Multistrangeness production in heavy ion collisions

Nuclear Physics B (Proc . Suppl .) 24B (1991) 221-233 North-Holland

MULTISTRANGENESS PRODUCTION IN HEAVY ION COLLISIONS R . MATTIELLO, C. HARTNACK, A .V . KEITZ, J . SCHAFFNER, H . SORGE and H. STÖCKER* Institut für Theoretische Physik, J .W . Goethe Universität, Frankfurt am Main, Germany and C . GREIFER Inptitijt für Theoretische Physik, Universität Erlangen, Germany The creation 4i , f multistrange objects (strangelets and multi hypernuclei) in heavy ion collisions is contrasted with the occurrence of strangelets in astrophysics .

INTRODUCTION

0

pernovae and neutron stars are rather in thermal

The possible existence of strange quark matter droplets

equilibrium . The initial momentum distribution in

(strangelets) offer fascinating astrophysical implications

heavy ion collisions, in contrast, is far from equi-

for the physics of the big bang, dark matter, supernova

librium: It can be represented by two separated

explosions and the structure of neutron stars . However,

spheres in momentum space .

a detailed experimental approach towards strangelets is difficult with events so remote in space and time . Re-

Both the strangelets from the early universe, su-

0

A high strangeness density is predicted in the inte-

cently, an alternative experimental approach has received

rior of neutron stars [2], while there is zero strange-

much attention, namely the production of strangelets in

ness in ground state nuclei .

relativistic heavy ion collisions [1] . How can we hope to establish the conditions for strangelet formation in the

0

essary for strangelet formation is predicted in neu-

fleeting moments (10-22 sec) of such a heavy ion reaction? 0

0

tron stars due to Q-equilibrium . In nuclear colli-

The largV baryon number in astrophysical strangelets

sions, even if strangeness is produced, it can only

is to be contrasted with a total mass number A less

be produced in

than 500 in heavy ion reactions .

hypercharge in strong interactions . Q-equilibrium

Baryon densities of Lo

-C .,

Loo

Energy densities of - 10eo are expected values in supernova explosions, while the initial nuclei have just co = Loom - 0 .15GeV/fm-3 . 1n the early universe, e even diverges for

i H

0.

0

r, 199i - Elsevier Science Publishers B .V .

pairs due to the conservation of

Neutron stars, supernovae and early universe have total charge zero just as the strangelets hopefully present .

In contrast, nuclear collisions exhibit a

charge to mass ratio of roughly 1/2, thus the charge needs to be depleted in order to make a strangelet .

'invited speaker 0920-5632/91/$03 .50

ss

(r - 10- '°sec) can not be established during the brief encounter of nuclei, T'ott _ 10-22 sec .

10eo are predicted in the

interior of neutron stars while densities of nuclei - 0 .17fm-3 . are at the nuclear ground state 0

Furthermore, the net strangeness enrichment nec-

All rights reserved .

R. Mattiello et al./Multistrangeness production in heavy ion collisions

222

e The strangelets predicted in neutral quark stars have approximately zero temperature, and also in supernova collapses the entropy is small, S/A N 1. The high bombarding energies of relativistic nuclear collisions imply on the other hand very high temperatures .

The strangelets are most interesting for astrophysics if they are absolutely stable . However, in nuclear collisions we may also study short lived, metastable strangelets and multi hypernuclei . How can these many obstacles for strangelet creation in high energetic heavy ion collisions be circumvented? % 'e will discuss in the following the above topics consecutively and show how heavy ion physics and astrophysical questions are connected to each uthet. For the ca?culatiofls sham.: :a Sect. 1-4 we used ti-,îi Vlasov Uehling Ulrlenbeck (VUU) model [3, 4] and the so-called (R)QMD ( (Relativistic) Quantum Molecular Dynamics. ) -model as a theoretical tool to investigate hadron-hadron hadron-nucleus and nucleus-nucleus reactions and to gain more detailed insights in the dynamical structure of relativistic heavy inn reactions . The basic ingredients of the RQMD model are the propagation of all hadrons on classical trajectories including density dependent mean field interactions . Binary stochastic scattering processes with Pauli blocking corrections are taken into account to simulate the important quantum features which are not present in ordinary molecular dynamics but turn out to be the most important part of interaction at high energies. As an extension of the nonrelativistic QMD the RQMD approach uses a covariant formalism called Hamiltonian constraint dynamics [5] which allows for a classical microscopic Nbody theory which is essentially Lorentz invariant . Furthermore, the RQMD model takes into account varticle production via the possibility of choosing randomly the formation and decay of highly excited intermediate hadronic states (r,!sonances or strings) in each binary

hadron hadron collision . The effective masses, branching ratios and decay widths are either determined via experimental data or a phenomenological string fragmentation scheme. Total, elastic and inelastic cross sections are irn" lemcinted generally by exclusive and inclusive measurements. For unexplored binary collision types the RQMD uses phenomenological approaches like particle exchange models, s-channel resonance formation and the Additive Quark Model (AQM) . 'I he RQMD treats explicitely the space-time structure of highly excited states via stringphenomenology. The interaction of such highly excited hadronic states with the nuclear medium is done in the spirit of the constituent quark picture using Additive Quark Model assumptions. Constituent quarks at the ends of those excited objects may interact without time delay but with reduced cross sections while newly created (di)gnark pairs need a. formation time before th,~y may constitute hadrons .

1 . BARYON STOPPING AND DENSE MATTER FORMATION The only possibility to study a nuclear system with high baryon number in the laboratory are heavy nuclei like Ag, Pb, U. Large densities may be achieved in the compression phase of high energetic collisions of those massive ions due to show, wave formation [6, 7] and the stopping power of nuclear matter. For the stopping of two colliding nuclei, i.e. the transfer of the dominant initial longitudinal momentum into particle production and thermal degiees of freedom, the collision term is quite relevant . This can be seen in Fig. 1 where is shown the scaled final rapidity distribution dP!ld(Y; Yp) (where hp is the initial mean rapidity ofthe projectile) for the (massive) system Pb+Pb, b < 3fm, at 200 and 1000 AMeV calculated with QMD and the corresponding reaction at 160 AGeV calculated with RQMD (histogram) . The distribution changes frorn initially two peaks at projectile and target rapidity into one maximum at cm rapidity. Note the similar shape over three orders of magnitude

R. Mattiello et al./Multistrangeness production in heavy ion collisions difference in the incident energy! The scaled rapidity distribution indicates that the same number of particles have lost the same fraction in rapidity. Keep in mind that the initial rapidity distributions are settled around different rapidities . Therefore, for higher energies less particles are stopped to very low longitudinal momenta. A decrease of the cross section increases the mean free path and thus causes drastic effects on the rapidity distribution. At intermediate energies the strong stopping ofheavy systems has been confirmed by experiment. for smaller systems the stopping is less strong and the rapidity distributions gets rather flat. This has also been confirmed by the Plasticball experiments (for the intermediate energies) and by the NA35 group (for high energies) . Fig. 2 shows RQMD calculations for the system S+S at 200 AGeV incident energy. The histogram marks the flat distribution. of th, baryons and the full line the widely spread rapidity distribution of negative charged particles, which are dominantly pions produced at midrapidity. Note the excellent agreement between calculation and data [S] .

223

30

10 0

0

2

`

Rapidity

6

FIGURE 2 Rapidity distribution for the system S+S at 200 AGeV, baryons (histogram) and negative particles (full line) .

Pb+Pb b<3 fm ~ 300

Z

100

oL

G 0.2GeV à 1Gev 160GeV

, 0.0

10

0.5

rapidity Y/YP

0®

1.0

(Lab)

FIGURE 1 Scaled rapidity distribution for the system Pb+Pb b < 3fm for 200 AMeV, 1 AGeV and 160 AGeV incident energy.

Ô

ot

06 02 00

FIGURES 3 and 4 Ti, :.volution of energy density (top), baryon density (mi, , end isotropy for Pb(l0AGeV)+Pb.

224

R. Mattiello et al./Multistrangeness production

Let us consider now the densities reached in high energy collisions of heavy nuclei . Fig. 3 shows the time evolution of the energy and baryon density in the cell of maximum energy density during a centr,::tl collision of Pb+Pb at 10 AGeV incident energy. The cells are given a finite size of about 6fm3. We see baryon densities of more than 10 times ground state density and energy densities up to 3 GeVfr-3 . A normal superposition of transpareatly passing nuclei would yield (including the -y factor) a maximum density of less than 6 times ground state density which is exceeded by far. Furthermore, regions with an energy density of more than 1GeVfrn 3 are very large and they live for several fm/c, afterwards the volume of high density drops quickly. From those high densitiy regions one may hope to gain a lot of interesting signals . 2. THERMALIZATION AND COLLECTIVITY In order to understand hot and dense nuclear matter as a compressed equilibrated state in terms of macroscopic quantities like density, temperature and pressure, we have to check whether the system reaches (local) equilibrium. In the ideal case the system has to stop from two Fermi ellipsoids (in momentum space) in tire initial state to one sphere in each space point in the final state. One condition for isotropy - as a first approach - is the ratio of the squared momenta < pT > /( 2 < pz >) in the cm frame of each phase space cell. The time dependence of this ratio can be taken from the analysis of Pb+Pb at 10 AGeV incident energy. We see in Fig. 4 that the system finally reaches nearly thermalization . A similar behaviour is found in the analysis of the system Au+Au at 200 and 800 AMeV incident energy, where high degrees of isotropy (about 70-80°10) are reached . The experimental verification of macroscopic states in relativistic heavy ion reactions is rather difficult because to date there exist rco unique observables which can test the macroscopic properties of the compressed matter zone during the nucleus-nucleus reaction . Re-

in

heavy ion collisions

cent calculations of dilepton spectra within our model approach showed that electromagnetic probes, in contrast to hadronic particles which are strongly modified by final state interactions, may serve as a direct measure of densities and in-medium effects [9, 10] . Fowever, at least some observables seem to be sensitive Io the collective behaviour of the participating nucleons, namely the collective transverse flow (bounce off) and the so-called off-plane squeeze discussed in the follov-ing. 2.1 Bounce off The analysis of the bounce off has been proposed rather early in order to get some information about the internal pressure of the hot compressed system and thus about the repulsion of dense ratter . The transverse flow increases with the mass of the system and depends on the impact parameter and the equation of state. Let us focus on the mass and ¬i.crgy d.pandence . Fig . 5 shows VUU calculations of the transferred transverse momentum pl' =< pxsign(Y - Y(cm)) > for Ca (dashed), Nb (full) and Au (dash-dotted) . We see that the values for the larger systems are higher than for the smaller ones. The flow increases with energy and seems to saturate to a constant value. Fig. 6 shows a calculation of RQMD for

X+X Hard EOS VUU

0 Nb-b=3 C Ca-b=2 6 Au-b=3 ,-. . G 500 1000 1500 2000 Lab energy IMeV)

2500

FIGURE 5 Energy dependence of pjr for Au, Nb and Ca, VUU hard eos.

R. Mattiello et al.%Multistrangeness production in heavy ior. collisions Pb+Pb b < 3fm at 160 AGeV without potentials (histogram) and a corresponding calculation of QMD (also without potential) at 1 AGeV incident energy (dashed lines). Note the nearly identical slope of the flow curves. We see bounce off effects even at the highest energies!

Au+Au b<3fm no potential

N C7

x

0.05 000 0.05 T --'I

0.0

.

O 1GeV ri 150GeV i

0.5

-

i

1

1.0

rapidity Y/YP (Lab) FIGURE, 6 px(Y/Yp) for Pb+Pb at 1 AGeV and 160 AGeV, no potential . 2.2 Out of Plane Squeeze The transverse momentum in plane has its maximum at projectile and target rapidities and is dominated by rather `cold' matter . Now it is interesting to learn something about the behaviour of hot participant matter Au(4OOMeV)+Au b=3fm

225

stopped to Y = Yc m, where the transverse flow vanishes < pz >;,,e, 0 by construction . Let us consider the azimuthal (cp) distribution of the particles where W is the inclination angle betwecu gT and the x-axis . Fig. 7 shows the azimuthal distribution at cm rapidity for the system Au (400 MeV) + Au. The histograms show the experimental data of the Plasticball collaboration [11] and the triangles denote QMD calculations at fixt:d impact parameter b = Min calculated with a soft equation of state including momentum dependent interactions (mdi) . The frame to the left shows the dn/d~p distribution in the unrotated (pz =beam axis) frame, the mid column depicts the do/dcp distribution after a rotation into the principal axis system of the momentum ellipsoid obtained from the sphericity analysis [12]. Both figures show a maximum at 90°, i.e. perpendicular to the reaction plane, and minima at 0° resp. 180°, i.e. in the reaction plane . The peak is much more significant in the rotated system and becomes even more prominent if we convolute the distribution with the transverse energy of the particles, as we can obtain from the distribution of the total transverse energy per ~p-bin, d E ET/dcp on the r.h.s of the figure. We see ageneral qualitative agreement of the structure of the squeeze between data (histogram)

Au(4OOMeV)+Au b=3fm

FIGURE 7 Azimuthal distribution in the unrotated and in the rotated system.

R . Mattiello et al./Multistrangeness production in heavy ion collisions

226

and calculation (triangles) .

Let us now keep on the transverse energy distribution taken in the rotated system end regard the peak-to-valley ratio RE of the transverse energy distribution. Fig. 8 shows the mass dependence of RE for QMD calculations with hard and soft equation of state plus momentum dependent interactions (HM resp. SM) . Note the linear dependence on the -mass number . This linear dependence is also sp.r ir, Uie experimental data (bullets) . This is a genuine collective phenomenon. Note also the differences between HM and SM. AX(400Mey)+ AX b

.

a

0.25 b.x

3. STRANGENESS PRODUCTION

1_,_4 SM

T .-*

50

100

150

mass A

Let us now turn to very central collisions with a high degree of isotropy. The experimental determination of the reaction plane is done by calculating the vector Q = Fj PT - sign(Y` - Y-) [l.8] . One strategy to determine very central events is to look on high multiplicity events with small 1Q) [16] . Fig. 9 shows the contour plot of the invariant Y - pT/m plane for the system Au+Au b < Min soft equation of state -I- mdi for events with JQ1/A < 40MeV using the Plastic ball filter for the analysis. Most particles have a rapidity around 0 in the cm system (stopping) and a maximum at a fi nite pT/m 0.1. This maximum has nearly the same position for protons, deuterons, alphas and intermediate mass fragments . This may be a signature for compression waves in very central heavy ion collisions.

200

FIGURE 8 Mass dependence of the peak to valley ratio RE for QMD, HM, SM and Data at 400 AMeV incident energy.

Aufl00MeVhAu b<51m G/AK0M&V ,&>0 88 PbF SM

0.8

Strangeness does not appear in ordinary ground state nuclear matter but should be sensitive to dense compressed and excited nuclear matter states. E.g . kaons with their rather small absorption cross section constitute an interesting probe to study some properties of the high density zone [17]. As an example we show in Fig .10 the kaon excitation function for Au-I-Au which exhibits a strong dependence on the eos . However kaon produc10"? 10-1

0.6

U :3 10-1

6 z 10i

0.2 0.0

10-6 -0 6 -0 4 -0 2 0.0 0 .2 0.4 0 6 Y

alt nuc.

FIGURE 9 Contour plot of very central nearly isotropic events of Au+Au in the Y - pT/m plane.

10-7

FIGURE 10 Excitation function of the kaon to nucleon ratio far Au-)"Au, b = 3fm, hard and soft eos .

R. Mattiello et al./Multistrangeness production in heavy ion collisions tion is also sensitive to the momentum dependent forces [18]. Strangeness, in particular the K/x-ratio, was considered for a long time as an appropriate signature for a phase transition to the QGP because of the results of thermodynamic (and chemical rate) calculations [19, 20] . Therefore, the observation of enhanced K/7r ratios in the reaction Si(14 .5AGeV)Au at AGS [21] and the enhanced production of A (A) particles even in the light ion reaction S(200AGeV)S at CERN [22] has received much attention .

mt -mo (GeV/C 2)

FIGURE 11 Transverse enrgy spectra of positively charged particles in the reaction Si(14 .5AGeV)Au . Calculations (RQMD 1 .07) are compared with data points from Ref. [28] . The rapidity range is 1.2 < y < 1 .4. The histograms represent the RQMD results for p (straight line), 7r+ (dasheddotted line) and K+ (dashed line) . The symbols denote the E802 data: circles (p), dots (7r+) and squares (K+). In addition an exponential fit to the RQMD results is shown which clearly demonstrates the different apparent "temperatures" . Earlier RQMD-calculations [23] have shown that the observed enhanced K/7r-ratios in the reaction 5i (14 .5 AGeV) Au can be understood without the formation of a Quark-Gluon plasma (see Fig. 11) . We demonstrated that roughly an equally large contribution to the stcange particle yields stems from the secondary interaction of produced particles and the primary interaction of baryons. All contributions from baryon-baryon, mesonbaryon and meson-meson collisions together have to be

227

taken into account to describe properly the final amount of produced strangeness. In fact, in central Si+Au reactions a strong K+ enhancement (factor of 2) and moderate K- enhancement (25 %) relative to the pion yields is found from recent RQMD calculations [9] . The overall agreement for strange particles between RQMD and E802 data is surprisingly good, if one takes the complex reaction dynamics into account [9] . This is a severe signature for the importance of non-equilibrium effects on particle production as well as for the drawbacks of pure thermodynamic calculations. E.g. simple fragmentation schemes like FRITIOF fail to explain_ those results . They assume that the projectile nucleons move on straight lines through the target . Both excited projectile and target nucleons decay independently after the actual collision process has ceased. Therefore additional strange production channels by meson-baryon and meson-iiieson interactions are definitely neglected. Two trivial effects - kinematical suppression of high energy 7r N collisions and nearly the same strangeness N

0(200AGeV)Au

û int c?

z

too 10 -t

1 .5
~ A O NA35 data

MOW --- FRITIOF(totat)

~n 10-a

A

0(200AGdV)Au _

10t m ~3 10°

~S 10-a

~.,

K°.

2

Jim

1.7
RQMD --- FRITIORtotaU

0

1 pt (GeV/c)

2

FIGURE 12 Transverse momentum spectra of A and K° in the reaction O(200AGeV)Au . The data points are from Ref. [22].

228

R. Mattiello et al./Multistrangeness production in heavy ion collisions

suppression as in pp - explain why calculations which are based on a pure 7r N gas show no relevant strangeness enrichment for AA collisions at AGS energies at all [24]. The basic reason for enhanced K/7r ratios is that in contrast to 7r N other meson-baryon interactions forming the same resonances enrich the strangeness, because - in a small percentage of all interactions - they produce kaons, but they do not increase the net number of pious in the

system. One interesting question is: can we see the importance of rescattering also at higher energies and in connection with the production of strange particles? In Fig. 12 we compare the experimental yields with RQMDcalculations for A, Ii° particles and all hyperons in the reaction 0(200AGeV)Au . FRITIOF fails to explain the A yields but RQMD describes again excellently the absolute values as well as the transverse momenta. On the other hand, the strange (anti-)particle yields in pA and light ion reactions like S(200AGeV)S can not be explained within the RQMD approach. Here, the RQMD underpredicts the measured values by a factor of roughly 1.5- 2. This makes clear that the rescattering argument is probably not the whole truth . Moreover, one has to think about new phenomena and e.g. medium effects seem to be a very promising way to improve the understanding of strange (anti-)particle production [15, 14, 9] .

4. MASSIVE REACTIONS AND MEMO-PRODUCTION As we have seen before multiple collisions per hadron ensure that a system starts to equilibrate which might be suited to search for the most interesting collective effects . In particular all exotic multistrange objects need for their formation large strange particle numbers, high degree of equilibration and large densities . These requirements should enlarge their production probabilities due to simple coalescence arguments . In o:de. to get this kind of states one should therefore use high energies to produce enough strangeness and energy density, and

heavy nuclei to gain as much equilibration as possible.

Fig. 13 shows - as a prediction of the RQMD model the dN/dy distributions of hyperons in the central reaction Pb(160AGeV)Pb and in Fig. 14 are depicted the production probabilities of several kinds of exotic baryon-clusters . We used in this case simple momentum space coalescence and varied the coalescence parameter which is actually two times the cms momentum of the two participating baryons . These first simple estimates for the production rates of multi strange states are Pb(160AGeV)Pb 60

total

A

20 0

0

2

iX r ,_~

4

6

Rapidity FIGURE 13 Rapidity distributions of several types of hyperons as a prediction of the RQMD model for th- reaction Pb (160 AGeV) Pb.

10° > 10-1 10-s 10-3 10 -1 50

100

150

200

250

po (MéV )

FIGURE 14

Production probabilities of exotic baryon clusters calculated with the RQMD for the system Pb(160AGeV)Pb .

R . Mattiello et al . /Multistrangeness production

remarkably high. Therefore, ultrarelativistic heavy ion collisions seem to provide a scenario for the formation of metastable exotic multihypernuclear objects, i.e. a metastable combination ofdifferent strange baryons with or without additional nucleonic degrees of freedom. The Relativistic Mean Field (RMF) model is able to reproduce measured single particle energies of different hypernuclei . The application of this very successful model to multi A-hypernuclei shows that those exotic objects are in many cases much more stable at the time scale of the strong interaction than the corresponding nuclei without strange degrees of freedom . The situation gets even more interesting once a new degree of freedom, i.e. the double strange hyperon E" is introduced . This is analogous to the discussion of strangelet stability [25]. Simple energy conservation arguments allow for the existence o3 metastable multi strange hypernuclei with even f, = SfA - 1 if hyperons with S > 1 (e.g. F(S = 2)) are taken into account. Within the RMF model these metastable exotic multistrange objects (MEMOS) are not excluded if the (universal) coupling constants extracted from hypernuclear data are employed. These objects can be negatively charged while carrying positive baryon number . If the degree of stopping and thermalization at high densities is large enough, as we have shown as a prediction of the RQMD approach, the argumentation with more simple models like e.g. thermodynamic rate equations seems to be again reasonable. We refer in this context to the next section where is drawn a rough picture of how strangeness and charge is distilled during a first order phase transition from a QGP into the final hadronic phase, and how this way a metastable and cooled strangeness enriched quark matter droplet is formed . However, the predicted large production probabilities for strange matter (clusters), the collective effects (flow, high degree of stopping ) and the simple measurement of negatively charged objects with small charge to mass ratios may stimulate experimentalists to look for such possible exotic channels in high energy heavy ion collisions.

in heavy ion collisions

229

5. HOW TO COME TO STRANGELETS? In the foregoing sections the dynamics of ultrarelativistic heavy ion collisions was extensively presented and explored by use of the microscopic RQMD - model. In the spirit of this workshop the production of multiple strange hadrons and the baryon stopping were emphasized . Concludingly, strangeness saturation in phase space is achieved by the nonequilibrium dynamics . However, one should be aware of the fact, that the energy and baryon densities reached are so large, that a phase transition to a quark gluon plasma (QGP) may have occured .

Several hadrons are localized in, let's say, 1 fm3 and are treated as single unique particles, although they nearly have to overlap completely. This degree of freedori is not incorporated in the model, because it is based solely on a hadronic (and string-like) scenario. In the following wP want to sketch some reasons why the production of strange quark matter clusters, if they do exist in principle, is very likely, if a baryon rich and hot QGP is created in such collisions. Explicit calculations, the nonequilibrium aspects of the phase transition, like meson and nucleon radiation, the cooling of the system and, indeed, the distillation and possible survival of strangelets are summarized more detailed in another contribution to this volume [2S]. At first sight there seems to be no chance to succeed: The net strangeness of the QGP is zero from the onset, although an equal, however large, number of strange and antistrange quarks has been produced by gluon fusion [29] . So there must be some physical mechanism which separates the strange quarks from their antiparticles, otherwise strangelet. nrnduction is ;iot reasonable! 5.1 The Distillation Mechanism Consider the phase transition of the QGP to the hadron gas at some critical temperature [27]. How does the strange and antistrange quarks hadronize during this transition? There is no reason why these different quarks do hadronize in the same manner and time, especially if

R. Mattiello et al. /Multistrangeness production in heavy ion collisions

230

one thinks of a baryon rich system (which one has to look at because of the large stopping menti( ned above) . It is `simple' for the antistrange quarks to materialize in kaons K(qg) because of the lots of light quarks . The possible strangeness content in the two different phases is schematically drawn in Fig. 15. During an equilibrium phase transition a large antistrangeness builds up in the hadron matter while the QGP retains a large strangeness V HG

V QGP

' QGP

S

S

K° H G + K

QGP,~ o < S >tot

-

< S >HG

< S >HG< 0 + < S>QGP = 0

FIGURE 15 Schematic picture of the separation of strangeness during the phase transition.

500

FIGURE 16 Fraction of strange quarks to all quarks present in the QGP as a function of pa and the volume fraction X . Note that f, can exceed 0.5. The path of an isentropic expansion is also shown .

exceso.. This separation will occur only when the system carries a positive net baryon number. In Fig. 16 we show the fraction of strange quarks to EM quarks present in the QGP as a function of the baryon chemical potential pe and the volume fraction X of the hadron phase to the total system, i.e. VHad/(VHad + VQGP) [27] .

At the beginning of the phase transition (VHad = 0) the well known result p, = 0 is recovered, s and s quarks are produced in pairs only. On the other hand, for vanishing QGP (VQGP = 0) zero net strangeness leads to a nonzero value of the strange chemical potential p, > 0 [27]. Different strange particle production shows up in the dominance of the associated production over the direct pair production at finite baryon density. During the coexistence of the two phases, an additional channel opens up for the strangeness: besides the ass~,,ciated pair production in the hadron gas it is possible to have, for example, associated production of a IC meson in the sector of the hadron gas phase and the squark staying in the QGP . This leads to the ratio of s to anti-s-quarks larger than 1 in the quark phase and to a diminished hyperon abundance, the hyperons being too massive, in the hadronic gas sector at finite net baryon densities . This enormous enrichment opens up the possibility that s-quarks may be bound not only in hyperons and strange mesons, they could form strange quark clusters which might be metastable objects . Furthermore, rapid kaon emission leads to a finite net strangeness of the expanding system. This results in an even stronger enhancement of the s-quark abundance in the quark phase. Indeed it was shown that these prompt kaon (and, of course, also pion) emission may cool the quark phase, which then condenses into metastable or stable droplets of strange quark matter [30] . 5.2 The Cooling Mechanism Recently Barz et al. [31] presented nonequilibrium rate equation calculations, which suggested that nucleon

R. Mattiello et al./Multistrangeness production in heavy ion collisions evaporation heats up (non)strange quark droplets, which in response evaporate completely. This, in fact, seems to make strangelet production unfeasible . However, we have shown before [30] that for the large bag constants (B+ = 235 MeV) employed here strangelets indeed cannot be formed . Of course, they would in fact neither be stable nor metastable : The mass of a quark matter droplet (at zero temperature) is much too large to 1400 MeV, as compared to be stable, E/A - 6B+ the nucleon mass, 940 MeV . In response, the surplus of ti 450 MeV/A can heat up the cold blob quickly. Oa the other hand explicit cooling calculations have been performed [32] for rather cold (T - 20 - 50 MeV) and very large (A - 105° ) stable strange quark matter globs formed in the early universe : An effective nucleon binding en igy 1,, ---- mnn - 3pq » 0 is found due to detailed balance for nucleons and antikaons evaporated from the surface . In our recent calculations (see Ref. [28]) the chemical potentials p4 and p, of the evolving droplets (as the time is getting large and the temperature T is strongly decreasing to 7' - 10 - 20 MeV) are : -r oo) - 200 - 275 MeV , (B+ --+ oo) - 300 - 325 MeV

e 1) p q (t p.(t

= 145

MeV) ;

231

In addition, the differential of eq. (1) is 0(E/A) = 27TOT. Combining these two expressions and integrating from the initial temperature T; to T = 0 yields the final baryon number of the strangelet : Afin*' = A(Ti) exp (

. n -ÎT2) For In - 250 MeV and Ti - 20 MeV, a tot a! of - 92 percent of the initial baryon number would remain in the droplet. Hence, evaporation of baryons from quark matter will be suppressed at very low temperatures and will cool the droplet, because there is simply not enough energy available to power the evaporation . 6. CONCLUSION In conclusion, we have demonstrated that although on first sight the conditions for strangelet formation in relativistic heavy ion collisions appeared not to be very promising, these systems can be driven by the dynamics of the reaction of very heavy ions to become a - possibly prolific - source of strange quark matter droplets of masses A - 6 - 400: o Shock formation enforces high baryon densities. o Nuclear stopping yields high excitation energies.

" 2)1t9(t --+ oc) - 200 - 250 MeV , - 350 - 400 MeV (B+ = 160 MeV). lis(t --+ oo)

o The momentum distributions quickly transform to nearly equilibrated states.

Thus In - 120 - 350 MeV is indeed positive in contrast to the claim in Ref. [31]. Now, to illustrate how stahlo strangelets cool and survive, lit us consider for the moment just nucleon evaporation : The energy per baryon of a strangelet at small temperature and zero pressure is approximately given by

o Inelastic collisions - off equilibrium - result in high strangeness yields .

E

(E)

A

A

+

7T_

s

ti

~

-

Tom,., V

(1)

The emission of a nucleon will decrease the energy per baryon of the blob : 0

T) AA,

(E) = A(

AA < 0 .

These processes are the key mechanism to form a quark gluon plasma in high energy heavy ion reactions. If such a novel state of matter is indeed separated through a first order phase transition from the dense baryonic matter, it will most, probably constitute a source of (metastable) strangelets, otherwise it may result in MEMO formation . o The abundantly produced ss pairs can be separated chemically by the distillery phenomenon at

R. Mattiello et al. /Multistrangeness production in heavy ion collisions

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the phase boundary due to large chemical potentials p, and pB . ®These strangelets need not be in # equilibrium, they may be observed in t < tp = 10''-"sec . e The strangeness distillation also yields a distillation of charge Q, such that Z/A may even become less than zero which in turn facilitates an experimental detection of these heavy negative particles . e 7c, K, p emission carries away heat, entropy and antistrangeness, thus cooling the strangelet. e Metastable exotic multistrange objects with similarly extreme properties (Z/A, e, etc.) may be formed in heavy ion collisions, also without QGP formation . They may constitute a directly competing doorway state to the strangelet . ACKNOWLEDGEMENT C.H. and H.St . wish to thank Dr. H.-J . Reusch and Dr. H. Bahnvsky from IBM, Wissenschaftliches Zentrum Heidelberg for valuable support in optimizing and speeding up our computer codes of VUU and QMD . This work was supported by the Deutsche Forschungsgemeinschaft, the Bundesministerium für Forschung und Technologie and by Me Geseiiscnait Mr aciwe ioîien ischung

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