Recent results from the CERES experiment at the SPS are reviewed. Emphasis is
put on the centrality and beam energy dependence, and the results are put into
perspective with findings at lower and higher beam energies. The rather weak
beam energy dependence of the HBT radii maybe understood in terms of a
transition from baryon to pion dominated freeze-out. The observed short
lifetimes end emission durations are presently in contradiction to results from
model calculations.Comment: Invited talk at the International Workshop XXX on Gross Properties of
  Nuclei and Nuclear Excitations - Ultrarelativistic Heavy-Ion Collisions, Jan.
  13-19, 2002, Hirschegg, Austria. 11 pages, 8 figure

Appelshäuser, Harald

English

arXiv

Recent results from the CERES experiment at the SPS are reviewed. Emphasis is put on the centrality and beam energy dependence, and the results are put into perspective with findings at lower and higher beam energies. The rather weak beam energy dependence of the HBT radii maybe understood in terms of a transition from baryon to pion dominated freeze-out. The observed short lifetimes end emission durations are presently in contradiction to results from model calculations

Appelshäuser, H

CERN Document Server

Pion Interferometry: Recent results from SPSHarald Appelsha¨userPhysikalisches Institut der Universita¨t HeidelbergPhilosophenweg 12, D-69120 Heidelberg, GermanyAbstractRecent HBT results from the CERES experiment at the SPS are re-viewed. Emphasis is put on the centrality and beam energy dependence,and the results are put into perspective with results at lower and higherbeam energies. The rather weak beam energy dependence of the HBTradii may be understood in terms of a transition from baryon to piondominated freeze-out. The observed short lifetimes and emission dura-tions are presently in contradiction to results from model calculations.1 IntroductionWhile single particle momentum distributions give only indirect insight to thespace-time evolution of the system created in high energy heavy ion collisions,the lifetime and the spatial extent of the pion source as well as the existenceof collective velocity elds at the time of thermal freezeout can be probed bythe study of Bose-Einstein momentum correlations of identical pions via HBTinterferometry [1]. The width of the correlation peak at vanishing relative mo-menta reflects the so-called length of homogeneity of the pion emitting source.Only in static sources can the length of homogeneity, in the following alsocalled ’source radius’, be interpreted as the true geometrical size of the sys-tem. In a dynamic system, the occurence of space-momentum correlations ofthe emitted particles due to collective expansion generally leads to a reductionof the observed source radii, depending on the strength of the expansion andthe thermal velocity of the pions√Tf/mt at thermal freeze-out [2]. A dieren-tial analysis of the HBT correlations in bins of the pair transverse momentumkt=12j ~pt,1 + ~pt,2j thus provides valuable information about the properties of thecollective expansion of the system [3].To obtain most detailed information about the space-time evolution thethree-momentum dierence vector ~q of two like-sign pions is decomposed intocomponents, ~q=(qlong, qside, qout). Following Bertsch and Pratt [4], qlong is themomentum dierence along the beam direction, calculated in the longitudinalrest frame (LCMS) of the pair, qout is parallel to the pair transverse momentum~kt and qside is perpendicular to qlong and qout.The correlation function is dened as the ratio C2(~q)=A2(~q)/B2(~q) wherethe ’signal’ A2(~q) is the probability to nd a pair with momentum dierence ~qin a given event and the ’background’ B2(~q) is the corresponding mixed-eventdistribution.The normalized correlation functions are t by a Gaussian:C2(~q) = 1 + λ exp(−R2longq2long −R2sideq2side−R2outq2out − 2R2outlongqoutqlong), (1)with Rlong, Rside, Rout being the Gaussian source radii and λ the correla-tion strength. The cross-term R2outlong appears as a consequence of space-timecorrelations in non-boost-invariant systems.2 Results from SPSPion HBT interferometry analyses have been performed by a number of ex-periments at SPS [5, 6, 7, 8]. A systematic study of the centrality dependenceof HBT radii around midrapidity from Pb+Au collisions at all three presentlyavailable SPS energies, 40, 80, and 158 AGeV, was recently presented by theCERES collaboration [9]. Details of their analysis can be found in [10].0 0.5 0 0.5 0 0.5 0 0.540 AGeV80 AGeV158 AGeV25-15% 10-15% 5-10% <5%CERES Pb+AuHBT preliminarykt (GeV/c)0246Rlong (fm)Fig. 1: Rlong vs. kt [10]. The lines represent fits to the data (see text).The kt-dependence of the longitudinal source parameter Rlong is shown inFig. 1 for the three dierent beam energies and as function of the centralityof the collision. Similar to previous studies, a strong decrease of Rlong withkt is observed, characteristic for a strong collective longitudinal expansion,where the length of homogeneity is entirely saturated by the thermal lengthscale √Tf/mt. For the case of longitudinal boost-invariance, Rlong can beconnected to the lifetime τs of the system, the time elapsed between the onsetof expansion and kinetic freeze-out by Rlong=τs(Tf/mt)12 [2].The slight but systematic overall increase of Rlong with centrality and beamenergie is reflected in a correspondingly longer lifetime when applying the aboveexpression to the data and assuming Tf=120 MeV (see ts in Fig. 1). Theobserved lifetimes at the SPS are 6-8 fm/c.0 0.5 0 0.5 0 0.5 0 0.540 AGeV80 AGeV158 AGeV25-15% 10-15% 5-10% <5%CERES Pb+AuHBT preliminarykt (GeV/c)0246R side (fm)Fig. 2: Rside vs. kt [10].0 0.5 0 0.5 0 0.5 0 0.540 AGeV80 AGeV158 AGeV25-15% 10-15% 5-10% <5%CERES Pb+AuHBT preliminarykt (GeV/c)0246R out (fm)Fig. 3: Rout vs. kt [10].The transverse source parameter Rside is closely related to the true geomet-rical transverse extension of the system at freeze-out. Consequently, a weakerkt-dependence is observed for Rside (Fig. 2), indicating the presence of radialflow. A slight but systematic increase of Rside with centrality is measured at allbeam energies, as expected from simple collision geometry. The beam energydependence is surprising: largest Rside and the strongest kt-dependence are ob-served at the lowest energy. This led previously to the conclusion that radialflow may reach a maximum at the lower SPS energies [11]. We will discussbelow that the extraction of the radial flow velocity from the kt-dependence ofRside at the lower SPS energies might be questionable. At 158 AGeV, a radialflow velocity of about 0.5c was obtained from the analysis of single particlemt-spectra and Rside(kt) [5, 12].Many authors have discussed that a strong rst order phase transition witha large latent heat can lead to a retardation of hadronization during the mixedphase and consequently to a long duration of pion emission [4, 13, 14, 15,16]. This should be observable via a strong increase of the outward sourceparameter Rout with respect to Rside. However, no long-lived source has beenobserved so far. At SPS, Rout (Fig. 3) is similar to Rside, indicating a shortpion emission duration and a sudden freeze-out.3 Beam energy dependenceA large amount of pion interferometry data have been published by exper-iments at AGS, SPS, and RHIC. This allows for a systematic study of thesource parameters over a wide range of beam energies. It has been arguedthat the HBT null eect [17], the absence of any beam energy dependence,in particular when going to RHIC, is the actual surprising result from HBTinterferometry.In Fig. 4 are shown the kt-dependences of Rlong,Rside, and Rout in centralPb(Aa)+Pb(Au) collisions at dierent beam energies [18, 10, 19]. Indeed, nodramatic variation of any of the source parameters can be observed. However,a closer inspection reveals some interesting features. Rlong is approximatelyconstant from AGS to the lower SPS energies, but develops a signicant in-crease within the SPS regime and towards RHIC, indicating a smooth increaseof the lifetime.Most interesting is the behaviour of Rside: It is gradually decreasing atsmall kt up to top SPS energy, connected with a continuous flattening of thekt-dependence. At RHIC, Rside is again larger than at SPS while the shape isnot yet well measured, at least the pi−pi− sample looks rather flat. Naivly, theflattening indicates a decrease of the radial flow velocity as function of beamenergy, in contradiction to the present understanding [20].Rout shows a rather weak energy dependence, possibly indicating a shallowminimum at the lower SPS energy.0246Rlong (fm)2 AGeVE8954 AGeVE8956 AGeVE8958 AGeVE89540 AGeVCERES80 AGeVCERES158 AGeVCERESRHICSTAR0246Rside (fm)02460 0.3Rout (fm)0 0.3 0 0.3 0 0.3 0 0.3 0 0.3 0 0.3 0 0.3kt(GeV/c)Fig. 4: kt-dependence of HBT radii around midrapidity in central Pb(Au)+Pb(Au) collisionsat different beam energies. The data are from [18, 10, 19].A straight-forward investigation of the freeze-out properties can be per-formed by relating the measured source parameters to an eective freeze-outvolume, Vf=2piRlongR2side. Assuming freeze-out at constant density [21], weexpect Vf to scale linearly with the charged particle multiplicity. Fig. 5 showsVf as function of the number of participants at 40, 80, and 158 AGeV. A lin-ear scaling with Npart is indeed observed at all three energies, consistent withthe assumption of a constant freeze-out density, since the number of chargedparticles was found to scale close to linear with Npart at SPS [22].2004006008001000100 200 300 400Npart2piRlongRside2  (fm3 )0.15<kt<0.25 GeV/c40 AGeV80 AGeV158 AGeVCERES Pb+AuHBT preliminaryFig. 5: Vf as function of Npart at different SPS energies [10].05001000150020001 10 102<kt>≈0.16 GeV/cE895CERESSTAR pi-pi-√s(GeV)2piRLongRSide2  (fm3 )Fig. 6: Vf in central Pb(Au)+Pb(Au) collisions as function ofps (see text). E895 pointsare at < kt >=0.15 GeV/c [18], STAR is at < kt >=0.17 GeV/c [19], CERES points arethe average of their bins at < kt >=0.12 and < kt >=0.2 GeV/c [10].But the beam energy dependence is surprising: There is no clear hierarchyvisible in Fig. 5 as expected from the increase of multiplicity by about 50%between 40 AGeV and 158 AGeV; the smallest Vf are observed at 80 AGeV.Obviously, the freeze-out volume scales with multiplicity as long as multiplicityis controlled via centrality, but it does not scale accordingly as multiplicitychanges with beam energy.The comparison of Vf at dierent beam energies from AGS to RHIC shedssome light on this: The freeze-out volume Vf is gradually decreasing withinthe AGS energy range, reaches a minimum at SPS and then increases towardsRHIC, as demonstrated in Fig. 6.Clearly, a simple relation between multiplicity and freeze-out volume can-not hold. On the other hand, it is plausible to assume that at low energiespions interact mainly with nucleons, while at high energies pion-pion scatter-ing dominates. Is the transition from nucleon to pion dominated freeze-outcharacterized by a minimum in Vf at SPS?11010 21 102√s(GeV)dN/dy midp–p-p–p+p–pi-p+p–+pi-100012001400Neff (fm2 )0.511.521 102√s(GeV)V f/Neff (fm)Fig. 7: Left: Midrapidity yields of different particles vs.ps. Upper right: cross sectionweighted sum of particle yields (see text). Lower right: ratio Vf/Neff vs.ps.In Fig. 7 (left) the midrapidity density of pions [23, 24, 25, 26] and pro-tons [27, 28, 11, 29, 30, 31] in central Pb(Au)+Pb(Au) collisions is shown asfunction ofps. The pion yield increases monotonically with beam energy.The total proton (p+p) yield at midrapidity drops from AGS to SPS and staysapproximately constant between SPS and RHIC because the decreasing num-ber of net protons is compensated by p-p production. The sum of pions andprotons, however, is still a monotonic function ofps.At this point, the dierent cross sections σpipi and σpiN have to be considered.In Fig. 7 (upper right) the cross section weighted sum of pions and protonsNeff=2 Np+p¯ σpiN+ 3 Npi− σpipi is shown 1. For the cross sections σpipi=10 mb1Note that there are a few simplifications: the protons are multiplied by 2 to account forand σpiN=65 mb are assumed. Indeed, the cross section weighted sum of pionsand nucleons at midrapidity is non-monotonic and exhibits a minimum at SPS.As a consequence, the ratio Vf/Neff , which has the dimension of a length, isapproximately constant (Fig. 7, lower right). This result suggests Vf/Neff1 fmas a universal freeze-out condition.In this picture, the relatively weak beam energy dependence of HBT sourceparameters can be understood as an interplay between the decreasing (andeventually levelling o) (p+p) yield and the increasing pion multiplicity atmidrapidity, if their dierent cross sections with pions are taken into account.It is interesting to obtain a detailed understanding of the role of protons forpion freeze-out at low energies. The strong momentum dependence of the σpiNcross section may aect the kt-dependence of Rside at low beam energies andcause the flattening of the kt-dependence with increasing beam energy, as theimportance of protons ceases. At the lower SPS energies, where protons arestill important, the interpretation of the kt-dependence of Rside in terms ofradial flow may be questionable, and possibly breaks down at AGS.4 DiscussionSingle particle spectra and azimuthal anisotropies at SPS and RHIC have beenwell reproduced by state-of-the-art hydro+cascade calculations [32, 33, 34].However, they fail to reproduce the measured HBT parameters, in particularthe lifetime of the system is grossly overestimated.In these models, the early plasma phase is described by hydrodynamicsassuming an ideal plasma EOS with a rst order phase transition and a mixedphase with an adjustable latent heat. At the end of the mixed phase, hadronsare created assuming a thermal phase space population superimposed by thecollective velocity eld created by the plasma pressure. After hadronization,hadrons are rescattered using a hadronic cascade code.In [35] the response of the hydro+cascade calculation to dierent choicesof the latent heat is well documented. From this investigation, it becomesobvious that the choice of a relatively large latent heat of 0.8 GeV/fm3, neededto describe the SPS single particle data, is mainly driven by the observed massdependence of the inverse slope parameters. Smaller latent heat produceslarger flow velocities before hadronization and therefore too hard spectra, inparticular for the multi-strange baryons which do not follow the linear scalingbehaviour observed for pi, K, p [36]. On the other hand, a small latent heatthe neutrons, which is not completely correct for the lowest beam energies. Also the role oflight nuclei and other produced particles is neglected.would lead to an early acceleration of the matter and therefore to a fasterdilution and shorter lifetime, in particular of the hadronic phase, which issuggested by the HBT measurements.This leads to a closer inspection of the data as represented in Fig. 8 (left).For some of the particle species, the observed inverse slope parameter scaleslinearly with the particle mass, consistent with the assumption of a commonflow velocity. There are, however, a number of exceptions which do not followthis rule (φ, , Ω). This was explained by their small cross sections with thesurrounding matter, hence they are expected to participate less in the collectivemotion.00.20.40.60 0.5 1 1.5 2M (GeV/c2)T(GeV)NA49NA44WA98WA97NA50pi K φρ/ωpΛ ΞΩd00.20.40.60 2 4 6NA49NA44WA98WA97NA50nquarksT(GeV)Fig. 8: Left: Inverse slope parameter vs. mass of hadrons at SPS. Right: Inverse slopeparameter vs. number of constituent quarks.On the other hand, it is evident that the data separate into two groups:All mesons have similar slopes, and the same is true for baryons. One maytherefore as well correlate the inverse slope with the number of constituentquarks inside the hadron, rather than with the hadron mass (Fig. 8, right).Also here a scaling behaviour can be observed, and almost all particles areconsistent with this trend. Note that the large inverse slope of the φ observedby NA49 [37] is experimentally still under debate, since there is also a mea-surement by NA50 [38], giving a much smaller number.The physical picture which arises from this representation is dierent fromthe common interpretation: collective motion has completely developed beforehadronization, with constituent quarks being the flowing objects. Hadrons areformed by coalescence of constituent quarks, preferentially if they are closein phase space, thereby adding their momenta. When hadrons acquire mass,momentum is conserved which leaves the momentum spectra unchanged. Inthis picture, the data are consistent with a kinetic freeze-out temperature of0.12 GeV, a collective quark flow velocity of√1/3 and an eective quarkmass of 0.33 GeV: T=0.12 + 1213 0.33  nquarks (dashed line in Fig. 8, right).Most of the explosive power of the system would be assigned to the early,pre-hadronic phase of the collision, thereby qualitatively explaining the shortlifetimes observed by HBT. It also suggests that the hadronic mass scale isno more relevant in the early phase of the collision, as naively expected for adeconned partonic system.References[1] S. Pratt, Phys. Rev. Lett. 53 (1984) 1219.[2] A.N. Makhlin and Yu.M. Sinyukov, Z. Phys. C39 (1988) 69.[3] S. Pratt, T. Cso¨rgo¨, and J. Zimanyi, Phys. Rev. C42 (1990) 2646.[4] G. Bertsch, Nucl. Phys. A498, (1989) 173c, S. Pratt, Phys. Rev. D33(1986) 1314.[5] NA49 Collaboration, H. Appelsha¨user et al., Eur. Phys. J. C2 (1998) 661.[6] NA44 Collaboration, I.G. Bearden et al., Eur. Phys. J. C18 (2000) 317.[7] WA98 Collaboration, M.M. Aggerwal et al., Eur. Phys. J. C16 (2000)445.[8] WA97 Collaboration, F. Antinori et al., J. Phys. G27 (2001) 2325.[9] H. Appelsha¨user, INT-RHIC Winter Workshop 2002, Seattle.[10] H. Tilsner, PhD Thesis, Universita¨t Heidelberg (2002), publication inpreparation.[11] CERES Collaboration, D. Adamova et al., Nucl. Phys. A698 (2002) 253c.[12] B. Tomasik, U.A. Wiedemann, and U. Heinz, nucl-th/9907096.[13] G. Bertsch, M. Gong, and M. Tohyama, Phys. Rev. C37 (1988) 1896.[14] G. Bertsch and G.E. Brown, Phys. Rev. C40 (1989) 1830.[15] D. Rischke, Nucl. Phys. A610 (1996) 88.[16] D. Rischke and M. Gyulassy, Nucl. Phys. A608 (1996) 479.[17] M. Gyulassy, INT-RHIC Winter Workshop 2002, Seattle.[18] E895 Collaboration, M.A. Lisa et al., Phys. Rev. Lett. 84 (2000) 2798.[19] STAR Collaboration, C. Adler et al., Phys. Rev. Lett. 87 (2001).[20] N. Xu and M. Kaneta, Nucl. Phys. A698 (2002) 306c.[21] I. Pomeranchuk, Dokl. Akad. Nauk SSSR 78 (1951) 884.[22] WA98 Collaboration, M.M. Aggerwal et al., Eur. Phys. J. C18 (2001)651.[23] E895 Collaboration, J.L. Klay et al., publication in preparation.[24] NA49 Collaboration, M. Gazdzicki, Proceedings of this Conference.[25] STAR Collaboration, C. Adler et al., Phys. Rev. Lett. 87 (2001).[26] STAR Collaboration, C. Adler et al., Nucl. Phys. A698 (2002) 64c.[27] E895 Collaboration, J.L. Klay et al., Phys. Rev. Lett. 88 (2002).[28] E917 Collaboration, B.B. Back et al., Phys. Rev. Lett. 86 (2001) 1970.[29] NA49 Collaboration, H. Appelsha¨user et al., Phys. Rev. Lett. 82 (1999)2471.[30] NA49 Collaboration, G. Veres et al., Nucl. Phys. A661 (1999) 383c.[31] STAR Collaboration, C. Adler et al., Phys. Rev. Lett. 86 (2001) 4778.[32] S. So, S. Bass, and A. Dumitru, Phys. Rev. Lett. 86 (2001) 3981.[33] S. So, Proceedings of this Conference.[34] D. Teaney, J. Lauret, and E.V. Shuryak, Nucl. Phys. A698 (2002) 479.[35] D. 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Pion Interferometry: Recent results from SPS

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