is relatively easy to conceive of different modelsof the reaction which, given a number of free parameters, can yield results in agreementwith one measured value. It is hard to imagine that two distinctly different reactionechanisms could lead to similar systematic behavior ; this is certainly not so when one

co pares a QGP reaction picture with the HG picture.

Page 5: Strange and hot matter

ING STRANGE PARTI

3p. (fm

3) = 1.04

T

1- 1501.160 eV

47r

afels l / Strange and hot inatter

t is instructive to recall the magnitude of backgrounds expected for the multi strange(anti) baryons .

e

/

1p,, ratio seen at I

at

s = 63

e

is only 0.06±0.02the central rapidity region 151, corresponding

value of about 0.12 if cobeen made a

e

jL.

e expected

c e

'cal-equili rium result is of 0(1) [6] .

s

2.1. Hot matterI recall first key results of the grand canonical approach to quantum statistical

chanics . I will use these results assuming local equilibrium only and will all for thekinetic development of the strange quark population .

The statistical variables of the system are the temperature T and the chemical po-tentials pi of the different conserved quark flavors u, d, s . It is convenient to introduce

1&q = (I&d + j ea)/2 ,

'6

-

d -Au a

AB _ -31A9 i

5here, jag is "quark" chemical potential, acn is the baryo-c e 'cal potential

d as de-scribes the (small) asymmetry in the number of up and down quarks due to the neutroexcess in heavy ion collisions . I will usually ignore 8u and, when discussing the proper-ties of the hot matter, focus mostly on temperature and the quark (or baryon) chemicalpotential . Given Z (FLQ, /j, Y), the grand caionical partition function, thermodynamicvariables such as pressure, entropy, energy, and baryon densities are obtained in theusual way. The results are for the QGP through first order in a. are well known [71,and I refrain from repeating these here in their entirety. However, as gluons are a keyfactor in strangeness production, I note that the gluon content of a QGP fireball canbe estimated from

which gives for a typical temperature of 200 (resp. 240)

eV a value of 0.6 (resp.1) fm-s for a. = 0.6 and 0.3 (rasp . 1.4) fm-3 for a. = 0.5 . A quark-gluon phase ofradius 3-4 fm (inferred from

BTinterferometry to be the size of the pion source) wouldhave 200-400 gluons, substantially more than in models of highly-excited nuclear matterwhich do not invoke the formation of a locally deconfined phase.

In the hadron gas, it is customary to assume that practically all strong interactionsare contained in the particle spectrum [3] . Hence, ZA is approximated by the sum of thepartition functions of all the individual hadron species, each treated as a noninteractinggas with residual interactions due to non-vanishing elastic cross sections between thedifferent components (the dominant inelastic interactions are accounted for by the res-onance spectrum) . In summing the different hadronic resonances, it is sufficient to useBoltzmann statistics for the different components . Furthermore, because very heavyhadronic states are very infrequently produced (making the assumption of equilibriuminappropriate) and even if in equilibrium would be present in minute quantities, thesum over hadrons is limited empirically to hadrons of mass nah <_ 2GeV.

correctionfor finite hadron size has to be made along the lines of the van der

aals correction(in which the total volume available to the gas is reduced by the sum of all particlevolumes) .

Using these ingredients within the so-called bootstrap theory, it has been possi-ble to successfully connect the QGP and HG phases phenomenologically, establis

(61,

9

Page 6: Strange and hot matter

tcoroitarythe different

portancetential in the plas

the QGJ net zero strangeness isiderably different from zero (inbsermtion of a u. which

strangeness phase space wfreely-moving str

anti cation of thekvin v-û, S-W, and Pb-Pb c

gent num,a special cozero states of di

cM str

withnt wui

0.6) QGP of energy densityis ob.- -,r

hases remhis phase

fthelies 40it is comparable in magnitude to j&9 - see below) .

most vanishes in coincidence with a nearly fully-saturateduld constitute evidence for the formation of a phase with

e quarks, SM a conclusion would be of great relevance for thein particular if it occurs in widely differing circumstances

Hisions, tutu at differi

Ing

s'S))V-

EjITgi 'k -Yi e-

RafwMI I Sirmige and hot niatter

tentials where we expect the phasethe phase separating boundary

e of an igloo . The conditiondects the igloo onto the (AB, T)escribed que-fitatively by a per-0-3), for IAB ~ 6W MeV; a

sformation from QGP to HG occurs,eness < a - ! >= 0 1'101 . The practical

the value of the strange chemicalhistory of the hadronic matter . In

eneral, in the HG, it, is con-

ti

weltscomposite particle abundancesa statistical model, factors which control the formation of composite particles in

ages matter [11] a,re: statistical multiplicity factors gi, referring to thedegeneracy of thei(= u, d, s) component, and characterizing also the likelihood of finding among randomly

pi/Tassembled quarks, the suitable spin-isospin of the particle ; chemical fugacities Aj = ewhich define the relative abundance of quarks and anti-quarks (Xq =

In order toflow for the absence of chemical equilibrium, I introduce a factor 'ji, to :5 -yj :5 1) foreach quark flavor. The difference between Iwd A is that -y is the same for both quarksand antiquarks a the s=e Havor: N = ly I

willassume that, for light flavors, the

-y-factor is effectively unity, but will allow for the possibility that strange quarks arenot in absolute chemical equilibrium: 0 :5 -y. :5 1. The probability to find a compositeparticle thus becomes

For a composite particle at energy E = Ej Ej , Eq.(7) becomes simply a phase spacefactor times the Boltzmann exponential e-EIT factor.

I OR now show that this counting rule allows me to describe the relative abundancesof strange baryons and antibaryons at fixed m-L. All baryons considered have spin 1/2,but they include spin 3/2 resonances which become spin 1/2 states through hadronicdecays . This is implicitly contained in the counting of theparticles by taking theproductof the quark spin degeneracies ; since in all ratios to be considered this factor is thesame, I shall ignore it . As the method of measurement distinguishes the flavor content,I keep explicit the product A \-factors ; -y. will enter when one compares particles with

er of strang, quarks and antiquarks [12] .

Despite these precautions,21.~ation arises in considering hyperons as there are two different chargegent isospin: the experimental abundances of A and I (1=0) implicitly

include, respectively, the abundance of E0 and E0 (1=1, 13=0), arising from the decayAO+,y(74 MeV), and similarly for EO. These states are not appropriately counted

since I identify flavor content separately and consider spin degeneracies to be equal;

Page 7: Strange and hot matter

hence the true a un ances must e corrected y a factor 2 (e.g . the

abundancepresented is really the

+

® abundance). Especially in dealing with BE, there issignificant difference: S/

= 2 - r/(

+

®), the latter being the observed quantity. IComparing spectra of particles within overlapping regions of

., all statisticspectral factors cancel, n

their respective abun

c

function o fu

iti

e:

The cascade and lambda ratios can easily be related to each other, in a way which showsexplicitly the respective isospin asymmetry factors and strangeness ugacity de nd ce.Eq.(g) implies :

RA

=

R2 . eaa1slTeep®lT ,

Ra _

A . e-ajslTeep,/T .

Eq. (9) is generally valid, irrespective of the state of the system (

AdiA;a

AdA2 s

J. Rafclski / Strange and hot niatter

Ad~AU1A8~

Ad I UAS

.

G or

21 thank Chengqian Gong and Herndt Müller for bringing this point to my attention .

5c

2.3 .

aryo-c emi-al potentialSince the asymmetry b1L is expected to

e small (see below), Eq.(9) determines thevalue of the baryo-chemical and strange potentials to great precision (because of thefactor 6 in the exponents) . The value emerging from such an analysis will correspond tothe conditions prevailing in the source of the strange (anti-) baryons . Other methods ofmeasurement of the baryo-chemical potential have been proposed in the past, more ori-ented towards the final state of the hadronic gas [13] . The baryo-chemical potential Bin the final stage of hadron gas phase can be determined conveniently from K+IK- orK,/® ratios . These are sensitive to 11 because of large strangeness exchange cross sec-tions which rapidly establish the relative chemical equilibrium between different speciesof strange particles . (This is true even if absolute chemical equilibrium of strangenessis not attained in the hadronic gas phase.) It was noted recently $ that the magnitudeof the K-phase space may be noticeably impacted at high baryon density by residualinteractions arising from tho large elastic kaon (qs) - nucleon scattering amplitude . There--ult presented here is not affected by these considerations .

2.4 . Strangeness chemical potentialGiven the importance of the value u, = ®, Y will now take a closer look on how big

Ez7 is at non-zero baryon density assuming relative chemical equilibrium . Using thegrand partition function in the Boltzmann approximation for hadrns carrying eitherstrange quarks or strange antiquarks, assuming relative strangeness equilibrium (withstrangenesq conservation) and restricting attention to the dominant singly strange par-ticles and ignoring the anti-hyperons (good assumptions in HG), I find :

As/T = lia/T -1ln(I + AY/WK) = u IT -

1ln(1 + ny/nfc) .

(10)2

2Here, Wä denotes the size of the hadronic phase space . The last equality exploits thefact that even if the magnitude of the phase space for hyperons and kaons is not known,

11 thank U. Heinz for his remarks and discussions which lead to correction of any earlier point of view[12] that this doubling was already contained in the degeneracy factor .

Page 8: Strange and hot matter

sure ut ansisolate the

the same for both strstrangeness content we considered [141 .

i-protons, anti-1

ti-c

ca

À

-1

fR=

It is interesting to note that the product ofr the unknown

he factor -y. accouadon and the

nderstand the processesstudy how this factor chanlonger-lived fireball should have a greater value of -y, . For thewill for the largest systems (hopefully) approach unity, but for a hadronic gas, a con-siderably smaller value will be found. Therefore, it would seem natural to measure [bytoken of Eq415)] the excitation function of -y, for large colliding systems, hoping to seea rather dramatic rise in its value as the energy becomes sufficient to reach QGI'. Alsoof interest is how this factor increases as; the size of the colliding nuclei increases, or ase impact parameter (multiplicity) changes.

2-

2-

Uantity J"-

is for much of our ignorance about the dynamics of strangenessroach to equilibrium of the strange quark abundance . In order to

f strangeness formation, it is of considerable importance toas as conditions change. For example, a larger and therefore

GP, the value of %

2I s .

Ish / Strat?ge a

!cal equilibriutios above, it did not appear because it is

parks. It enters where particles of differings, I now consider ratios of abundances of

es:

c

i miter

Q13) and (14) leads to a simple expression

(13)

cspin asymmetry described by bp is of course rather small. I can estimaten factor encountered Now

forthe case of QGP phase: I count the number 3f

Page 9: Strange and hot matter

u an

down quarks an conuclei

r,<

(Pz> - < i >

Al

AdIT(I + rTA> - < là >

1+

IrT) 2

-

3

1 + (I&

)

Pu

ere the last equality arises because

/x

«1. In the tube model, in whidinucleons in

e target in the

at

ofthe is

in symmetric projectile participate in tfireball, r. is 1.086 or the Sulphur-Tungsten collision ( f =

,

=

7) an

1.1b- collisions .

pare it to the ratio brought into collision

y the coll

fclykï / Strange

hot inatterand

287c

o any of the recent strangeness results reported at C

an

suggest thepresence of new physics, or c

we deal with these data on the basis of known nhnomena, without invoking the local color de-confinement implicit in the concept of theG ? A clear answer to this question is, in

y opinion not possible yet, but a numberof noteworthy results pointing in this direction have emerged already.

First, in all the pertinent

NL and CER

experiments reported at this

tin

(Icounted two

NLexperiments -

802, E810, and five CERN experiments - NA3 , NA 5,NA36, NA38,

85), strangeness production enhancement (by a factor of 2.5 ± .5)as compared to the results of scaled p - p and/or p - A reactions has indeed beenseen . These confirm solidly the initial reports made in 1987/88 by the

NL-E802 andthe CERN-NA35 experiment [15] . (Particularly noteworthy was the 1988 report byGazdzicki of the NA35 collaboration, in which he emphasized that, while there was en-hancement of strange particle yield per multiplicity in nuclear collisions, no sign of thiseffect was seen in p - A collisions.) As I have shown this enhancement alone d

notimply the need for new physics, but it does suggest a high density state of matter, forwhich the QGP phase is a natural candidate .

order to obtain more specific results,one must analyze the recently reported strange antibaryon signals of the NA35, NA36and WA85 experiments . In the near future, there will be much more refined and statis-tically significant results from the NA36 collaboration, as well as high statistics resultsfrom the A85 experiment . Thus, the present evaluation is only a first "glimpse?. Italso addresses just one experimental condition: the 200 GeV/A S-run at CERN [16] .

3. Spectra o strange (anti-) baryonsOf considerable importance to my analysis are the NA35 A and

rapidity spectrapresented by R. Stock at QM'90 [17] . While the A distribution is rather flat (span-ning the projectile to target fragmentation region), the dA/dy distribution is stronglycentered at yc

and, indeed, the relative abundance A/IL at y = ycm is nearly 0.8 -a first indication that the ® abundance is originating in a central fireball . This pic-ture is confirmed by the d(B - ®)/dy distribution which shows two pronounced peaks,in the projectile and target rapidity regions, respectively. Thus, much of the A signalderives from meson rescattering in the baryon rich projectile and target fragmentationregions . The rate of

_production in S-S collisions is about 120 times greater than

that in p-p collisions . By contrast, there is only 36-fold enhancement in the negativelycharged tracks (predominantly pions), so that the specific

yield experiences a three-fold enhancement (and probably a 10-fold enhancement if only the central region is

Page 10: Strange and hot matter

288c

considered) . The multiplicity of

per triggered event is stated to be 1 .5 . This is a trulysurprising result which cannot even remotely be explained by cascading in a hadronicgas (the probability of A formation decreases with the moderation of the beam energy,and there is large final state annihilation in such a microscopic picture) .

The accommodation o the

results by the most recent version of the VENUS stringmodel [181 is accomplished at the expense of creating a big hole in the central rapidity-yield . The yield of

particles traces out the baryon number distribution in rapidity.Thus it would seem that VENUS achieves a high central 1-yield by the artifice of thereduced annihilation associated with a baryon-depleted central region . As a consequencethe d(A- )/d rapidity spectrum is very peaked in the projectile - target fragmentationregions, with little remaining yield at central rapidity. In my judgement, this result isin essence in disagreement with the experiment, even though a superficial look maysuggest a qualitative agreement .

Another feature of the reported strange particle spectra is the unusually high tem-perature (slope parameter) [which I read as T = 220 ± 20 MeV 3] . It is important thatthe statistically significant spectra of both NA35 and WA85 are consistent with inter-pretation of the slopes as temperature (spectra for different particles lead to the sameresult) .

To appreciate the significance of this high temperature, it is worthwhile to recall afew practical results about transverse mass spectra . For particles with large scatteringcross sections (such as pions), the observed slopes (shapes) of transverse mass spectra atlow m_i provide us with information about the freeze-out temperature T' of that par-ticular particle species in the hadron gas [one should, of cause, also expect considerablecontamination from the decays of (heavy) resonances] . Moving to higher values of mlmeans that one is probing deeper into the history of the excited matter, at the sametime progressively escaping the distortion of the spectral shape by decay products -valculations [191 suggest that pl > 1 OeV suffices . Strange particle spectra can exhibithigher temperatures because they originate preferentially either from earlier periods ofthe evolution of the fireball or from particularly high-impact events .

In principle, there is considerable ambiguity in the meaning of temperature whencollective glow is present . A system, initially at T = To, cools in part by flow/expansion .y the time freeze out occurs (at T = Ti < To), we may still have a slope characterized

by To (or an even higher value for the most massive particles in the composite system),but the true thermal properties and hence the chemistry of particle abundances maybe dictated by the value Tl , which remains unmeasured . On the other hand, if theslopes differ for particles of different mass, one can make an effort to model the flow andthus recover the intrinsic temperature . The result is that the high pl tail of the pionspectrum reflects the initial temperature of the system (before transverse expansion setsin) . The absence of transverse flow is recognizable by the fact that slopes for particles ofgreatly different mass (7r, , A) are equal. This seems to be the case for the experimentalresults presented by VVA85, obtained in a narrow rapidity window and for high pi.

I conclude this initial discussion by noting that these experimental results supportthe use of a local equilibrium model in the discussion of the multi strange particle spec-tra emerging from a central fireball .

J . Rafelski / Strange and hot matter

'There are systematic differences in the way different groups fit the transverse mass spectra, using oftensimple forms rather than thermally motivated shapes appropriate for the particular measurement.

Page 11: Strange and hot matter

3.

ultistrange antibaryonsI now study the high rn1 , central y strange anti-baryon abundances emerging from

high energy nuclear collisions of 200 GeV/A S--+W . The characteristic and descrip-tive nature of this signature of quark gluon plasma formation will be quantitativelyaddressed .

The results from the experiment WA85 at CERN [20] were presented by J.P. I{inson .Of particular note is the fact that the abundance of neutral anti-cascades (99a) isunusually enhanced, in particular when compared to the abundance ofcascades and anti-lambdas (9ûd). I will now show that the experimental results of the WA85 collaborationcan be interpreted in terms a local equilibrium model and strongly suggest QGP-basedstrangeness production and reaction evolution .

I begin with a brief selection of the results of concern here . First, the E- /'E- ratiois

J . Rafelski / Strange and hot matter

289c

Rw := SE- /E - = 0.39 ± 0.0

for y E (2.3, 3.0) and pl > 1GeV/c .

(17)

Note that, in p-W reactions in the same (pl , y) region, a smaller value for the RV ratio,namely 0 .27 ± 0.06, is found . The I/A ratio is :

R.A := 1i/A = 0.13 ± 0.03 for y E (2.4, 2.8) and pl > 1GeV/c .

(18)

In Eq.(18), corrections were applied to eliminate hyperons originating from cascadingdecays . The ratio RA for S-W collisions is slightly smaller than for p-W collisions inthe same kinematic range. I note that we ought to be cautious _about the v,bundanceof A's as it may be affected by strangeness exchange reactions K(sq) - N(qqq) afterthe fireball has disintegrated . (The fact that A generically includes E° as well has noimpact on the ratio RA) . Rather important results obtained in the kinematic domainof Egs .(17, 18) are :

_

M_

;Z_= 0.6±0.2,

r=0 .20±0.04, = =1.2±0.4, -=0.40±0.08.(l9)

ii + £°

A + E°

A

AIn Eq.(19),I have assumed that the yield of the two different isospin components isapproximately the same. The fact that the more massive and more strange anti-cascadeexceeds at fixed ml the abundance of the anti-lambda is most striking, even thoughthe experimental error makes any firm conclusion impossible at present . These resultsare inexplicable in terms of particle cascades [21] taken at their face-value. The relativeyield of ~- appears to be 5 times greater than seen in the p - p ISR experiment [5] .

The observed particles are all at transverse momenta above 1 .2 GeV/c. This rela-tively high intrinsic momentum may mean that these particles were made early in thecollision, rather than in the final stages (where the details of the unknown mechanism ofhadronization are important for the abundances of different particles) . It is, at present,not evident that these high pl particles truly differ from the bulk of the reaction prod-ucts . Nor is it obvious that there is a hadronization period - it is conceivable thatthe entropy rich, small QGP drop probably at the origin of these particles evaporatesdirectly and completely into the vacuum . I will not assume a QGP as the source of thestrange (anti-) baryons measured by WA85. One does not have to make any assump-tions about the specific nature of the state of matter formed, except that it is subjectto local thermal equilibration .

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in a

J . Rafelski / Strange and hot matter

e the implications of these data for the local equilibrium model parametersin last section? First using Eq.(15), I obtain: -y. = NFO-.48 ± 0.17 = 0.7 ± 0.1 .collision system considered so far is near to absolute chemical equilibrium

eness, but -y. is still noticeably different from unity.s for the values of the chemical potentials, they are determined by the two forms

f the Eq.(9). Ignoring for the moment the isospin asymmetry factor, I find: ju,1T =167 .ln(RE/RA2) = 0.52±0.1, and a/T = OJ674n(RA/Rj) = -0.03±0.06, irrespectivef the composition of the source (HG or QGP) of the strange (anti-) baryons . While Aq

is appreciable, suggesting considerable baryon density, ju, vanishes within the precisionof the measurements . This indicates exact symmetry between the produced strange andanti-strange quarks, which can only occur in either :

I

baryon number free fireball of arbitrary composition;

(before re-equilibration or hadronization) ;

in a HG A the magic point in (T, As) parameter space for which the size of thephase space for strange and anti-strange baryons accidentally agree (see Eq. (12)) .

s there is a clear baryon asymmetry (c.f. the substantial value of u,IT), one can discardthe first alternative . The last option is not very plausible, but clearly it must still beexcluded by experiment (finding in a differing collision environment, with another setof T and it., that it . continues to be vanishingly small). The pure QGP phase is theonly plausible explanation of the result 1L, = 0.

Figure 1 . Domain of baryo-chemical potential AB and temperature T (it, = 0.03 ±0.06,-y,, = 0.7 ± 0.1 not shown) . Cross in shaded area: result corresponds to valuescharacterizing a thermal source of the strange (anti-) baryons observed by the experi-ment WA85. Dashed line : QGP perturbative energy density e =1 Gev fm-1 ; straightlines : Entropy per baryon S/B = 30, 35 in perturbative QGP. Hatched area : range ofha ronic gas phase.

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FE LACES

J. Rafelski / Strange and hot matter

29 1 c

Given the above model independent value of p, associated with the high

l >1 .5 GeV part of the central strange baryon and anti-baryon spectra, I obtain if bpais assumed to be non-zero : pea/T(1 + 0.58pi/pv) = pd/T = 11n(r/i~) = 0.47 f 0.03 . Thisimplies : pza /T = 0.46 f 0.08 and biz,IT = 0.041 f 0.007 . These results together with,u, = 0 and Egs .(13, 14) can be used to predict other strange anti-baryon ratios .

Despite the remarkable consistency of these results with the picture of a dense fire-ball consisting of QGP, it is worthwhile to remember that the present four data points(RA, R=-, R� R,) only serve to fix the statistical parameters (AQ , it ., -Y,) of the primordialphase. Suspicious listeners will note that I have used three parameters to "fit" fourdata points. The "fit" is, however a natural unstrained one and leads to the remarkableresult p, = 0, -+, = 0.7 . This point can be taken further . In Figure 1, I show the valuesof it.,T resulting from this study: the cross in the shaded area appears in middle of theQGP domain, at an energy density exceeding the bench-mark value of 1 GeV fm-s, ina region characterized by entropy per baryon S/H=30-35.

3.3 Final remarksI have shown that in studying the formation of rare strange particles, one can obtain

very precise and detailed information about the highly excited nuclear matter formed inrelativistic heavy on collisions . Full event characterization with considerable precisionis needed to fix the parameters of the system essential to a basic understanding of thestate of matter formed . Measurement of excitation functions for quantities such as 7,and it, would lead to a definitive understanding of the high density source of theseparticles .

The observed substantial enhancement of production rates of multistrange anti-baryons 2 in nuclear collisions, in particular at central rapidity and at highest transversemasses, cannot be obtained so far in microscopic reaction models [21] . I cannot imaginehow to interpret these data other than in terms of an evaporating drop of quark-gluonplasma [12] . However, the data are still fragile (at the level of only a few standard devi-ations) . Our tentative conclusion, is that the source of the high ml centrally producedanti-cascades is the primordial and/or explosive QGP state of matter with T ^_" 220 ± 20MeV and ILB ^_r 310 f 30 MeV.

Acknowledgements: I would like to thank the organizers and, in particular, F . Plashfor their generous support . I thank M. Danos and E.D. Davis for pleasant company andstimulating discussions which helped shape this report .

1

H.C. Eggers and J. Rafelski, Int . Journal of Mod. Phys. A6 (1991) 1067, andreferences therein .

2

P. Koch, H. Mfiller and J . Rafelski, Z. Physik A324 (1936) 3642.3

P. Koch and J. Rafelski, Nucl . Phys . A444 (1935) 675 .4

R. Matiello, H. Sorge,

. St5cker and

. Greiner, Phys . Rev. Lett . 63 (1939)1459 .

5

T.

kesson et. al ., AFS-ISR Collaboration, Nucl . Phys . G246 (1964) 1 .6

. Jacob and J.

afelski Phys . Lett .

192 (1937) 432 .7

see. e.g : J . Rafelski and

.

anos, in: " adrons and Heavy Ions", ed.

.D.eiss, Springer Lecture Notes in Physics 231 (1955) 361 .

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8

R. Hagedorn, 1. Montvay and j . Rafelski, "Thermodynamics of Nuclear Matterfrom the Statistical Bootstrap Model", Erica proceedings, "Hadronic Mattar atxtreme Density", N. Cabbibo and L. Sertorio, e'litors ; also CERN TIi-260578) .agedorn and J. Rafelskt in: "Statistical Mechanics of Quarks and Gluons",

Satz, North Holland, Amsterdam 1981, p.237 ; R . Hagedorn, in : Quarkattar '84, Springer Vol . 221 (1985), ed. K. Kajantie, and references therein .

10

J. Rafelski, Phys. Lett . B190 (1987) 167.11

J. Rafelski and M. Danos, Phys. Lett . B192 (1987) 432.12

J. Rafelski Phys. Lett . B262 (1991) 333 .13

R Koch, J . Rafelski and W. Greiner, Phys. Lett . B123 (1983) 151.14

J. Rafelski, Phys. Rep. 88 (1982) 331.15

In: "Hadronic Mattar in Collision 1988", P. A. Carruthers and J. Rafelski,editors, World Scientific, Singapore 1989 .

16

For further details of the diverse strangeness experiments, the reader shouldconsult the other reports in this volume.

17

R. Stock, Nucl . Phys . A525 (1991) 221c .18

K. Warner, "Strange Particle Enhancement in Heavy Ion Collisions," these pro-ceedings .

19

J. Sollfrank, P. Koch and U. Heinz, Regensburg preprint TPR-91-17: "Is therea low-p_L anomaly in the pion momentum spectra from relativistic nuclear col-lisions?" .

20

S. Abatzis et al ., WA85 Collaboration, "Strange Particle Production in Sulphur-Tungsten Interactions at 200 GeV/c per Nucleon," theses proceedings .

21

L . Csernai, N .S . Amelin, E.F. Staubo and D . Strottman, Bergen University Re-port 1991-14, table 4, and private communication ; see also N.S . Amelin et al .,"Collectivity in Ultra-Relativistic Heavy Ion Collisions," these proceedings .

9ed.