Nuclear Physics A525 (1991) _523c-526~ North-Holland, Amsterdam

523~

SEARCH FOR COLLECTIVE FLOW IN RELATIVISTIC HEAVY-ION COLLISIONS

USING TRANSVERSE MOMENTUM SPECTRA OF EMITTED HADRONS’

I<. S. Lee”), E. Schnedermann ‘) J Sollfrankb), and Ulrich Heinzb) ,

a) Department of Physics, Chonnam National University, Kwangiu 500-757, Korea b, Institut fiir Theoretische Physik, Universitst Regensburg, D-8400 Regensburg, FRG

We report on a recent analysis of the transverse momentum spectra for various identi-

fied hadron species from nuclear collisions at BNL and CERN for signs of collective flow.

The aims of this analysis are: (i) to establish to what extent the presently available data

on hadron production are compatible with the simple picture of a highly excited, locally

equilibrated “fireball” m the collision zone which in the final stages undergoes collective

expansion, and (ii) to obtain with the help of this model estimates for the amount of energy

deposited in the collision zone and the fraction converted into collective transverse motion.

The a.nalysis is not biased towards quark matter formation and uses throughout a simple

hadron resonance gas as equation of state. However, we find values for the estimated initial

energy density which would allow for the presence of a mixed phase in the initial state.

Our analysis has been presented in detail in Ref. 1. Here we show only some of the most

important results and state our conclusions.

The model assumes local thermalization of the collision zone at an early stage and subse-

quent hydrodynamical expansion at constant entropy. The observed momentum distribution

of emitted particles is assumed to be locally thermal at freeze-out, but boosted relative to

the observer by the local collective flow velocity of the expanding fireball. The freeze-out hy-

persurfase is determined from kinetic considerations, comparing local scattering with global

expansion time scales. Freeze-out occurs in a particle specific way, i.e. weakly interacting

particles freeze out earlier than strongly coupled ones.

For simplicity the expansion is taken to be spherically symmetric. This seems to be

largely justified for the BNL experiments [2] w h ere the y-distribution is compatible with

that of a spherically expanding fireball [2,1]. For CERN energies this approximation breaks

down, but the model is still expected to give adequate average information on the transverse

expansion aspects after integration over rapidity [l].

The model has two free parameters: the initial baryon and energy densities. The tempe-

rature and transverse flow at freeze-out follow from the freeze-out criterium by conservation

t \f’ork supported in part by Deutsche Forschungsgemeinschaft, grant He1283/3-1, by Bun- desministerium fiir Forschung und Technologie (BMFT), g rant 06 OR 764, and by the Korean Science and Engineering Foundation (KOSEF), grant 893-0202-002-2.

0375.9474/91/$03.50 0 1991 - Elsevier Science Publishers B.V. (Nod-Holland)

524c KS. Lee et al. / Collective jlow in relativistic heavy-ion collisions

of baryon number, entropy and energy. Fig. 1 shows that the pT-spectra of pions, kaons,

protons and deuterons from 14.5 A GeV Si+Au collisions at BNL [2] can simultaneously be

described by an expanding fireball of initial energy density 1 GeV/fm3 and baryon density

pi 2: 4~0, corresponding to an initial temperature of about 160 MeV, which freezes out

at Tf = 105 MeV and pf - 0.3~0 with an average transverse expansion velocity of 0.44

c. A clear signature for this flow is the appreciable flattening of the pi spectra for heavier

particles relative to the pions; this feature appears to be absent in p+Au data from the same

experiment [3].

A puzzling feature appears in the new data on antiprotons [3] and A’s [4]‘from Si+Au col-

lisions: both particle species have steeper mT-spectra than even the pions, while our picture,

assuming simultaneous freeze-out with the protons, predicts nearly the same (much flatter)

slope as for protons. The discrepancy may indicate a lack of equilibration for antiprotons

and hyperons and deserves further investigation.

Fig. 2 shows a similar analysis of the 200 A GeV S+S data at CERN [5]. In this

representation, where we use mu rather than the transverse kinetic energy mT - ma on

the horizontal axis, the systematic flattening of the spectra for heavier particles appears

as a general concave curvature in the plot. The evidence for flow resides in the deviation

from a straight line which would correspond to thermal emission without flow. Clearly the

evidence for flow is less striking than for the BNL data, because above my all spectra can

be equally well described by a straight line with constant slope of Terr = 200 MeV (this

was not possible for the deuterons from BNL, showing that there the tendency for flattening

slopes continued to about rnr 21 3 GeV). In Fig. 2 essentially all the curvature is due to the

pions, and it is not even fully accounted for by the flow model, leaving an excess at small

my.

We have therefore begun to investigate the question to what extent the low-mT rise of

the pion spectra could be due to contributions from decays of hadron resonances formed

in the collision and thereby fake a flow signal. We found that for the rather low freeze-out

temperature Tf = 105 MeV resonance contributions are very small and cannot alone explain

the behaviour of the pion spectrum. However, as shown in Fig. 3, at higher temperatures

their effect becomes very strong: We obtain a nearly perfect fit to the pion spectrum alone by

using a static fireball (i.e. without flow) at T=200 MeV, with a very small baryon chemical

potential ~~=200 MeV corresponding to the low baryon/pion ratio [5,6] observed near

central rapidity in the S+S collisions, by adding to the direct (thermally emitted) pions those

from the two-body decays of p and li* mesons, the A and lowest C’ resonance, and from the

three-body decays of the w and 17 mesons. While the p and w are very important, due to their

large abundance and very steep decay spectra, the baryon resonances are comparatively rare

and only provide the icing on the cake.

Further analyses of resonance contributions to other particle spectra and their separation

from flow effects are presently under way.

KS. Lee et al. / Collective flow in relativistic heavy-ion collisions 525~

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526~ KS. Lee et al. / Collective flow in relativistic heavy-ion collisions

REFERENCES

[I] I<. S. Lee, U. Heinz, E. Schnedermann, TPR-90-18, submitted to 2. Phys. C

[2] E802 toll., T. Abbott et al., Phys. Rev. Lett. 64 (1990) 847

[3] E802 toll., Y. Miake et al., this conference

[4] E810 toll., this conference

[5] NA35 toll., H. Strijbele et al., in: The Nuclear Equation of State, (W. Greiner, ed.),

NATO AS1 Series B, Plenum, New York, 1990