Utilizing a hydrodynamical model for the freeze-out stage in heavy-ion
reactions, we extract from resolved transverse hadron spectra at midrapidity an
inverse slope parameter (temperature) $T_{Pb} =$ 120 MeV and an averaged
transverse flow velocity $v_{\perp Pb}^{aver} =$ 0.43 c in central collisions
of Pb + Pb at 158 AGeV.Comment: 6 LaTeX pages 5 eps figure

Kaempfer, B.

English

arXiv

Kämpfer, B.

Qucosa

Evidence for low freeze- out temperature and large transverse flow in central collisions of Pb + Pb at 158 AGeV

Qucosa – Hemholtz-Zentrum Dresden-Rossendorf

FORSCHUNGSZENTRUM ROSSENDORF e.v. FZR FZR-149 August 1996 Preprint Burkhard Kämpfer Evidence for low freeze-out temperature and large transverse flow in central collisions of Pb + Pb at 158 AGeV Forschungszentrum Rossendorf c.V. Postfach 51 01 19 . D-01314 Dresden Bundesrepublik Deutschland Telefon (0351) 260 3258 Telefax (0351) 260 3700 E-Mail kaempfer@fz-rossendorf.de Evidence'for low freeze-out temperature and large transverse flow in central collisions of Pb + Pb at 158 AGeV Institut für Theoretische Physik, TU Dresden, 01062 Dresden, and firschungszentrum Rossendorf, PF 5101 19, 01314 Dresden Utilizing a hydrodynamical model for the freeze-out stage in heavy-ion reactions, we extract from resolved transverse hadron spectra a t  midrapidity an inverse slope pararneter (temperature) Tpa = 120 MeV and an averaged transverse fiow velocity V"; = 0.43 C in centraI collisions of P b  + P b  at 158 AGeV. Recently the (yet preliminary) transverse momentum spectra of T*, xO, I{*, I<:, A, A at midrapidity, resulting in central collisions of Pb + Pb at bearn energy 158 AGeV, have been reported [I, 2, 31. To analyze these spectra one can utilize a hydrodynamical description of the freeze-out stage. The concept of hydrodynamics for describing heavy-ion collisions has a long history, and quite sophisticated models have been proposed for modeling the hadron dynamics at freeze-out (for a survey cf. [4]). The general interest in hydrodynamics is motivated by the fact that this approach is intirnately related to the use of the equation of state of strongly interacting matter. Within such a framework the chiral symmetry restoration or the phase transition from hadron matter to a quarkigluon plasma appear as particularly interesting. It is still one of the ultimate goals in the realm of heavy-ion physics at relativistic energies to search for signals of deconfined matter. Now, it seems that only a combination of various observables can help to pin down information on the state of maximurn density and excitation energy. Sometimes penetrating probes, like dileptons and photoris, are considered as favorable signals for the diagnostic of the early stage in thc Course of colliding nuclei. Hadrons, otherwise, carry mainly information on the late stages of disassembling matter due to the strong interaction. However, if initially a state of hot and dense matter is formed, then the resulting strong pressure let the system rapidly explode, and a collective flow develops as a consequence. Guided by such ideas one can try to elucidate whether experimental hadron spectra siipport the predictions of thermodynamical and hydrodynamical concepts. Indeed, in refs. [5, 61 it is claimed that in silicon and gold induced reactions at BNL-AGS energies the hadron abundances and the spectra point to thermal and hadrochemical equilibrium. Also in sulfur induced reactions at CERN-SPS energies this concept is anticipated with a freeze-out temperature of Ts = 160 MeV [7] ,  which is in the region where the dcconfinement transition is expected. Here we would like to point out that the available data set [l, 2, 3, 51 in central Pb + Pb reactions at CERN-SPS energy favors a freeze-out temperature of 120 MeV and an avcraged transverse flow velocity of 0.43 C. Therefore, thc puzzling situation arises that in tlic sulfur induced reactions a much higher freeze-out temperature appears than in lead reactions. We base our analysis on the hydrodynamical modeI with linear veIocity profile at freczc-out tinic V.,. [4]. The trarisversc momentum distributions then read in J3oltz- mann approximation where p = arcth(vl(f)), vl(J)  = t v l e r  J, and v y  is the averaged transverse flow ve- locity; m l  = J= denotes the transverse mass of the hadron species i; I. and Ii, are Bessel functions. The normalization constants = gi R~.,.rf.,. X i  e x p { T ) / ~ ( t l c ) ~  depend on the chemical potentials pi, phase space occupation factors X; and particle degeneracies gi- This model relies on boost-invariant scaling hydrodynamics and a unique freeze-out time in both longitudinal and transverse directions. While the net proton rapidity density looks in Pb + Pb collisions quite flat in the interval 1 < y < 5: the negative hadrons show a pronounced bell-shaped rapidity distribution [l]. There- fore the applicability of the model (1) is restricted to a sufficiently narrow interval at midrapidity. (The rapidity distributions could be adjusted by a suitable dependence p(y) [SI together with the selection of a finite rapidity range.) With the model(1) one can easily describe the slopes of the resolved hadron spectra of pions, kaons, protons and lambdas [I] by a set of parameters T, vy? where T ( v y )  can vary over a wide range for given slopes. In fitting the transverse spectra, which are parametrized in ref. [l] by m,:rL du = Ci exp(-mr/Ti), one observes that, for thc values T; reported in table 1 in ref. [I] for Pb + Pb at 155 AGeV, all of the quotcd hadron spectra measured by the NA49 collaboration are uniquely described by Tpb = 120 MeV and V"; = 0.43 C. This Situation is different from S + S and S + NT, Au, where such a focus of the curves T(vL) for the various hadrons does not occur [4]. In this respect the Pb + Pb data point to a clear flow Signal for the first time. Our fitted spectra together with the data from ref. [I] are displayed in fig. 1 (for details of acceptance corrections, error bars and rapidity binning cf. [I]). Most remarkably is the change of the spectra's shapes when changing the hadron rnasses. As Cross check one can compare with the preliminary wo spectrum of the WA93 collaboration [3] and finds very good agreement in the available transversc monientum range of p l  = 0.5 - 2.5 GeV. We emphasize that our fit describes very well thc data shown in ref. [5], namely all negatively charged hadrons for rnl - n ~ ,  = 0.015 - 1.85 GeV, Ir" for ml - rnK  = 0.015 - 1 GeV, and the net baryons ($1 - (-1 for r n ~  - rn, = 0.015 - 1.42 GeV. In addition, thc prelixninary NA44 data P] of p" arid Pi* in Ihc ranges m l  - mp = 0.01 - 0.87 GeV and m l  - r n K  = 0.01 - 1.12 Cct', rcsptactively. strongly Support our values of Tpb snd V";. The situation is qiiite difkrerit for Ibe I preliminary NA44 ii- data P]. In the low r n ~  range3 which is not covercd by tlic S.449 data, there is a pronounced leveling off not described by our model. A careful analysis of feeding bg resonance decays is required to decide whether a large chemical potential of pions [9] is needed for describing these details. A possible interpretation of the values of Tpb and v"g, with respect to the difference to  the values Ts and V"' = 0.27 C extracted for Sulfur induced reactions at CERN- SPS energies [6] ,  could be that the larger System Pb + Pb develops more collectivity and stays for a longer time in contact up to freeze-out temperature, while the smaller Systems S + W, Au disassemble earlier at lower transverse flow velocity but higher mean kinetic energy (temperature) of the hadrons. Interestingly, our dynamical code [10], which employs a linear transverse velocity profile and a resonance gas model equation of state and initial conditions appropriate for lead reactions, consistently results in ~ f e r =  0.45 C. Here we do not speculate on a possible chemical equilibrium. In this respect the normalization factors Ni need still an interpretation by studying the chemical freeze- out, which does not need to be identical with thermal freeze-out [4]. By the above definition of Al;. one cari try to deduce some combinations of chernical potentials and phase space occupation factors. However, at the present early stage of the data analyses one could come to less reliable results. EtOr instance, the rapidity densities d N i / d y  obtained from a m l  integration of our fitted spectra and experimental data fits in ref. [l] differ up to a factor 2. Nevertheless in a first attempt [5] to interpret the hadron yield ratios, a chernical freeze-out temperature of 160 MeV is found. While this value, when identified with thermal freeze-out , is consistent wi t h the transverse spectra of all negative hadrons, I{+, and net baryons for the model (1) with v y  = 0.3 C [5], it is disfavored essentially by the proton and lambda data [I, 21. In ref. [ll] the dragging coefficient between pions and nucleons is calculated and is found to be too small that pions and nucleons are likely to flow with the Same velocity. In this respect the circumstantial evidence for a common transverse fiow of all hadrons could be traced back to emerge from an early overdense (and possibly deconfined) stage, which triggers the onset of the flow. But it should be emphasized that more accurate data, in particular in a wider trsnsvcrse momentum range, are needed to come ta firm conclusions. P\ h e r  rapidity binriing is desirable to understand thc longitudinal dynamics, too. Also feeding by resonarice decays must be included in an advanced analysis. In siimmary, within a hydrodynamical model we estract from thc transverse mo- I, mentum spectra of resolved hadrons a thermal freeze-out temperature Tpb = 120 MeV arid averaged transverse flow velocity V"; = 0.43 C in central Pb  + Pb collisions a t  158 AGeV. Acknowledgments:  M. Gaidzicki and N. Xu are gratefully acknowledged for in- forming me on the data analyses of tbe NA49 and NA44 collaborations prior to publi- cation. I am indebted to J .  Cleymans, U. Heinz, B. Müller, O.P. Pavlenko, I<. Redlich, and J. Stachel for useful conversations on transverse flow. This work is supported by BMBF grant 06DR666. References [I] P.G. Jones et al. (NA49 collaboration), contribution to QM'96, Heidelberg 1996, to be published in Nucl. Phys. A [TZ] N. Xu et al. (NA44 collaboration), contribution to  QM'96, IIeidelberg 1996, preprint LA-UR-96-2580, to published in Nucl. Phys. A 131 H.H. Gutbrod et al. (WA98 collaboration), GSI report 1-96 (1996), p. 57 [4] U. Heinz, Nucl. Phys. A 566 (1994) 205c, E. Schnedermann, J .  Sollfrank, U. Heinz, NATO ASI 303B (1993) 17.5, U. Heinz, K.S. Lee, E. Schnedermann, NATO ASI 216B (1989) 385 [5] J. Stachel, plenary talk at QM796, Heidelberg 1996 [6] P. Braun-Munzinger, J. Stachel, J.P. Wessels, N. Xu, Phys. Lett. B 344 (1995) 43 [7] P. Braun-Munzinger, J. Stachel, J.P. Wessels, N. Xu, Phys. Lett. B 365 (1996) 1 [8] C. Slotta, J. Sollfrank, U. Heinz, AIP conference proceedings 340 (1995) 462 191 M. Kataja, P.V. Ruuskanen, Phys. Lett. B 243 (1990) 181 [10] B. Kämpfer, O.P. Pavlenko, 2. Phys. C 62 (1994) 491 [ll] P. Levai, B. Müller, Phys. Rev. Lett. 67 (1991) 1519 Figure  capt ion 4. Fig. 1: Fits of the resolved transuerscr momcntum spectra of hadrons (a: r, b: I<", C: I<:, d: e: h, h). The preliminary data are from rcf. [I]. Our nornializal,ion factors J% are given in tbe keys. (a) pions (b) kaons I I (d) Protons 5s (e) Lambdas 102 I I I 

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Evidence for low freeze-out temperature and large transverse flow in central collisions of Pb + Pb at 158 AGeV

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