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THE STRANGE QUARK GLUON PLASMA

Johann Rafelski", U. Heinzb, J. Letessierc, J. Sollfrankb and A. Tounsic "Department of Physics, University of Arizona, Tucson, AZ 85721 binstitut fiir Theoretische Physik der Universitiit,D-93040 Regensburg CLPTHE, Universite Paris 7, Tour 24, 5e et, 2 Place Jussieu, F-75251 CEDEX 05

ABSTRACT The mechanisms producing the strange quark flavor in high energy nuclear collisions are discussed and a dynamical picture developed for the build up of strangeness. The parameters characterizing strangeness phase space population are discussed and are related to measurable quantities. Circumstantial evidence for the formation of the deconfined phase (quark- gluon plasma, QGP) is presented, based on anomalous strange antibaryon abundances seen. It is argued that further experimental data will make the identificationof QGP definitive.

1. STRANGENESS AS AN OBSERVABLE OF QGP: Finding uncompromising signs of the transitory presence of the Quark-Gluon Plasma phase in the debris of the high energy nuclear collision has become the obsessive preoccupation of the high energy heavy ion theorists. The idea to use for this purpose the strange particles is not new and in the past dozen years strange particle production in heavy ion collisions and in particular their importance as diagnostic tool has been discussed a few times already at Rencontres de Moriond [l]; in the past 18 months considerable progress has occurred which allows us to return to the topic again, both in this report and in the parallel presentation of U. Heinz [2]. In order to appreciate these developments in full it is necessary to recall that the dynamical processes of strangeness production were from the beginning recognized as an essential element in the understanding of the high density matter in the central fireball. The principal novel development in this context is that we have learned to use the experimental results to meter some important elements of these dynamical processes. U. Heinz [2] has presented a detailed thermal fireball model picture of relativistic heavy ion collisions and has developed the characteristic patterns of behavior expected of strange particles emerging from QGP and HG fireballs. In particular and under the assumption of 622

the relative chemical equilibrium of the strange baryons and antibaryons one can argue con­ vincingly that the experimental data are inconsistent with the source being a thermal, normal gas of hadronic resonances (HG). However, the evidence for the formation of a QGP fireball is not yet persuasive as it depends on the picture of hadronization which remains still unproven, despite detailed comparison of the theoretical predictions to the available experimental results. We should record that although strangeness enhancement has been for a long time pre­ dicted to occur in association with the QGP state, it can not alone be taken as decisive evidence for this novel physical state. Alternate pictures of the reaction could, in principle, be developed, which also comprise general strangeness enhancement. However, the QGP state stands out not only as an effectiveprodu cer of strangeness, but also as a state which contains a rather high strangeness density, and I have yet to see a proposal which can mimic this latter and more characteristic feature of the QGP phase. In a fully strangeness saturated QGP phase at T = 250 MeV, the thermal strange quark density is up to 0.8 strange particle pairs per fm3. The high density phase is rather simply observable: we can anticipate easy formation of hadrons in particular in an explosive disintegration process. In the hadronic multiple strange gas phase we typically find a 3 times lower strangeness density at the same thermal conditions (viz. same temperature and chemical potentials, which are the observable quantities), aside of the likely further reduction in density due to reduced occupancy of the strange particle phase space. This expected huge strangeness pair density in QGP phase is in my opinion the main point of interest and should be relentlessly pursued by further measurement of the diverse strange particle signatures. It is hard to imagine another scenario in which in par\icular the strange antibaryons would be abundantly produced. Normal hadronic interactions are not effective in producing these particles; a further reduction of the normal reaction background is accomplished by considering antibaryons, as none of the constituent quarks of these particles is brought into the collision zone by the colliding nuclei. Therefore I have made the suggestion to study the relative abundances of the anti baryons ":"', pin order to test for the presence IT, A, of the deconfined phase [3] . The point is that while in normal hadronic interactions the relative abundance of these particles is rapidly decreasing with increasing strangeness, in QGP based reactions [4] all these abundances are expected to be similar at fixed provided that the rnl., dynamics is such that we can observe the primordial abundances. It is useful to recall the magnitude of backgrounds expected for the production of the multi strange (anti) baryons. The high pl.-ratio of ":"'/Y (where Y are the hyperons) seen = A, I; qqs at = 63 GeV is only 0.06±0.02 in the central rapidity region [5] and would be expected vSNN to be smaller at the energies � 14 GeV presently available in nuclear collisions. How­ ever, the expected quark-gluonvS matterNN result with saturated phase space [4] is up to ten times greater and such greatly enhanced yields have been recently reported by the \VA85 collabora­ tion [6], and have been fully analyzed to show considerable anomaly [7, 8].

2. STRANGENESS PHASE SPACE OCCUPA NCY: Rates for production of pairs in the ss QGP phase were often calculated [9]. The relaxation time constant which characterizes the scale of time needed to saturate the phase space was determined to be of the order of 10-23 s, while the similar study in hadronic gas phase yields a 10 - 30 times slower [10] rate at the same temperature and baryo-chemical potential. This difference in effective rate is mainly due to the presence of gluons in QGP, and to the reduction of the threshold for formation in QGP. ss gluons be Because can created and annihilated easily in interactions with other gluons and light quarks, the gluon density is believed to most closely follow the evolution of temperature in the course of the QGP evolution. Gluons also play a major role in the dynamics of the 623

QGP - HG phase transition, also because they carry much of the QGP entropy. It is therefore interesting to note that in an indirect way strangeness demonstrates the dynamical presence of glue degrees of freedom. Note that the typical time scale for the creation and decay of a central fireball can be estimated as the time to traverse at light velocity, the fireball diameter 2R, i.e. 2 4 10-23 s. Therefore the difference in the strangeness relaxation time constant � x in the two phases- (QGP, HG) of dense matter is of great importance. In order to quantify the strangeness production in the dynamical situation of the rapidly evolving heavy ion collision, it is convenient to introduce the phase space occupancy /, [7]: since the thermal (kinetic) equilibration occurs at a considerably shorter time scale than the (absolute) chemical equilibration of strangeness, /, is the global factor describing how far the momentary phase space momentum distribution is away from the equilibrium value n0:

n,(p, t) = /, (t)n ( T(i), µ,(i)) , (1) i; :;" fi; where the i dependence is contained in the statistical parameters. /, thus characterizes approach to equilibrium n;;' of the phase-space distribution n, of strange particles - absolute strangeness chemical equilibrium corresponds to /, = 1. I will argue below that it is indeed quite easy to measure the value of /,, and thus the understanding of the behavior of /, under changing conditions of the colliding nuclei such as the volume occupied by the fireball (varying size of the colliding nuclei and impact parameter), the trigger condition (e.g. the inelasticity), the collisions energy of colliding nuclei (searching for the threshold energy of abundant strangeness formation) is a very important practical element in understanding the behavior of the high density hadronic phases. The theoretical dynamical model to study /, (t) can be easily developed: it arises from a standard strangeness population evolution equation [ll] by introduction of the definition Eq.(1) and the allowance of the dilution occurring as consequence of the natural volume growth (expansion) [10]. Detailed balance assures that the production and annihilation processes are balancing each other as 1. I obtain: /, --> (2) where N00 = Vn;;' and = 0.5n;:"/A, with dN/dVdt being the (invariant) strangeness r, A = production rate per unit time and volume which can be computed from elementary (QCD) processes [ll]. The second term on the left hand side of Eq. (2) arises from the combination of the dilution term arising from the expansion of the volume occupied by the system with the definition Eq.(1) of strange quark density which involves /,. It is interesting to note that this term is very small: for adiabatic expansion at constant specific entropy per baryon, we have a time independent T3V. Since also n;;' 3T3/rc2 x2K (x) with x m/T we have = 2 = d(ln N00)/dtladia d(ln x2K (x))/dt, and the last term is a rather slowly changing function = 2 of x(t) = m/T(t). This demonstrates the theoretical advantage of using /, in the description of strangeness production phenomena. Ignoring the second term in Eq. (2) the well known solution is: dt 1> (t) tanh [" (3) = ( Jo 2r,(T(t)) ) ' where t1 is the life span of the fireball. Assuming that there is no appreciable change in r, with time (due to dependence) the shape of /,(tr) is the same as the (normalized) shape T- of n,(t)/n;;' given already in [ll]. More comprehensive studies of /, (ti) including the dilution effect for both QGP and HG phases have been carried out numerically (10], but considerably 624 greater effort is required today (see below).

3. FINA L STATE: The favorite heavy ion collision scenario looks perhaps like this: very rapid thermalization of the fireball energy in a central high energy nuclear collisions in which numerous radiation quanta (gluons) are formed, followed by glue based formation of strange quark pairs. The next step is the formation of final state hadrons, either in the process of general QGP decomposition or in radiative emission from QGP. It is in this step that particles are formed that are ultimately observed in the experiment. How can we observe enhancement of certain particles originating in a central fireballor another similar high density state? First note that the relative probability to find a composite particle per unit of phase space volume d3id3ji/(27r)3 becomes d6N e (4) J3£J3ji/ (27r)3 - N g,. A''"f· ,. -Ei/Tr IT'. The overall normalization of the yield which involves recombination probabilities of quarks is not easily accomplished,N but the relative yields, separately for baryons and mesons should be well described by Eq. (4). For a composite particle at energy = the Boltzmann E 'L;; Ei exponential factor arises naturally from Eq.(4). In order to arrive at measured spectra e-E/T an integration of the resulting (Boltzmann) spectrum over suitable regions is required, where it is convenient to introduce the variables m.L, y with = m.Lsinh(y -ye), E m.L cosh(y - yc) PH = and is the rapidity of the central fireball particle source. In general, a more complex model Yr is developed allowing for longitudinal and transverse matter flow [2]. The factors in Eq. (4) which control the formation of composite particles in dense matter are: the Boltzmann exponential, statistical multiplicity factors referringto the degeneracy g;, of the i( = d, s) component, and characterizing also the likelihood of findingamong randomly u, assembled quarks, the suitable spin-isospin of the particle; chemical fugacities which define A; the relative abundance of quarks and anti-quarks with .\;1 ). The factors allow for = '"f; the approach to absolute chemical equilibrium (in general(.\9 0 1) for each quark flavor :'S '"f; :'S (normally one takes 1. It is pretty easy to determine in this (composite) particle 'Yu,d = production picture the key quantity 'Ys : a complete cancellation of all phase space factors occurs when I consider a suitable product of the abundances of baryons and anti-baryons, for example: = - . • (5) fs A A 2 :::: m.i>mlu' We see that an increase in 'Ys is associated with::::-1 an increase in abundance of the 'stranger' particles as compared to their 'less strange' partners. This reflects on the qualitative claim that higher density strangeness source is more effective in producing the multi-strange clusters. It should be noted that when using Eq.(5) a correction must be applied to account for the fact that the observedparticle abundances comprise all the decay products from more massive hadronic resonances. One finds [7, 8] that 'Ys 0.75 ± 0.1 for the S-W results [6]. This value = agrees in qualitative terms well with the theoretical results which can be extracted from the calculations presented in [10] for a 3 fm radius initial plasmadrop at initial temperature of 250 MeV: I find 'Ys (t -> 0.7, with an error as large as 50% due to the assumed values oo) '.:::' of the QCD parameters such as the coupling constant and the strange quark mass m., not a, to mention the systematic uncertainty associated with use of first order QCD perturbative expansion. However, the very precise experimental result obtained by the WA85 collaboration [6) implies need for considerable improvement in the theoretical calculations! 625

The observed enhancement of (relative) production rates of multi-strange anti-baryons 3 in nuclear collisions, in particular at central rapidity and at highest transverse masses, cannot be obtained so far in microscopic reaction models. I cannot see how to interpret these data other than in terms of an explosively evaporating drop of quark-gluon plasma, in particular considering the substantial hadronic multiplicity seen. On the other hand it is very difficultto develop a reaction model which comprises not only the formation of QGP but also the correct dynamical evolution in the hadronization process which would preserve the properties of QGP in the relative particle abundances. Despite these still unresolved issues I hope to have convinced you that we are at the verge of the QGP discovery by means of a comprehensive study of the strange particle production - the only self-consistent picture we could findso far [7, 8, 12] in order to interpret the strange particle data at 200 GeV A involves the formation of a thermal QGP fireball hadronizing without establishing an equilibrium hadronic gas phase. Since there are many predictions one can make which will confirm or falsify this hypothesis QGP formation followed by non- equi­ librium hadronization, it will be possible to tighten the argument considerably and perhaps decisively in the forthcoming rounds of experiments.

Acknowledgement: JR was supported in part by US-Department of Energy under grant DE­ FG02-92ER40733, JR and UH were supported in part by NATO-CRG-910991, UH and JS were supported in part by DFG, BMFT and GSI. JL and AT are at LPTHE, Unite associee au CNRS.

References [1] J. Rafelski in proceedings of Rencontres de Moriond, J. Tran Thanh Van, editor, Editions Frontieres, see in particular: XVI/2 (1981) p.619; XII/2 (1982) p.625; XXII/2 (1987) p.519; XXIII/2 (1988) p.135 . [2] U. Heinz et. al., Strangenessand Entropy Production in Relativistic Nuclear Collisions, in this volume.

[3] J. Rafelski, Phys. Rep. C88 (1982) 331

[4] J. Rafelski and M. Danos, Phys. Lett. B192 (1987) 432; and M. Jacob and J. Rafelski, Phys. Lett. B190 (1987) 173; and J. Rafelski, Nucl. Phys. A418 (1984) 215c

[5] T. Akesson et al. (!SR-Axial Field Spect. Collab.], Nucl. Phys. B246 (1984) 1

[6] S. Abatzis et al. (WA85 SPS Collab.], Phys. Lett. B 270 (1991) 123; and B 259 (1991) 508

(7] J. Rafelski, Phys. Lett. B262 (1991) 333 and Nucl. Phys. A544 (1992) 279c (8] J. Letessier, A. Tounsi, U. Heinz, J. Sollfrank, and J. Rafelski, Phys. Rev. Lett., in press (1993); and Strangeness conservation in hot fireballs, submitted to Phys. Rev. D.

[9] For a recent review see: H.C. Eggersand J. Rafelski, Int. Journal of Mod. Phys. A6 (1991) 1067

[10] P. Koch and J. Rafelski, Nucl. Phys. A444 (1985) 678; and P. Koch, B. Miiller and J. Rafelski, Phys. Rep. C142 (1986) 167; and Physik A324 (1986) 3642 Z. (11] J. Rafelski and B. Miiller, Phys. Rev. Lett. 48 (1982) 1066; and 56 (1986) 2334(E) (12] J. Sollfrank, M. Gazdzicki, U. Heinz and J. Rafelski, Chemical Freeze-out Conditions in Central S-S Collisions at Ge VA, manuscript in preparation. 200