PARTON CASCADE DESCRIPTION OF HEAVY-ION COLLISIONS AT CERN? K. Geiger. Physics Department, Brookhaven National Laboratory, Upton, N.Y , U.S.A.

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1 PARTON CASCADE DESCRIPTION OF HEAVY-ION COLLISIONS AT CERN? K. Geiger Physics Department, Brookhaven National Laboratory, Upton, N.Y , U.S.A. There seems to be a general consensus now that a rst glimpse of a QGP-like eect has become visible in the beautiful NA50 data on J= production and the `anomalous supression' phenomenon. On the other hand, it is still widely believed that the dynamics of heavy-ion collisions at CERN SPS energy is predominantly governed by soft, nonperturbative physics. This is ironic: after all, it is unlikely that a QGP could be formed if the underlying dynamics were essentially soft, rather than that it requires intense quarkgluon production with sucient cascade-like reinteractions which drive the matter to large density and equilibrium. Therefore, I advocate in this contribution that for ultrarelativistic nucleus-nucleus collisions a description based on the pqcd interactions and cascade evolution of involved partons can and should be used, owing to the claim that short-range parton interactions play an important role at suciently high beam energies, including CERN energy p s ' 20 AGeV. Here mini-jet production which liberates of quarks and gluons cannot be considered as an isolated rare phenomenon, but can occur quite copiously and may lead to complex multiple cascade-type processes. 1 Introduction A QCD-based space-time model that allows to simulate nucleus-nucleus collisions (among other particle collisions), is now available 1 ) as a computer simulation program called VNI [1] (pronounced Vinnie). It is a pqcd parton cascade description [2, 3], supplemented by a phenomenological hadronization model [4], with dynamically changing proportions of partons and hadrons, in which the evolution of a nuclear collision is traced from the rst instant of overlap, via QCD parton-cascade development at the early stage, parton conversion into pre-hadronic color-singlet clusters and hadron production through the decays of the clusters, as well as the fragmentation of the beam remnants at late times. (I will in the following refer to the parton-cascade/cluster-hadronization model as PCM, and to its Monte Carlo implementation as VNI.) The PCM description has been used [3] to provide very useful insight into the dynamics of the evolution of the matter at energies likely to be reached at BNL RHIC and CERN LHC. The experimental data for these will, however, come only in the next millennium. Recently, D. Srivastava and myself have taken steps to investigate collisions at the CERN SPS and compare the model calculations with the increasing body of experimental data, thereby addressing the the question: Can one really use the PCM picture already at the SPS energies ( p s 17{20 AGeV)? Recall that the parameters of the models were xed by the experimental data for pp (pp) cross-sections over p s = 10{1800 GeV, and e + e? annihilation [3]. The nucleon-nucleon energy 1 ) The program is available from Czechoslovak Journal of Physics, Vol. 48 (1998), Suppl. S1 37

2 K. Geiger reached at SPS is well within this range. Indeed, as shown in [5, 6], this approach does remarkably well in comparison to the gross particle production properties observed at CERN SPS. This came as a surprise, since no attempt was made to ne-tune the model to the data. Fig. 1. The rapidity distribution of negative hadrons for most central collisions of sulfur nuclei at CERN SPS [6]. 2 Comparison with CERN SPS data In Figs. 1 and 2, I have plotted examples of the results of [5, 6], for the relatively `light' system S +S and for the most `heavy' system Pb + Pb. The rst plot shows the rapidity distribution of negative hadrons in central collisions of sulfur nuclei, whereas the second plot shows the transverse mass spectra of negative hadrons in central lead-lead colisions. In comparison with the corresponding experimental data, it is evident that a decent description is obtained, and this without any adjustments of parameters. The analysis of [5] concluded: (i) The simulations of heavy-ion collisions give a good overall description of the CERN SPS data on rapidity and transverse energy distributions, the multiplicity distributions, as well as a reasonable description of the transverse momentum distribution of hadrons. This success may be taken as a `posthum' justication of the applicability of a pqcd parton description even at CERN SPS energies. (ii) Contrary to wide-spread belief, at CERN SPS energy the `hard' (perturbative) parton production and parton cascading is an important element for particle production at central rapidities - at least in Pb + Pb collisions. In eect it provides almost 50 % of nal particles around mid-rapidity. `Soft' (non-perturbative) parton interactions on the other hand are found to be insignicant in their eect on nal-state particle distributions. 38 Czech. J. Phys. 48/S1 (1998)

3 Parton Cascade Description:: : Fig. 2. The transverse mass spectra of negative hadrons (?, K?, and p) successively scaled down by an order of magnitude. The predictions are normalized to the data at m T? m = 0.9 GeV [5]. 3 Implications for J= suppression Let me now turn to the problem of the observed strong suppression of J= production in Pb + Pb collisions, following a recent work [7] by B. Muller and myself. In particular, I would like to discuss briey the A-dependence of the absorption of the J= by comoving produced hadronic matter. The key element in the following arguments is the fact that, for most nuclear collision systems at the relatively low center-of-mass energy of the CERN-SPS experiments, perturbative mini-jet production is largely due to quark-quark scattering, because the typical value of Bjorken-x probed is hxi > 0:1, where the gluon density is small. This implies that shadowing eects are negligible as explained in [7] and the critical momentum p crit where these eects turn on, lies below the perturbatively accessible range of momenta p? 1 GeV at the SPS energy, and may just begin to reach into it for the Pb + Pb system. If this is correct, then all mini-jet production involving momenta p? 1 GeV lies safely above p crit. As immediate consequence, the density of comovers which can eectively interact and absorb the J= at the SPS grows like A 2=3, or (A 1 A 2 ) 1=3 in asymmetric collisions. This is a much stronger A-dependence than naively expected and embodied in most comover suppression models [8]. It also implies a stronger impact parameter or E T -dependence of comover suppression than predicted by existing models. Quantitative support for these speculations comes from recent calculations of secondary particle production in the parton cascade model, using VNI [1]. The calculations predict that the energy density produced by scattering partons (minijets) at central rapidity grows by a factor of more than 2 between S + U and Pb + Pb, compatible with the scaling law (A 1 A 2 ) 1=3, but much faster than expected Czech. J. Phys. 48/S1 (1998) 39

4 K. Geiger ε(τ) (GeV/fm 3 ) 10 1 Pb+Pb S+U partons y-y cm < 0.5 z < 0.5 fm r T < 4 fm clusters + hadrons τ (fm) Fig. 3. Time evolution of the energy density of the partonic matter in the central slice of the collision systems S + U and Pb + Pb at CERN-SPS beam energies of 200 AGeV and 158 AGeV [7]. in the usual Glauber model approach which predicts (A 1=3 1 + A 1=3 2 ), in which case increases only by 30 %. ε/t 4, 3p/T J/ψ melts Y melts ε 2 GeV/fm 3 5 GeV/fm 3 15 GeV/fm 3 ε/t 4 3p/T 4 (MILC Coll., Ref. 18) T (GeV) Fig. 4. Equation of state for two-avor QCD [9], showing energy density and pressure p as a function of temperature T and coresponding energy densities with the location of the "melting" points of the J= and states [10]. In Pb + Pb collisions the initial partonic energy density is predicted to reach 5 GeV/fm 3 at times < 1 fm/c in the comoving reference frame (Fig. 3). For a thermalized gas of free gluons and three avors of light quarks this corresponds to an initial temperature T i 230 MeV, clearly above the critical temperature T c 150 MeV predicted by lattice-qcd calculations [9] shown in Fig. 4. On the 40 Czech. J. Phys. 48/S1 (1998)

5 Parton Cascade Description:: : other hand, the parton density 2 GeV/fm 3 predicted for S + U collisions (Fig. 3), just lies at the upper end of the transition region in the equation of state from lattice-qcd. VNI without afterburning VNI with afterburning dn/det Et Fig. 5. Distribution of transverse energy production in minimum bias collisions of Pb+Pb at CERN SPS, as calculated with VNI [1]. Fig. 6. For 1:1 2:3, the correlation between E veto, the energy deposited in the forward beam calorimeter, and E?, the energy harnessed in transverse direction, from VNI. The temperature T D required for dissociation of the J= bound state due to color screening is known [10] to be higher than T c, namely T D 1:2 T c = 180?200 MeV. The parton cascade model results are therefore compatible with the experimental nding that there appears to exist no signicant comover-induced suppression of Czech. J. Phys. 48/S1 (1998) 41

6 K. Geiger J= in S + U collisions, but a large and strongly impact parameter dependent eect is observed in Pb + Pb collisions. It must be stressed that the model results do not contradict the experimental data collected at the SPS, as one might suspect, since it is usually claimed that those are fully consistent with the Glauber picture, in particular with the transverse energy production (Fig. 5) and the linear E?? E veto relation (Fig. 6), both which are in good agreement with the corresponding measured data [11]. 4 Photon production by cascading partons Photons have remained one of the most eective probes of every kind of terrestrial or celestial matter over the ages. Thus, it is only betting that the speculation of the formation of deconned strongly interacting matter - some form of the notorious quark-gluon plasma - in relativistic heavy-ion collisions, was soon followed by a suggestion [12] that it should be accompanied by characteristic production of photons. The eectiveness of photons in probing the history of such a hot and dense matter stems from the fact that, after production, they leave the system without any further interaction and thus carry unscathed information about the circumstances of their birth. This is a very important consideration indeed, as the formation of a partonic plasma is likely to proceed from a hard-scattering of initial partons, through a pre-equilibrium stage, to perhaps a thermally and chemically equilibrated state of hot and dense partonic matter. Here I concentrate on photons coming from the early partonic stage in such collisions. I will not consider other sources of photons, e.g., those that accompany the late hadronic stage, after the partons have hadronized. During the partonic stage, photons emerge from two dierent mechanisms: rstly, from collisions between partons, i.e., Compton scattering qg! q of quarks and gluons and annihilation q q! g, q q! of quarks and antiquarks; secondly, from radiation of excited partons, i.e. electromagnetic brems-strahlung q! q of timelike cascades initiated by quarks. Whereas the former mechanism has been studied in various contexts [13], the latter source of photons is less explored [14], although, as I shall show, it is potentially much richer both in magnitude and complexity. Prompt photons from both parton collisions and brems-strahlung are ideally suited to test the evolution of the partonic matter as described by the PCM. They would accompany the early hard scatterings, the approach to thermalization and chemical equilibration if these are achieved at all. Let me rst discuss the aspect of collisional photon production from parton collisions. This is straightforward, and is included in the PCM in terms of the elementary 2! 2 processes which yield photons, that is, the annihilation and Compton processes, q q! g; q q! ; qg! q, the Born cross-sections of which are well-known [15]. In the PCM approach these processes are within perturbative QCD if the momentum q? transferred in the parton collision is larger than some cut-o q? 0 [2]. (This cut-o is introduced in the c.m. frame of the colliding partons, and thus one may have contributions even for smaller transverse momentum in the nucleus-nucleus c.m. frame.) 42 Czech. J. Phys. 48/S1 (1998)

7 Parton Cascade Description:: : Next I turn to the aspect of radiative photon emission from parton showers initiated by collisions, which is a more complex issue. There are some important and interesting dierences between a branching leading to production of photons as compared to gluons, which have been pointed out in detail by Sjostrand [14]. (i) Consider an energetic quark produced by a hard scattering, which can radiate gluons and photons competitively. The branchings q! qg and q! q appear in the PCM on an equal footing and as competing processes with similar structures. The probability, for a quark to branch at some given virtuality scale Q 2, with the daughter quark retaining a fraction z of the energy of the mother quark, is given by: s dp = 2 C F + em dq 2 2 e2 q Q z 2 1? z dz (1) where the rst term corresponds to gluon emission and the second to photon emission. Thus, the relative probability for the two processes is, P q!q P q!qg / 2 emheq i ' 1 s C F 200 ; (2) using em = 1=137, s = 0:25, he 2 qi = 0:22 and C F = 4=3. Thus, one notices that the emission of photons is strongly aected by the perturbative QCD eects. This does not mean, though, that one can simulate emission of photons in a QCD shower by simply replacing the strong coupling constant s with the electromagnetic em and the QCD color Casimir factor C F = 4=3 by e 2 q. One has to keep in mind that the gluon, thus emitted, may branch further either as, g! gg or as g! qq, implying that the emitted gluon has an eective non-zero mass. As the corresponding probability for the photon to branch into a quark or a lepton pair is very small, this process is neglected and the photon is taken to have a zero mass. (However, if one wishes to study the dilepton production from the collision, this may become an important contribution [16]). (ii) The radiation of gluons from the quarks is subject to soft-gluon interference which is accounted for by imposing an angular ordering of the emitted gluons. This is not so for the emitted photons. To recognize this aspect, consider a quark which has already radiated a number of hard gluons. The probability to radiate and additional softer gluon will get contributions from each of the existing partons which may further branch as q! qg or g! gg. It is well-known [17] that if such a soft gluon is radiated at a large angle with respect to all the other partons and one would add the individual contributions incoherently, then the emission rate would be overestimated, as the interference is destructive. This happens because a soft gluon of a long wavelength is not able to resolve the individual color charges and observes only the net charge. The probabilistic picture of PCM is then recovered by demanding that emissions are ordered in terms of decreasing opening angle between the two daughter partons at each branching, i.e., restricting the phasespace allowed for the successive branchings. The photons, on the other hand, do not carry any charge and only the quarks radiate. Thus photons are not subject Czech. J. Phys. 48/S1 (1998) 43

8 K. Geiger to angular ordering. Pictorially, the branching structure in QCD is `pine-tree' like, whilst in QED it is `oak-tree' like. (iii) The parton emission probabilities in the QCD showers contain soft and collinear singularities, which are regulated by introducing a cut-o scale 0. This regularization procedure implies eective masses for quarks and gluons, m (q) e r = m2 q ; m(g) = 0 e 2 ; (3) where m q is the current quark mass. Thus the gluons cannot branch unless their mass is more than 2m (g) = e 0, while quarks cannot branch unless their mass is more than m (q) + e m(g). An appropriate value for e 0 is about 1 GeV [2]; a larger value is not favored by the data, and a smaller value will cause the perturbative expression to blow up. These arguments, however, do not apply for photon emission, since QED perturbation theory does not break-down and photons are not aected by connement forces. Thus, in principle quarks can go on emitting photons till their masses reduce to current quark masses (or, in a dense matter environment, to the corresponding `in-medium' Debye mass). It has also been suggested that if the connement forces screen the bare quarks, the eective cut-o can be of the order of a GeV. These arguments suggest that one can choose the cut-o scale 0 in (3) separately for the emission of photons and that the study of photon emission can provide valuable insight about connement at work by comparing the characteristics of gluon versus photon radiation from quarks. Let me now turn to our results which I present in four examples: S+S ( p s = 20 AGeV) and Pb+Pb collisions ( p s ' 18 AGeV) at CERN-SPS, as well as S + S and Au + Au collisions at RHIC energy p s = 200 AGeV. For the following, it is useful to keep in mind, that the initial partonic composition of the colliding nuclei is very dierent for the two energies: at SPS, by far the main component are the quarks, with relative proportions N q : N g 1 : 0:4, whereas at RHIC, the gluons play the dominant role, with N q : N g 1 : 1:9. In Fig. 7 I have plotted the production of single photons from such a partonic matter in the central rapidity region for Pb + Pb system at SPS energy. The dotdashed histogram shows the contribution of Compton and annihilation processes mentioned above. The solid and the dashed histograms show the total contributions (i.e., including the branchings q! q) when the mass scale 0 in (3) for the photon production is taken respectively as 0.01 and 1 GeV. One sees that prompt photons from the quark branching completely dominate the yield for p? 3 GeV, whereas at larger transverse momenta the photons coming from the collision processes dominate. The reduction of 0 for the q! q branching is seen to enhance the production of photons have lower transverse momenta as one expects. I have also shown the production of single photons from pp collisions for p s 24 GeV, obtained by WA70 [18], NA24 [19], and UA6 [20] collaborations scaled by the nuclear overlap for zero impact parameter for the collision of lead nuclei. The solid curve gives the perturbative QCD results [21] for the pp collisions scaled similarly. The dashed curve is a direct extrapolation of these results to lower p?. 44 Czech. J. Phys. 48/S1 (1998)

9 Parton Cascade Description:: : Fig. 7. The radiation of prompt photons from partonic matter in central collision of Pb (158 AGeV) + Pb nuclei at CERN SPS. The dot-dashed histogram gives the contribution of only the collision processes. The dashed and the solid histograms give the contribution of the collision plus branchings when the 0 for the q! q branching is taken as 1 and 0.01 GeV respectively. The pp data at p s 24 GeV scaled by the nuclear overlap function for the central collision of lead nuclei and the corresponding QCD predictions (solid curve, arbitrarily extended to lower p T ) also shown for a comparison. q 0 T denotes the transverse momentum cut-o above which the hard scatterings are included in the PCM. In Fig. 8 I have plotted the transverse momenta of the single photons in several rapidity bins for Pb + Pb and S + S systems at SPS energy. One sees that the transverse spectra scale reasonably well with the ratio of the nuclear overlap for central collisions for the two systems T PbPb =T SS 15.4, which is indicative of the origin of these photons basically from a collision mechanism. The slight deviation from this scaling seen at lower p? results in a 20% increase in the integrated yield at central rapidities. This is a good measure of the multiple scatterings in the PCM. In fact one nds that the number of hard scatterings in the Pb + Pb system is 17 times more than that for the S + S system, which also essentially determines the ratio of the number of the photons produced in the two cases. I also note that the inverse slope of the p? distribution decreases at larger rapidities, which is suggestive of the fact that the densest partonic system is formed at central rapidities. Finally in Fig. 9 I have plotted our results for S + S and Au + Au systems at Czech. J. Phys. 48/S1 (1998) 45

10 K. Geiger RHIC energy in the same fashion as Fig. 8. One sees that the inverse slope of the p? distribution is now larger and drops only marginally at larger rapidities, indicating that the partonic system is now more dense and spread over a larger range of rapidity. Even though the p? distribution of the photons is seen to roughly scale with the ratio of the nuclear overlap functions for central collisions T AuAu =T SS 14.2, the integrated yield of photons for the Au + Au is seen to be only about 12 times that for the S + S system at the RHIC energy. I have again checked that the number of hard scatterings for the Au + Au system is also only about 12 times that for the S + S system. Fig. 8. The radiation of single photons from S + S(200 AGeV) and Pb + Pb(158 AGeV) collisions in dierent rapidity bins. The inset shows the rapidity distribution of the radiated photons. The results for the S+S collisions have been scaled by the ratio T PbPb=T SS 15:4 for central collisions. 0 for the quark branching q! q is taken as 0.01 GeV. This contrasting behavior at SPS and RHIC energies exhibited in the gures can be understood as follows. At the SPS, the partonic system can reach energy densities up to 5 GeV/fm 3 as discussed before. Hence, multiple scatterings become important, especially for heavier colliding nuclei. At RHIC, the energy density can easily become twice as large, and the Landau-Pomeranchuk suppression may play a counteracting role. In the PCM this eect is mimicked, rather crudely, by inhibiting a new scattering of partons till the passage of their formation time after a given scattering. Some other observations are worthwhile commenting on: Firstly, recall such 46 Czech. J. Phys. 48/S1 (1998)

11 Parton Cascade Description:: : Fig. 9. The radiation of single photons from S + S and Au + Au collisions in dierent rapidity bins at RHIC energy p s = 200 AGeV. The inset shows the rapidity distribution of the radiated photons. The results for the S + S collisions have been scaled by the ratio T AuAu=T SS 14:2 for central collisions. 0 for the quark branching q! q is taken as 0.01 GeV. branchings of the partons produced in hard collisions correspond to a next-toleading-order correction in s. These are known to be considerably enhanced for collinear emissions. The parton shower mechanism incorporated in the PCM amounts to including these enhanced contributions to all orders, instead of including all the terms for a given order [22]. It may also be added that the rst-order corrections to the Compton and annihilation processes in the plasma have been studied by a number of authors [23]; however in the plasma, hq? 2 i 4T 2, thus their contribution is limited to very low transverse momentum. Clearly, hq? 2 i is much larger in the early hard scatterings, and thus the radiations from the emerging partons are much more intense and also populate higher transverse momenta, as seen in the present work. The large yield of photons from the branching of energetic quarks preceding the formation of dense partonic matter opens an interesting possibility to look for a similar contribution to dilepton (virtual photon) production in such collisions. One may conclude that the formation of a hot and dense partonic system in relativistic heavy-ion collisions may be preceded by a strong ash of photons following the early hard scatterings. Their yield will, among several other interesting aspects, Czech. J. Phys. 48/S1 (1998) 47

12 K. Geiger also shed light on the extent of multiple scattering encountered in these collisions. However, let me stress that I have only included the contribution of photons from the partonic interactions in this work. It is quite likely that the hadrons produced at the end will also interact and produce photons, as has been studied recently [24]. A comparison of those results with the present work shows that at the SPS energy the emission from the early hard partonic scatterings is of the same order as the photon production from later hadronic reactions, for p? 2{3 GeV, and dominates considerably over the same at higher transverse momenta. This work was supported in part by grant DE-AC02-76H00016 from the U.S. Department of Energy. References [1] K. Geiger, Comp. Phys. Comm. 104, 70 (1997), and references therein. [2] K. Geiger and B. Muller, Nucl. Phys. B369 (1992) 600. [3] K. Geiger, Phys. Rep. 258, 376 (1995). [4] J. Ellis and K. Geiger, Phys. Rev. D 54, 949 (1996); Phys. Rev. D 54, 1755 (1996). [5] K. Geiger and D. Srivastava, Phys. Rev. C56, 2718 (1997). [6] D. Srivastava and K. Geiger, h nuc-th/ i. [7] K. Geiger and B. Muller, h nuc-th/ i. [8] S. Gavin and R. Vogt, Nucl. Phys. A610, 442c (1996). [9] C. Bernard et al., Phys. Rev. D54, 4585 (1996). [10] F. Karsch and H. Satz, Z. Phys. C51, 209 (1991). [11] L. Ramello, NA38/50 Report. In: Quark Matter '97, Proc. 13th Int. Conf.on Ultra{ relativistic Nucleus{Nucleus Collisions, Tsukuba, Japan. [12] E. L. Feinberg, Nuovo Cim. 34A, 391 (1976); E. V. Shuryak, Phys. Lett. B78, 150 (1978); Sov. J. Nucl. Phys. 28, 408 (1978). [13] See, e.g.: J. F. Owens, Rev. Mod. Phys. 59, 465 (1987); J. Kapusta, P. Lichard, D. Seibert, Phys. Rev. D 44, 2774 (1991); Erratum-ibid D 47, 4171 (1993). [14] T. Sjostrand, Talk given at \Workshop on Photon Radiation from Quarks", Annecy, December 1991; CERN -TH.6369/92. [15] See, e.g.: E. Eichten, I. Hinclie, K. Lane and C. Quigg, Rev. Mod. Phys. 56, 579 (1984). [16] K. Geiger and J. I. Kapusta, Phys. Rev. Lett. 70, 1290 (1993). [17] A. Bassetto, M. Ciafaloni and G. Marchesini, Phys. Rep. 100, 203 (1983). [18] M. Bonesini et al., WA70 Coll., Z. Phys. C 38, 371 (1988). [19] C. De Marzo et al., NA24 Coll. Phys. Rev. D 36, 8 (1987). [20] G. Sozzi et al., UA6 Coll. Phys. Lett. B 317, 243 (1993). 48 Czech. J. Phys. 48/S1 (1998)

13 Parton Cascade Description:: : [21] J. Cleymans, E. Quack, K. Redlich, amd D. K. Srivastava, Int. J. Mod. Phys. A10, 2941 (1995). [22] QCD and Collider Physics, R. K. Ellis, W. J. Stirling, and B. R. Webber, Cambridge University Press (1996) p.157. [23] R. C. Hwa and K. Kajantie, Phys. Rev. D32, 1109 (1985); D. K. Srivastava and B. Sinha, J. Phys. G18, 1467 (1992); P. K. Roy, D. Pal, S. Sarkar, D. K. Srivastava, and B. Sinha, Phys. Rev. C53, 2364 (1996). [24] J. Cleymans, K. Redlich, and D. K. Srivastava, Phys. Rev. C55, 1431 (1997). Czech. J. Phys. 48/S1 (1998) 49