We analyse recent results on charged particle pseudo-rapidity densities from
RHIC in the framework of the Dual String Model, in particular when including
string fusion. The model, in a simple way, agrees with all the existing data
and is consistent with the presence of the percolation transition to the
Quark-Gluon Plasma already at the CERN-SPS. It leads to strict saturation of
the particle (pseudo-)rapidity density, normalised to the number of participant
nucleons, as that number increases. A comparison with recent WA98 data is
presented.Comment: 6 pages, 3 ps figures, Latex2e with amsmath. To appear in the
  Proceedings of the XXX International Symposium on Multiparticle Dynamics
  (Lake Balaton, October 2000

de Deus, J. Dias

Ugoccioni, R.

English

arXiv

We analyse recent results on charged particle pseudo-rapidity densities from RHIC in the framework of the Dual String Model, in particular when including string fusion. The model, in a simple way, agrees with all the existing data and is consistent with the presence of the percolation transition to the Quark-Gluon Plasma already at the CERN-SPS. It leads to strict saturation of the particle (pseudo-)rapidity density, normalised to the number of participant nucleons, as that number increases. A comparison with recent WA98 data is presented

Ugoccioni, R

Dias de Deus, J

CERN Document Server

PARTICLE RAPIDITY DENSITY AND COLLECTIVEPHENOMENA IN HEAVY ION COLLISIONSR. UGOCCIONI∗AND J. DIAS DE DEUSCENTRA and Departamento de Física (I.S.T.)Av. Rovisco Pais, 1049-001 Lisboa, PortugalWe analyse recent results on charged particle pseudo-rapidity densities from RHICin the framework of the Dual String Model, in particular when including string fu-sion. The model, in a simple way, agrees with all the existing data and is consistentwith the presence of the percolation transition to the Quark-Gluon Plasma alreadyat the CERN-SPS. It leads to strict saturation of the particle (pseudo-)rapidity den-sity, normalised to the number of participant nucleons, as that number increases.Asymptotically, as√s → ∞, with the number of participants xed, this densityapproaches again nucleon-nucleon density. A comparison with recent WA98 datais presented.The dependence of measurable quantities like charged particle density,transverse energy and J/ψ production rate on the number Npartof partici-pant nucleons in high energy heavy ion collisions is extremely important bothfor a better understanding of the initial conditions in the evolution of newlycreated dense matter and because it provides the information for discrimi-nating among dierent models.1,2,3,4,5,6In this contribution we analyse suchquantities in the framework of the Dual String Model (DSM).We start by building nucleus-nucleus collisions as resulting from superpo-sition of nucleon-nucleon collisions, in the way it is done in the Glauber modelapproach and its generalisations: in the DSM, i.e., the Dual Parton Model7with the inclusion of strings,8the valence quarks of the nucleon produce par-ticles, via strings, only once this is the wounded nucleon model case andproduction is proportional to the number NA of participant nucleons. As theenergy and NA increase the role of sea quarks and gluons increases, they in-teract and produce, again via strings, particles, and the number of collisionsν becomes the relevant parameter. One should notice that multiple inelasticscattering may occur either internally within a given nucleon-nucleon collisionor externally involving interactions with dierent nucleons.Following Ref. 9, and taking into account the above basic properties, we* Present address: Dipartimento di Fisica Teorica, via Giuria 1, 10125 Torino, Italyugoccioni: submitted to World Scientic on February 7, 2001 1now write an expression for the particle pseudo-rapidity density,dNdy∣∣∣∣NANA= NA [2 + 2(k − 1)α]h+ (νNA −NA)2kαh, (1)where h is the height of the valence-valence rapidity plateau, α is the relativeweight of the sea-sea (including gluons) plateau and k is the average number ofstring pairs per collision. Elementary multi-scattering arguments9give νNA=N4/3A . However, as we mentioned above, the diagram corresponding to sea-seascattering can be iterated with k  1 being, in general, a function of energy.The number of nucleon-nucleon collisions is, of course, NA + (νNA − NA) =νNA, and the number of strings is Ns = NA [2 + 2(k − 1)] + (νNA −NA)2k =2kνNA. The rst term on the right-hand side of Eq. (1) is just a sum overnucleon-nucleon scattering contributions (including internal parton multiplescattering) and we can thus writedNdy∣∣∣∣NANA=dNdy∣∣∣∣ppNA + (νNA −NA)2kαh (2)If external multiple scattering is absent, by putting νNA= NA, one obtainsthe wounded nucleon model limit; if k  1 we obtain the limit in whichmultiple scattering dominates.In Fig. 1, together with the PHOBOS data, we have presented the quan-tity1NAdNdy∣∣∣NANAas function of the c.m. energyps for the wounded nucleonmodel limitsolid lineand the multiple scattering dominance limitdottedline. Assuming that h and α are energy independent (constant plateaus), theenergy dependence of dN/dyjpp, obtained from a parametrisation of exper-imental data,6xes the energy dependence of k. We nd α = 0.05 andh = 0.75.In the DSM, strings may interact by fusing14,15in the transverse planeof interaction thus modifying the number and the distributions of producedparticles: in particular, due to the vector nature of the colour charge, a clusterof m strings will emit fewer particles that m separate strings.16The number of strings coming from nucleon multiple scattering thesecond term in Eq. (1)is NA(N1/3A − 1)2k and they occupy the transverseinteraction area SNA , which, for central collisions, is approximately givenby SNA’ pi(1.14N1/3A)2, such that the dimensionless transverse densityparameter η isη =( rs1.14)22kN1/3A (N1/3A − 1), (3)ugoccioni: submitted to World Scientic on February 7, 2001 2c.m. energy (GeV/nucleon)(1/N A)  dN / dη10 100 1000051015202530  PHOBOS Au+Au  NA49 Pb+Pb  WA98 Pb+Pb  HIJING Monte Carlo  CDF pp  UA5 pp  NA22 ppFigure 1. Pseudo-rapidity density nor-malised per participant pair as a function ofc.m. energy. The lines give predictions forthe wounded nucleon model (solid line), thepure multicollision approach (dotted line),and the Dual String Model, without fu-sion Eq. (2) (dash-dotted line) and withfusion Eq. (4) (dashed line). AA pointsare taken from Ref. 2,3,5, pp and pp¯ fromRef. 10,11,12,13 Dual String ModelNpartdNch/dη/(0.5Npart)HIST: HIJINGSaturation modelISRUA5PHOBOSAu+Au Collisions130 GeVs1/2=56 GeV200 GeV00.511.522.533.544.550 100 200 300 400Figure 2. Central charged particle rapiditydensity per participating pair as a functionof the number of participants. Results of HI-JING (histograms), EKRT predictions (dot-dashed lines) and DSM predictions (solidlines) for central Au+Au collisions at√s =56, 130, 200 AGeV. Also shown are resultsfrom pp and pp¯ collisions and PHOBOS data(Everything in the gure except the DSMcurves is taken from Ref. 5.)where rs ’ 0.2 fm is the string transverse section radius. Note that η increaseswith NA and, via k, also withps.When fusion occurs, Eq. (2) becomes61NAdNdy∣∣∣∣NANA=dNdy∣∣∣∣pp+ F (η)(N1/3A − 1)2kαh, (4)where F (η) is the particle production reduction factor,17F (η) ’√1− e−ηη. (5)It can now easily be shown18that the DSM with fusion predicts satura-tion of the particle rapidity densities per participant pair of nucleons as NAincreases. This prediction is compared to other models5,19,20in gure 2 andto experimental data from WA983in gure 3.ugoccioni: submitted to World Scientic on February 7, 2001 3Npart(1/N part)  dN / dy (a)0 100 200 300 40000.20.40.60.811.21.41.61.82NpartdN / dy(b)0 5 10 15 20 25 300510152025303540Figure 3. (a) Charged particle density per participant nucleon versus the number of partic-ipants; (b) absolute charged particle density versus the number of participants. The datafrom WA983refer to 158A GeV Pb+Pb collisions (lled circles), the open circle refers topp collisions21; the solid line results from Eq. (4) with α = 0.11 and h = 0.77.Furthermore, it is to be noted that the predictions for particle densitiesin central Pb+Pb collisions of the DSM without fusion and of the DSM withfusion are very dierent atps = 200 AGeV (RHIC) and atps = 5.5 ATeV(LHC) as can be seen in the following table:c.m. energy 200 AGeV 5.5 ATeVwithout fusion 1500 4400with fusion 700 1400Of course this model is essentially soft. The parameters of the elementarycollision densities, h and α, were assumed constant, all the energy dependencebeing attributed to the parameter k, the average number of string pairs perelementary collision. If h and α are allowed to grow with energy, as a result,for instance, of semi-hard eects, the parameter k may then have a slowerincrease than the one obtained here.Finally, one should consider the idea that string fusion eventually leads toa situation of percolation14,15with the formation of extended regions of colourfreedom, with the features of the expected Quark-Gluon Plasma. Indeedthe parameter η at the CERN-SPS has the value η  1.8, larger than thecritical density (ηc  1.12 1.17) which means that percolation transition isalready taking place atps = 20 AGeV, even allowing for non-uniform matterdistribution in the nucleus (ηc  1.5);22 this result is valid even with k = 1.The observed anomalous J/ψ suppression23 may then be a signature of theugoccioni: submitted to World Scientic on February 7, 2001 4percolation transition to the Quark-Gluon Plasma.14,15Indeed, in our simple approach,15 J/ψ and Drell-Yan production aretreated as rare events: this implies that their ratio is given by the product oftwo functions, one describing absorption of J/ψ (which we assume as usual tobe exponential in the amount of matter longitudinally traversed), the otherdescribing J/ψ (cc¯) suppression due to Debye screening. If we take the drasticposition that the latter is 100% eective if there is percolation, and ineectiveotherwise, then screening is described by the probability of non-percolation,which can be parametrised asPnon-perc(η) =[1 + exp(η − ηcac)]−1, (6)with ac a parameter linked to the nite size of the nuclear system. Thus wesee that the onset of the phase transition is characterised by a change in thecurvature of the J/ψ over D.Y. ratio from positive (during absorption) tonegative. This however is only a qualitative description: a quantitative oneshould probably take into account more details of the process (e.g., geometryvarying with impact parameter, resonances, . . . ).In conclusion, the DSM is a model with two components, the valence-valence component and the sea-sea component, the sea-sea component increas-ing its importance with energy and number of participants. This is somewhatsimilar to the HIJING Monte Carlo model, with soft and hard components.On the other hand, with fusion the DSM behaves, for large NA, similarlyto the EKRT model, but with strict saturation of the particle density perparticipant nucleon. However, in the original EKRT model the saturationcriterion in the transverse plane is stronger than in case of fusion of strings.Here, saturation in the interaction area is asymptotic (when η !1) while inthe EKRT model it occurs at nite density. This causes the decrease of theparticle density with NA in the EKRT original model.Probably dierent explanations, such as the ones based on string fusion,parton saturation, parton shadowing, are in some sense dual and refer tothe same underlying physics.9What is becoming clear is that saturation ofparticle density puts strong constraints in models, and limits the rise of the(pseudo-)rapidity plateau at RHIC and LHC.AcknowledgementsR.U. gratefully acknowledges the nancial support of the Fundação Ciência eTecnologia via the Sub-Programa Ciência e Tecnologia do 2o Quadro Comu-nitário de Apoio.ugoccioni: submitted to World Scientic on February 7, 2001 5References1. M. Gyulassy, these proceedings.2. B.B. Back et al., PHOBOS Collaboration, Phys. Rev. Lett. 85, 3100(2000).3. M.M. Aggarwal et al., WA98 Collaboration, preprint nucl-ex/0008004,(WA98/CERN).4. C. Lourenço, talk given at the Heavy Ion Day meeting in Lisbon, Portu-gal, April 2000.5. X.-N. Wang and M. Gyulassy, preprint nucl-th/0008014.6. J. Dias de Deus and R. Ugoccioni, Phys. Lett. B 491, 253 (2000).7. A. Capella, U.P. Sukhatme, C.I. Tan and J. Trân Thanh Vân, PhysicsReports 236, 225 (1994).8. N.S. Amelin, M.A. Braun and C. Pajares, Phys. Lett. B 306, 312 (1993);N.S. Amelin, M.A. Braun and C. Pajares, Z. Phys. C 63, 507 (1994).9. N. Armesto and C. Pajares, Int. J. Mod. Phys. A 15, 2019 (2000).10. M. Adamus et al., NA22 Collaboration, Z. Phys. C 37, 215 (1988).11. G.J. Alner et al., UA5 Collaboration, Physics Reports 154, 247 (1987).12. R.E. Ansorge et al., UA5 Collaboration, Z. Phys. C 43, 357 (1989).13. F. Abe et al., CDF Collaboration, Phys. Rev. D 41, 2330 (1990).14. N. Armesto, M.A. Braun, E.G. Ferreiro and C. Pajares, Phys. Rev. Lett.77, 3736 (1996); M. Nardi and H. Satz, Phys. Lett. B 442, 14 (1998).15. J. Dias de Deus, R. Ugoccioni and A. Rodrigues, Eur. Phys. J. C 16, 537(2000).16. T.S. Biro, H.B. Nielsen and J. Knoll, Nucl. Phys. B 245, 449 (1984).17. M.A. Braun and C. Pajares, Eur. Phys. J. C 16, 349 (2000).18. J. Dias de Deus and R. Ugoccioni, Phys. Lett. B 494, 53 (2000).19. K.J. Eskola, K. Kajantie, P.V. Ruuskanen and K. Tuominen, Nucl. Phys.B 570, 379 (2000).20. K.J. Eskola, K. Kajantie and K. Tuominen, preprint JYFL-3700 and HIP-2000-45/TH (hep-ph/0009246), Univ. of Jyväskylä and Univ. of Helsinki.21. C. De Marzo et al., Phys. Rev. D 26, 1019 (1982).22. A. Rodrigues, R. Ugoccioni and J. Dias de Deus, Phys. Lett. B 458, 402(1999).23. M.C. Abreu et al., NA50 Collaboration, Phys. Lett. B 477, 28 (2000).ugoccioni: submitted to World Scientic on February 7, 2001 6

Particle rapidity density and collective phenomena in heavy ion collisions

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