How can we explore the onset of deconfinement by experiment?
aa r X i v : . [ nu c l - t h ] N ov How can we explore the onset of deconfinement by experiment?
J. Aichelin ∗ , H. Petersen , S. Vogel , M. Bleicher SUBATECH, Universit´e de Nantes, EMN, IN2P3/CNRS4, Rue Alfred Kastler, 44070 Nantes Cedex 03, France , Institute for Theoretical Physics,Wolfgang Goethe University of Frankfurt, Germany Abstract
There is little doubt that Quantumchromodynamics (QCD) is the theory which describes stronginteraction physics. Lattice gauge simulations of QCD predict that in the µ, T plane there is a linewhere a transition from confined hadronic matter to deconfined quarks takes place. The transitionis either a cross over (at low µ ) or of first order (at high µ ). It is the goal of the present and futureheavy ion experiment at RHIC and FAIR to study this phase transition at different locations inthe µ, T plane and to explore the properties of the deconfined phase. It is the purpose of thiscontribution to discuss some of the observables which are considered as useful for this purpose. PACS numbers: ∗ invited speaker . INTRODUCTION The behavior of hadrons in an environment of finite temperature and density and thephase transition towards a deconfined phase in which quarks and gluons are the dominantdegrees of freedom is a central topic of theoretical nuclear physics since many years. Detailedcalculations have been revealed that hadrons react quite differently if the are brought in adense and/or hot environment. Vector mesons change their width but not their pole masswhen they are brought into a dense environment [1] whereas for K + mesons a substantialchange of the pole mass is predicted [2] but the width remains small. At low temperaturebut high density K − cannot be treated anymore as quasi particles having a quite compli-cated spectral function[3]. The different behavior of the different hadrons comes from theirdifferent interactions with their environment but many details of these interactions at finitedensity and temperature are not well knownStatistical calculations yield a chemical freeze out energy density of 1 . GeV /f m for finitechemical potentials, well below the energy density predicted by lattice gauge calculation forthe transition towards the deconfined phas where all hadrons become unstable. This decon-fined phase is not a weakly interacting plasma, as one has thought for quite a time, but aliquid which can be described by hydrodynamics much better than ever expected. Whenapplied to the scenario of an expanding quark gluon plasma these hydrodynamical calcu-lations describe quite well the experimental observations if they start out from a stronglyanisotropic initial state, caused by the geometry of the reaction partners, which expandswhile keeping local equilibrium.From all these calculations we have a qualitative understanding of strongly interactingmatter but from a quantitative understanding we are as far away as from an experimentalverification of the theoretical predictions. The many body theory of hadrons in matter iscomplicated and many details are neither experimentally accessible nor theoretically known.Therefore theoretical predictions differ quantitatively. Due to the limited computer capacityalso lattice gauge calculations have not converged yet to an exact temperature value atwhich the phase transition takes place. Even if in the next years progress will be made inthe theoretical approaches the ultimate goal is to verify the predictions experimentally andto convert theoretical predictions into experimental facts.In order to explore the properties of strongly interacting matter complicated experiments2ave been performed and designed - at RHIC, LHC and FAIR - in which in one singleheavy ion reaction several hundred particles are registered in the detectors. When regis-tered, however, all particles have to have their free mass and therefore one can only learnsomething about the properties of strongly interaction matter at high density/temperatureif one understands the time evolution of the system between the high density phase and thedetection.Several ideas have been launched to asses matter properties at high density/temperature:a) To measure resonances. The decay products reflect the particle properties at the pointof disintegration which may be at finite density. If the decay products interact strongly theseparticles are sensitive to moderate densities only because the resonance cannot be identifiedif one of the decay products interacts another time.b) To measure dilepton pairs. Because leptons do practically not interact with the ex-panding matter they may carry information on particles which have been disintegrated in adense environment. This we discuss in section II.c) To measure collective observables as discussed in section III.d) To measure particles which can only be produced at the beginning of the interactionwhen the density is quite high because later the available energy is too low. This is thesubject of chapter IV.In this contribution I will critically review the significance of some experimental observ-ables for the exploration of the high density zone at the future FAIR energies.To study the sensitivity of the different probes on the properties of high density zone weemploy the UrQMD model which has been successfully used to describe many of the stableand unstable particles observed at AGS and RHIC energies [4]. Details of this model maybe found in [5]. II. DILEPTONS
Using the UrQMD model we studied the time evolution of the ρ mesons which - due totheir short life time - disintegrate while the system is still in contact. Their decay products,especially the dileptons, have been suggested as a possible source of information on the highdensity zone of the reaction. In Fig. 1, left, we display the time evolution of the density asa function of time for different energies, ranging from E lab = 2 AGeV (SIS) to E cm = 2003GeV (RHIC). We display the average density in the rest system of the particles. Clearly,as expected, we see that with increasing beam energy the maximal density of the systemincreases. On the right hand side of the same figure we display the distribution of thedensities at the space-time points at which a ρ meson disappears during the reaction, eitherbecause it decays (dashed line) or because it gets reabsorbed (dotted line). It is evidentthat the higher the density the higher is the chance that the ρ meson becomes reabsorbed.Thus most of the ρ mesons which decay (and with a certain probability can be observedas a dilepton pair in the detectors) are produced at a late time, long after the system haspassed the high density. It is clearly visible that the ρ which disappear by decay comefrom a very low densities, close or below normal nuclear matter density. ρ mesons which areproduced at higher densities become that fast reabsorbed that decay becomes a rare process.One can of course discuss the details of this approach, especially the properties of the ρ athigh density. The conclusion that reabsorption and not decay is the dominant process athigh densities does not depend on these details. Therefore, dileptons coming from a ρ decayare not sensitive to system properties at high densities. It is remarkable that the averagedensity at the disintegration point of the ρ is at E lab = 30 AGeV even lower than at E lab = 2 AGeV caused by the higher particle multiplicity at higher energies. The fraction of ρ mesons which decay and of those which become reabsorbed we display in fig. 2 as a functionof time. Comparing fig. 1 and fig. 2 we see that decay dominates only when the system isdilute. Thus dileptons coming from resonance decays are sensitive to system properties atlow density only although they interact exclusively by electromagnetic interactions. III. COLLECTIVE OBSERVABLES
As said, at the energies we are interested in the system is strongly interacting. It istherefore possible that it acts collectively and that collective observables carry informationon the high density state. Especially if the system passes the phase transition to deconfinedmatter where (most of the) hadrons are not existing anymore as stable particles collectiveobservables are the only ones which may carry a direct information. There are many collec-tive effects possible which are still explored. Here we concentrate on one particular collectiveeffect which has been identified in ref. [7, 8] as a sign of the formation of a QGP. The phasetransition towards deconfined matter may soften the equation of state. Such a softening4 B / UrQMD-2.2, no collisions E lab = 11 AGeVE lab = 2 AGeV Au+Au @ AGS B / E lab = 160 AGeVE lab = 30 AGeV Pb+Pb @ SPS t [fm] B / E CM = 200 AGeV Au+Au @ RHIC -125 d N / d ( B / ) absorbeddecay -125 d N / d ( B / ) absorbeddecay
11 AGeV (Au+Au) B / -125 d N / d ( B / ) absorbeddecay
30 AGeV (Pb+Pb)
FIG. 1: Left: Time evolution of the density of central heavy ion reactions for energies ranging from E lab =2 AGeV E cm =200 AGeV. Right: Distribution of the density at which ρ mesons disappearfrom the system, either by reabsorption (dotted line) or by disintegration (dashed line). .20.40.60.81.01.2 % o f t o t a ll o ss , loss(destroyed), loss(decayed) % o f t o t a ll o ss , loss(destroyed), loss(decayed)
11 AGeV (Au+Au) t [fm] % o f t o t a ll o ss , loss(destroyed), loss(decayed)
30 AGeV (Pb+Pb)
FIG. 2: Fraction of the ρ meson which decay and which get reabsorbed (destroyed) as a functionof time for 3 Beam energies between 2 AGeV and 30 AGeV. p dir x = 1 M M X i p x,i sgn( y i ) , (1)which decreases as a function of the beam energy much faster than expected from an hadronicequation of state. For standard equations of state this effect is maximal around the FAIRenergies, where the system is expected to reach the softest point, i.e. has the lowest pressureto energy density ratio. Fig. 3 (from ref.[8]) shows the excitation function of p dir x in ahydrodynamical calculation. We see that after having reached a maximum, p dir x decreases toa minimum if the system becomes deconfined (QGP), whereas without the formation of aquark gluon plasma (had) p dir x there is not such a minimum. Thus measuring the excitation E kinLab [AGeV] < p x / N > d i r [ M e V ] Fig. 7 QGPHadAu+Au, b=3 fm
FIG. 3: The directed flow, p dir x , as a function of beam energy for Au+Au–collisions at b = 3 fm. Thefull line (crosses) corresponds to hydrodynamical calculations using the EoS with phase transition,the dotted line (open circles) to those with the pure hadronic EoS. From ref. [8]. function of p dir x will bring the presence of a quark gluon plasma to light. Unfortunatelythis interpretation is laboring under a misapprehension. Using the more elaborate UrQMDmodel in which local equilibrium is not enforced but particles interact by known (free) crosssections we obtain the excitation function of p dir x shown in Fig. 4 [9]. The reason for this formof the excitation function in UrQMD calculations is the change of the angular distribution7 -12 p x d i r ( G e V / c ) elasticdefault UrQMD -1 2 5 E lab (GeV) i n e l a s t i c i t y inelasticity @ y cm FIG. 4: Excitation functions for central Au+Au (Pb+Pb) reactions. Top: Directed flow p dir x ofnucleons with only isotropic elastic interactions (open squares) and with full elastic and inelasticcollision term (full squares). Bottom: Inelasticity (open triangles), from ref. [9] of the nucleon-nucleon cross section with increasing energy and the increasing probabilitythat resonances are produced which decay isotropically in their rest system. We see (top)that p dir x increases with energy if the nucleon-nucleons cross section were isotropic. Theincreasing anisotropy, seen in the NN data, produces, however, a maximum of p dir x followedby a decrease. At higher beam energies resonance production becomes important which ismeasured by the inelasticityInelasticity = P m i E total at y cm ± . . (2)The isotropic decay of the resonances creates an increase of averge transverse momentum ofthe particles in the system. The reabsorption of the decay products depends on the azimuthalangle and causes an observable increase of the in-plane flow p dir x . These two effects createin a realistic hadronic scenario an excitation function of p dir x which resembles strongly thatobtained in hydrodynamical calculations if a quark gluons plasma is present. The lesson8o be learnt from these studies is that collective observables in particular are complex andnot easy to interpret and that one has to be extremely carefully to identify an experimentalobservation with one of the theoretically proposed reaction scenarios before having excludedthat others may lead to the same predictions. IV. CHARMED HADRONS
At SIS energies it has turned out that strange hadrons are a very good tool to investi-gate the system at high density/temperature. The reason for this is the fact that strangehadrons have to be produced and that at SIS energies only in the initial phase, shortly afterprojectile and target start to overlap, nucleon nucleons collisions are sufficiently energeticto overcome the threshold ( √ s thres = 2.548 GeV, corresponding to a beam energy of 1.583GeV in pp collisions) for the production channel with the lowest threshold ( N N → K + Λ N ).Once produced the s quarks can still be exchanged between a baryon and a meson but theprobability that the s and ¯ s quarks annihilate is negligible. The charm multiplicity onlygives information on the high density zone because the threshold and hence the productionprobability depends strongly on the properties of the strange particles at the productionpoint. The initial momentum distribution is known from elementary collisions (and closeto that expected from three body phase space). One can therefore compare the initial andfinal momentum distribution and use the difference to study the interaction of the strangehadrons with the surrounding matter during the expansion.It is certainly tempting and also planned to follow the same strategy at FAIR energiesby replacing strange hadrons by charmed hadrons. At the highest FAIR energies ( E beam = 30 AGeV, corresponding to a center of mass energy of √ s = 7 . GeV for a nucleonpair we are slightly above threshold for charm production process with the lowest threshold(
N N → D − ( ¯ D )Λ c N , √ s thres = 5 . . GeV ) and therefore - as the strange mesonsat SIS energies - charmed hadrons can only be produced initially in the high density zone.Before the promising perspective to use charmed hadrons for a study of the high densityzone can lead to success a lot of work has to be accomplished. The general problem isrevealed in Fig. 5 and Fig. 6 which show the world data on charm production in elementarycollisions, compiled in ref. [10, 11]. On can see directly that at the energies of interest atFAIR ( √ s ≈ GeV ) only
J/ψ production has been measured which is less important at this9 -1 -1 J/ YY / p+N D+Dbar s ( s ) [ nb ] s [GeV] D+Dbar p +N J/ YY / s [GeV] FIG. 5: The cross section for D + ¯ D , J/ Ψ and Ψ ′ meson production in pN (left part) and πN reactions (right part). The solid lines show a parametrisations, whereas the symbols stand for theexperimental data. The J/ Ψ cross sections include the decay from χ c mesons. From ref.[10].FIG. 6: Cross section parameterizations for open charm mesons in comparison to the experimentaldata for pp . The upper solid lines denote the sum over all D/ ¯ D mesons. From ref.[11]. energy because this cannel has an higher threshold than N N → D − ( ¯ D )Λ c N . For the latter,dominant, channel not a single data point is known. Well above threshold many channelscontribute and the few existing data points for N N → D − ( ¯ D ) + X are not of help to singleout this cross section. There is an additional problem, already known from K − physics atSIS. The Λ c will have a considerable charm exchange cross section Λ c + π → D + N which is,however, completely unknown. Due to this process the produced c quarks will be transferredto charmed mesons. Why is this of importance? All charmed hadrons disintegrate before10hey reach the detector and therefore one has to identify them by their decay products.The most promising are energetic electrons and the K − π + channel. The branching ratio fordisintegration into electrons of Λ c (4.5 %) is much smaller than that of the corresponding D − meson (17.2%). Therefore, without knowing the repartition of the c quark between mesonsand baryons the observed electrons cannot be used to determine the charm productionmultiplicity in a heavy ion collision. This is also true, of course, for the K − π + channelwhich is only sensitive to the c-quark entrained in a meson.This lack of knowledge on the production cross sections of charmed hadrons in elementarycollisions is also a very strong limitation for any theoretical prediction for heavy ion collisions.Dynamical simulation programs like UrQMD or HSD [10, 11] need these cross sections asan input quantity. With the present knowledge of these cross sections a reliable predictionfor heavy ion collisions at FAIR energies is impossible. Once these cross sections are known,however, the excitation function of the multiplicity and hopefully also the experimentalmomentum distribution of the charmed hadrons which contain the desired information ofthe system properties at high density and temperature can be analyzed and - there I amquite sure - will reveal very interesting physics. [1] R. Rapp and J. Wambach, Adv. Nucl. Phys. 25 (2000) 1 (hep-ph/9909229)[2] C.L. Korpa and M.F.M. Lutz, Acta Phys. Hung. A22 (2005) 21 nucl-th/0404088.[3] M.F.M. Lutz, nucl-th/0212021, M.F.M. Lutz, E.E. Kolomeitsev Nucl; Phys. A730 (2004)392-416[4] H. Weber et al., Phys.Rev.
C67 (2003) 014904[5] S. A. Bass et al., Prog.Part.Nucl.Phys. (1998) 225[6] S. Vogel et al. arXiv:0710.4463[7] C.M.Hung, E.V.Shuryak Phys.Rev.Lett.
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