We introduce a transport approach which combines partonic and hadronic degrees of freedom on an equal footing and discuss the resulting reaction dynamics. The initial parton dynamics is modeled in the framework of the parton cascade model, hadronization is performed via a cluster hadronization model and configuration space coalescence, and the hadronic phase is described by a microscopic hadronic transport approach. The resulting reaction dynamics indicates a strong influence of hadronic rescattering on the space-time pattern of hadronic freeze-out and on the shape of transverse mass spectra. Freeze-out times and transverse radii increase by factors of 2 3 depending on the hadron species

Bass, Steffen A.

Bleicher, Marcus

Bravina, Larissa V.

Greiner, Walter

Hofmann, Markus

Stöcker, Horst

Zabrodin, Eugene E.

English

Bravina, Larissa

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:nucl-th/9902055 v1   22 Feb 1999Analysis of reaction dynamics at RHIC in a combinedparton/hadron transport approachS.A. Bass∗Department of PhysicsDuke UniversityDurham, NC, 27708-0305, USAM. Hofmann, M. Bleicher, L. Bravina†‡, E. Zabrodin‡, H. St¨ ocker and W. GreinerInstitut f¨ ur Theoretische PhysikJohann Wolfgang Goethe Universit¨ atRobert Mayer Str. 8-10D-60054 Frankfurt am Main, GermanyAbstractWe introduce a transport approach which combines partonic and hadronicdegrees of freedom on an equal footing and discuss the resulting reactiondynamics. The initial parton dynamics is modeled in the framework of theparton cascade model, hadronization is performed via a cluster hadroniza-tion model and conﬁguration space coalescence, and the hadronic phase isdescribed by a microscopic hadronic transport approach. The resulting re-action dynamics indicates a strong inﬂuence of hadronic rescattering on thespace-time pattern of hadronic freeze-out and on the shape of transverse massspectra. Freeze-out times and transverse radii increase by factors of 2 – 3 de-pending on the hadron species.∗Feodor Lynen Fellow of the Alexander v. Humboldt Foundation†Alexander v. Humboldt Fellow‡on leave of absence from the Institute of Nuclear Physics, Moscow State University, Moscow,Russia1Ultra-relativistic heavy ion collisions oﬀer the unique opportunity to probe highly exciteddense nuclear matter under controlled laboratory conditions and probably recreate a QuarkGluon Plasma (QGP), the highly excited state of primordial matter which is believed tohave existed shortly after the creation of the universe in the Big Bang (for recent reviewson the QGP, we refer to [1,2]).While there is currently a strong debate whether deconﬁned matter may have beenproduced at the CERN/SPS, it is widely expected that in collisions of heavy nuclei atRHIC a QGP will be formed. However, the deconﬁned quanta of a QGP are not directlyobservable because of the fundamental conﬁning property of the physical QCD vacuum.What is observable are hadronic and leptonic residues of the transient QGP state.Transport theory has been among the most successful approaches applied to the theoret-ical investigation of relativistic heavy ion collisions. Microscopic transport models attemptto describe the full time-evolution from the initial state of the heavy ion reaction (i.e. thetwo colliding nuclei) up to the freeze-out of all initial and produced particles after the re-action. The consequence for the RHIC energy domain is that both, partonic and hadronic,degrees of freedom have to be treated explicitly.In this letter we introduce a transport approach which combines partonic and hadronicdegrees of freedom on an equal footing and discuss the resulting reaction dynamics. In termsof physics concepts the time evolution of the heavy ion collision can be subdivided into threereaction stages: partonic evolution, hadronization and hadronic evolution/freeze-out.The initial partonic stage of the reaction is modeled according to the Parton CascadeModel (PCM) [3,4]: The nucleons of the colliding nuclei are resolved into their partonsubstructure according to the measured nucleon structure functions and yield the initialparton distributions. Parton interactions as described by perturbative QCD are used tomodel the evolution of the ensemble of partons during the high energy density phase of thecollision.To model hadronization, an eﬀective QCD ﬁeld theory [5] which fully describes the partondynamics including the formation of preconﬁned clusters is introduced. Color singlet statesare then formed via a conﬁguration space coalescence and a cluster ansatz [6,7].For the hadronic phase of the collision a microscopic transport approach is employed[8–11], containing string- and hadronic degrees of freedom. All hadronic states can beproduced in string decays, t-channel excitations, s-channel collisions or resonance decays.Tabulated or parameterized experimental cross sections are used when available. Resonanceabsorption and scattering is handled via the principle of detailed balance.Note that our approach does not include any parton-hadron interactions: partons ﬁrsthadronize when they cease to interact on a partonic level. Therefore the newly formedhadronic states do not exert any pressure on the partons and hadronization occurs as aunidirectional non-equilibrium process.2The technical realization of our approach uses the framework of VNI [12]1, both for theparton cascade model, as well as for the hadronization scheme. The Ultra-relativistic Quan-tum Molecular Dynamics (UrQMD) model [11,13] is employed for the hadronic transport,decays and rescattering. The UrQMD model has been extensively tested in the SIS, AGSand SPS energy domain [11], it provides a robust description of hadronic heavy-ion physicsphenomenology.Let us now turn to the reaction dynamics of central (impact parameter b ≤ 1 fm) Au+Aucollisions at RHIC energies (√s = 200 GeV per incident colliding nucleon-pair): The initialreaction stage in VNI is dominated by the formation of a dense partonic state. Rapidthermalization is caused in VNI by radiative energy degradation and spatial separation ofpartons with widely diﬀerent rapidities due to free streaming – at RHIC, thermalizationis predicted on a proper time scale of approximately 1 fm/c [14]. The thermalized QGP isinitially gluon rich and depleted of quarks due to the larger cross section and higher branchingratios for gluons [15]. The expansion then of course triggers the onset of hadronization,leading to a phase in which partonic and hadronic degrees of freedom [16] coexist.Starting point of our analysis is the time evolution (in c.m. time, tc.m.) of the rapiditydensity dN/dy of partons (i.e. quarks and gluons) and on-shell hadron multiplicities at|yc.m.| ≤ 0.5, depicted in the upper frame of ﬁgure 1. Note that there are no distinctlyseparate time scales for the three reactions stages discussed earlier in this article: hadronicand partonic phases may evolve in parallel and both, parton-parton as well as hadron-hadroninteractions occur in the same space-time volume. The overlap between the partonic andhadronic stages of the reaction stretches from tc.m. ≈ 1 fm/c up to tc.m. ≈ 4 fm/c for themidrapidity region. Our analysis shows that this overlap occurs not only in time but alsoin coordinate space – partonic and hadronic degrees of freedom occupy the same space-time volume during this reaction phase. Hadronic resonances like the ∆(1232) and theρ(770) (which are the most abundantly produced baryonic and mesonic resonance states)are formed and remain populated up to tc.m. ≈ 15 − 20 fm/c, indicating a considerableamount of hadronic rescattering. Hadron yields saturate at time-scales tc.m. ≈ 25 fm/c.Since resonance decays have not been factored into this estimate of the saturation time, thisnumber should be viewed as an upper estimate for the time of chemical freeze-out.Rates for hadron-hadron collisions per unit rapidity at yc.m. are shown in the lowerframe of ﬁgure 1, i.e. all hadron-hadron collisions for hadrons with |yc.m.| ≤ 0.5 were takeninto account. Meson-meson and meson-baryon interactions dominate the dynamics of thehadronic phase. Due to their larger cross sections baryon-antibaryon collisions occur morefrequently than baryon-baryon interactions. However, both are suppressed as compared to1the current version of VNI, 4.12, contains an erroneous rescaling of partons in coordinate space tothe light-cone located at the origin of the computational coordinate system instead of that deﬁnedby the respective production vertex of the parton. This erroneous rescaling has been removed forour calculations.3meson-meson and meson-baryon interactions. This is due to the large meson multiplicity,which creates a “mesonic medium” in which the baryons propagate.A comparison of calculations with and without hadronic rescattering shows that e.g. theproton and antiproton multiplicities change by a factor of two due to hadronic rescattering,whereas the ratio of their yields remains roughly constant. Evidently chemical freeze-outof the system occurs well into the hadronic phase and not at the “phase-boundary”. Thecollision rates indicate that interactions cease at tc.m. ≈ 30 − 40 fm/c at which point thesystem can be regarded as kinetically frozen out. Since the saturation of the hadron yieldsoccurs earlier, there is a clear separation between chemical and kinetic freeze-out.Figure 2 shows freeze-out time tf and transverse radius rt, d2N/(rtdrtdtf), for pions (leftcolumn) and protons (right column). The top row shows the result of parton cascading,hadronization and hadronic decays, but without hadronic reinteraction, whereas the lowerrow shows the same calculation with full hadronic dynamics. The contour lines have iden-tical binning within each column, but diﬀer between the two columns. Obviously hadronicinteractions have an enormous eﬀect on the freeze-out:The average freeze-out time for protons increases tenfold from 3.2 fm/c without hadronicrescattering to 27.4 fm/c with hadronic rescattering. The average transverse proton freeze-out radius increases from 3.6 fm to 13 fm.For pions tf increases from 6.3 fm/c to 18.6 fm/c and rt from 5.6 fm to 9.6 fm!Also, the overall shape of the distributions varies drastically: without hadronic rescat-tering, the emission of pions and particularly protons is more strongly restricted to thelight-cone than with rescattering. This may give rise to the speculation that HBT inter-ferometry may indicate a surface-like emission pattern in the case of negligible hadronicreinteraction and a bulk-like emission pattern in the case of strong hadronic reinteraction.In the proton d2N/(rtdrtdtf) distribution hadronic rescattering eﬀects also manifest them-selves through a second maximum at tc.m. ≈ 25 fm/c. It should be noted, however, thateven in the case of full hadronic rescattering, approximately 15% of protons and pions stillfreeze out directly after hadronization without any hadronic (re)interaction or decay at all.In contrast to the physics at the SIS and AGS, where (vector-)mesons propagate in adense baryonic environment (allowing e.g. for a search for the onset of chiral symmetryrestoration), the situation at RHIC is reversed: here the baryons propagate in a mesonicmedium. Therefore we shall now focus on the dynamics of baryons in the intermediateand late reaction stages: Figure 3 shows the collision number distribution for protons andhyperons around midrapidity. The collision number distribution shows a very slow decreasefrom Ncoll ≈ 5 to Ncoll ≈ 17, before falling oﬀ roughly exponentially. Approximately 15% ofthe protons and 6% of the hyperons do not rescatter at all. However, on average protonsrescatter 14 and hyperons 15 times. Baryonic rescattering is dominated (to 99%) by meson-baryon interactions – roughly 1/3 of those are elastic scatterings, 1/3 lead to the excitationof a discrete baryon resonance state with a resonance-mass below 2.2 GeV and 1/3 lead tothe excitation of a state in the high-mass resonance continuum with masses above 2.2 GeV.The rather small fraction of elastic scatterings serves as an indication that the system does4not fully thermalize in the course of the reaction.This massive hadronic rescattering does not only lead to changes in the freeze-out space-time distribution, but it also inﬂuences the momentum distributions of the baryons: Figure 4shows the dN/mtdmt-spectra for nucleons around midrapidity. The circles denote nucleonswhich have not rescattered after hadronization, whereas the squares refer to nucleons whichhave rescattered at least 4 times. The respective mt slope decrease by roughly 25% fromTNc=0 = 350 MeV to TNc≥4 = 270 MeV, thus indicating a softening of the protons in themesonic medium via rescattering. This softening is quite surprising since other microscopiccalculations at CERN/SPS and even RHIC energies in the framework UrQMD [18] andhybrid macro/microscopical [19] models ﬁnd massive rescattering leading to an additionalbuild-up of radial ﬂow and a respective increase in the mt slope.The eﬀects of hadronic reinteraction on the predictions of perturbative QCD based trans-port descriptions [12,17] have also been investigated in [16,20,21]. In [16,21] the analysiswas focused strongly on the inﬂuence of hadronic rescattering on inclusive hadronic spec-tra, whereas in [20] the partonic phase was not implemented in a fully microscopic fashion.In contrast to [16,20,21], here we have carried out an in-depth analysis of the underlyingreaction dynamics in the framework of a combined microscopic parton/hadron transportapproach. Our results show that a radial ﬂow analysis of hadrons and HBT correlationmeasurements may be best suited to experimentally estimate the importance of hadronicreinteractions at RHIC. A detailed analysis of these experimentally accessible phenomena isin preparation [22].In summary, we have introduced a novel transport approach combining partonic andhadronic degrees of freedom and discussed the resulting reaction dynamics. At midrapiditypartonic and hadronic degrees of freedom coexist between tc.m. ≈ 1 fm/c and tc.m. ≈ 5 fm/cin which numerous parton-parton and hadron-hadron interactions take place. There existsno spatial separation between the partonic and hadronic interaction regions. The space-timepattern of particle freeze-out is strongly modiﬁed by hadronic rescattering. Freeze-out timesand transverse radii increase by factors of 2 – 3 depending on the hadron species. Massiverescattering of baryons in a highly excited meson gas is observed, even though roughly 10%of the baryons do not rescatter at all and are directly emitted after hadronization. Therescattering also leads to a considerable softening in the baryon spectra.This work is dedicated to the memory of Klaus Kinder-Geiger. It was made possible onlythrough his active support and he would have surely been among the coauthors if he wasstill alive. S.A.B. acknowledges many helpful and inspiring discussions with Berndt M¨ uller.This work has been supported in part by the Alexander v. Humboldt Foundation and inpart by DOE grant DE-FG02-96ER40945, DFG, BMBF and the GSI Graduiertenkolleg“Theoretische und Experimentelle Schwerionenphysik”.5REFERENCES[1] J. Harris and B. M¨ uller, Ann. Rev. Nucl. Part. Sci. 46 (1996) 71.[2] S.A. Bass, M. Gyulassy, H. St¨ ocker and W. Greiner, J. Phys. G25 (1999) R1, hep-ph/9810281.[3] K. Geiger and B. M¨ uller, Nucl. Phys. B369 (1992) 600.[4] K. Geiger, Phys. Rep. 258 (1995) 237.[5] J. Ellis and K. Geiger, Phys. Rev. D52 (1995) 1500.[6] K. Geiger, Phys. Rev. D47 (1993) 133.[7] B. R. Webber, Nucl. Phys. B238 (1994) 492.[8] G. Peilert, A. Rosenhauer, H. St¨ ocker, W. Greiner, and J. Aichelin, Modern PhysicsLetters A3 (1988) 459.[9] J. Aichelin, Phys. Rep. 202 (1991) 233.[10] H. Sorge, H. St¨ ocker, and W. Greiner, Annals of Physics 192 (1989) 266.[11] S. A. Bass, M. Belkacem, M. Bleicher, M. Brandstetter, L. Bravina, C. Ernst, L. Ger-land, M. Hofmann, S. Hofmann, J. Konopka, G. Mao, L. Neise, S. Soﬀ, C. Spieles,H. Weber, L. A. Winckelmann, H. St¨ ocker, W. Greiner, C. Hartnack, J. Aichelin andN. Amelin, Progr. Part. Nucl. Physics Vol. 41 (1998) 225, nucl-th/9803035.[12] K. Geiger, Comp. Phys. Com. 104 (1997) 70.[13] M. Bleicher, E Zabrodin, C. Spieles, S. A. Bass, C. Ernst, S. Soﬀ, L. Bravina, H. Weber,H. St¨ ocker and W. Greiner, submitted to J. Phys. G.[14] K. Eskola and X. N. Wang, Phys. Rev. D49 (1994) 1284.[15] E. V. Shuryak, Phys. Rev. Lett. 68 (1992) 3270.[16] K. Geiger and R. Longacre, Heavy Ion Phys. 8 (1998) 41.[17] X. N. Wang and M. Gyulassy, Phys. Rev. D44 (1991) 3501.[18] M. Bleicher, C. Spieles, C. Ernst, L. Gerland, S. Soﬀ, H. St¨ ocker, W. Greiner andS.A. Bass, Phys. Lett. B in print, hep-ph/9803346.[19] A. Dumitru, S.A. Bass, M. Bleicher, H. St¨ ocker and W. Greiner, nucl-th/9901046[20] G. Bertsch, M. Gong, L. McLerran, V. Ruuskanen and E. Sarkinnen,Phys. Rev. D37 (1988) 1202.[21] Y. Nara, Nucl. Phys. A638 (1998) 555c.[22] S.A. Bass et al., in preparation6FIGURESFIG. 1. Top: time evolution of the parton and on-shell hadron rapidity densities at c.m.for central (b ≤ 1 fm) Au+Au collisions at RHIC. There exists a considerable overlap betweenthe partonic and hadronic phases of the reaction. Hadronic resonances are formed and remainpopulated up to ≈ 20 fm/c indicating a large amount of hadronic interaction. Bottom: Rates forhadron-hadron collisions per rapidity at c.m.. Meson-meson and to a lesser extent meson-baryoninteractions dominate the dynamics of the hadronic phase.7FIG. 2. Freeze-out time and transverse radius distribution d2N/(rtdrtdtf) for pions (leftcolumn) and protons (right column) around mid-rapidity (−1 ≤ yc.m. ≤ 1). The top row shows theresult of parton cascading, hadronization and hadronic decays but without hadronic reinteractionwhereas the lower row shows the same calculation with full hadronic dynamics. The contour lineshave identical binning within each column but diﬀer between the two columns.8FIG. 3. Collision number distribution for nucleons and hyperons around midrapidity: ap-proximately 15% of the protons and 6% of the hyperons do not rescatter at all. The distributionexhibits a slow decrease from Ncoll ≈ 5 to Ncoll ≈ 17 before falling roughly exponentially.9FIG. 4. dN/mtdmt spectra for protons around midrapidity. The circles show protons whichhave not rescattered after hadronization whereas the squares refer to protons which have rescatteredat least 4 times. The respective slope decreases by roughly 25% indicating a cooling of the protonsvia hadronic rescattering.10

Analysis of reaction dynamics at RHIC in a combined parton/hadron transport approach

Analysis of reaction dynamics at RHIC in a combined parton/hadron transport approach

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