Transport and hydrodynamical models used to describe the expansion stage of a
heavy-ion collision at the CERN SPS give different dilepton spectrum even if
they are tuned to reproduce the observed hadron spectra. To understand the
origin of this difference we compare the dilepton emission from transport and
hydrodynamical models using similar initial states in both models. We find that
the requirement of pion number conservation in a hydrodynamical model does not
change the dilepton emission. Also the mass distribution from the transport
model indicates faster cooling and longer lifetime of the fireball.Comment: 5 pages, 2 Postscript figures, contribution to the `International
  Workshop XXVIII on Gross Properties of Nuclei and Nuclear Excitations',
  Hirschegg, Austria, January 16-22 200

Huovinen, P.

Koch, V.

English

arXiv

eScholarship - University of California

Dileptons from transport and hydrodynamical models

Transport and hydrodynamical models used to describe the expansion stage of a heavy-ion collision at the CERN SPS give different dilepton spectrum even if they are tuned to reproduce the observed hadron spectra. To understand the origin of this difference we compare the dilepton emission from transport and hydrodynamical models using similar initial states in both models. We find that the requirement of pion number conservation in a hydrodynamical model does not change the dilepton emission. Also the mass distribution from the transport model indicates faster cooling and longer lifetime of the fireball

UNT Digital Library

arXiv:nucl-th/0002040 v1   15 Feb 2000LBNL-45192DILEPTONS FROM TRANSPORT ANDHYDRODYNAMICAL MODELSP. HUOVINEN and V. KOCHLawrence Berkeley National Laboratory (LBNL)1 Cyclotron Road, Berkeley CA 94720, USAAbstractTransport and hydrodynamical models used to describe the expansionstage of a heavy-ion collision at the CERN SPS give different dileptonspectrum even if they are tuned to reproduce the observed hadron spec-tra. To understand the origin of this difference we compare the dileptonemission from transport and hydrodynamical models using similar ini-tial states in both models. We find that the requirement of pion numberconservation in a hydrodynamical model does not change the dileptonemission. Also the mass distribution from the transport model indicatesfaster cooling and longer lifetime of the fireball.1 IntroductionElectromagnetic signals from relativistic heavy-ion collision directly probe theproperties of the dense matter created during the collision since their interac-tions with the surrounding matter are negligible. However, the observed leptonpairs and photons do not originate only at one temperature and density, butthe distribution is a complicated integral over the entire space-time history ofthe system. Therefore, to draw any conclusions of the observed yield, one hasto understand the evolution of the system and how it affects dilepton emission.The evolution of the system is a complicated many-body problem whichcan not be solved from basic principles but has to be described using phe-nomenological models instead. Various models based on hydrodynamics andtransport theory have been successfully used to describe the hadron data mea-sured in A+A collisions at the CERN SPS energies. However, when they areused to describe dilepton emission in the same collisions, the dilepton yieldsaround invariant mass 500 MeV differ roughly by a factor two [1, 2]. At thismass region the CERES collaboration at CERN has measured a significantexcess of dileptons over the estimated background [3]. It has been suggestedthat this enhancement might be an in medium effect or possibly a precursor ofchiral symmetry restoration [4], but before drawing any such conclusions onehas to understand why different expansion dynamics can lead to equally largeenhancements.To investigate the effect of expansion dynamics to dilepton production wehave compared the dilepton yields from three different models – transport,hydrodynamical model with zero pion chemical potential and hydrodynamicalmodel with conserved pion number.2 The modelsTo simplify the study of expansion dynamics we have kept the particle contentof the system as simple as possible. The only particles included are pions andrho mesons and the only production channel for electron pairs is ππ annihila-tion. No in-medium modifications of particle properties have been taken intoaccount, but all cross sections, widths etc. are those of free particles.The transport model we use is the relativistic BUU transport model de-scribed in ref. [5] and the hydrodynamical model the 2+1 dimensional non-boost invariant model described in ref. [6]. One of the important differencesbetween these models is that pion number is conserved in the transport modelbut not in the hydrodynamic model. The pion number conservation leads tonon-zero pion chemical potential which is one of the possible causes of the dif-ference in the dilepton yields [7]. To study the effect of non-zero pion chemicalpotential in the framework of a hydrodynamical expansion we made a newversion of the hydrodynamic model where the conserved baryon number isreplaced by a conserved pion number1.As mentioned the only dilepton production channel we consider is ππ an-nihilation. The cross section for this process used in the transport descriptionis given in ref. [5] whereas the thermal production rate used in the hydrody-namical description is the one calculated by Gale and Kapusta [8].We have checked the consistency of our calculations by imposing periodicboundary conditions to our models, initializing the systems in thermal andchemical equilibrium and checking that the equilibrium is maintained. In this1We define the conserved pion number as Nπ = nπ +2nρ, where nπ and nρ are the actualnumber densities of pions and rho-mesons respectively.case the dilepton emission from all three models is identical and correspondsto the thermal rate at this temperature.In the simulations of the actual heavy-ion collisions, the initial state of theevolution is chosen to reproduce the observed hadron spectra [1, 5]. However, inthe present calculations we use the same initial state for all models: a sphericalfireball with a radius of r = 8 fm in thermal and chemical equilibrium withno initial flow. The density profile is assumed to be Woods-Saxon with themaximum energy density of ǫ = 0.5 GeV/fm3 which corresponds to a maximuminitial temperature of T = 218 MeV, pion number density nπ = 0.38 fm−3and rho number density nρ = 0.20 fm−3. Initially the system contains 560pions and 260 rhos. The edge of the system is defined by the radius wheretemperature drops below the decoupling temperature of the hydrodynamicmodel. This temperature is set to be Tdec = 120 MeV in both versions of thehydrodynamic model whereas there is no need for a decoupling temperaturein the transport model. In the pion number conserving hydro decoupling atTdec = 120 MeV leads to an average pion chemical potential on the decouplingsurface of 〈µπ〉 = 75 MeV.3 ResultsSince the simulations of the actual heavy-ion collisions are tuned to reproducethe observed hadron spectra, we calculate the pion spectra as well. The re-sulting pt spectra of pions is shown in fig. 1. In the hydrodynamic model withzero chemical potential the pion number is not conserved and the number offinal pions is smaller than in the other two models. Another difference is thatthe effective equation of state of the transport model is softer than in the hy-drodynamic model. This is manifested in the slope of the pt spectrum which issteeper for transport calculation than for hydrodynamic calculation with zerochemical potential.The pion number conserving hydro gives almost similar pt slope comparedto transport. The steeper slope than in zero chemical potential hydro is easilyunderstood. When the system dilutes and pion number is conserved, a largerfraction of energy is stored in the mass of pions than in the case of zero chemicalpotential. This leads to faster decrease of temperature and the decouplingtemperature is reached at an earlier stage of evolution when the flow is lessdeveloped.Fig. 2 depicts the distribution of lepton pairs originating from ππ anni-hilations during the system evolution. The most striking feature is that thedifference between the two hydrodynamical models is tiny. The effect of in-Figure 1: The pt spectra of pions fromtransport and hydrodynamical mod-els.Figure 2: The mass distribution oflepton pairs from ππ annihilation intransport and hydrodynamical mod-els.creasing chemical potential and thus larger pion density is counterbalanced bythe shorter lifetime and faster cooling of the system leading to practically indis-tinguishable dilepton yields. However, the pion spectra from these two modelsare different. If the models are required to produce similar pion spectra, theinitial state of the model with zero chemical potential should be larger andhave lower initial temperature than the pion number conserving model. Thisdifference in the initial state would also lead to different dilepton production.Since the transport model and the hydrodynamic model lead to similarpion spectra their dilepton yields can be compared without reservations. Thedifference between these models is similar to that seen in the attempts toreproduce the CERES data. This supports our hypothesis that details ofexpansion dynamics do have a significant effect on the dilepton production.The shapes of the distributions look like the system in transport descriptioncools faster but lives longer than in hydro. Whether this is the case remainsto be investigated in more detail.We have demonstrated that the effect of the expansion dynamics on dilep-ton production is visible and that the non-zero pion chemical potential is notthe main cause of this effect. At the present stage of the work there are stillmany open questions like the temperature evolution in the transport descrip-tion and when and where the dileptons are emitted. It also has to be checkedhow the distributions change if all the models are required to produce similarpion spectra.AcknowledgementsThis work was supported by the Director, Office of Science, Office of HighEnergy and Nuclear Physics, Division of Nuclear Physics, and by the Office ofBasic Energy Sciences, Division of Nuclear Sciences, of the U.S. Departmentof Energy under Contract No. DE-AC03-76SF00098.References[1] P. Huovinen and M. Prakash, Phys. Lett. 450 (1999) 15.[2] V. Koch, nucl-th/9903008, Proceedings of 37th International WinterMeeting on Nuclear Physics, Bormio (Italy), Jan 1999;W. Cassing, E.L. Bratkovskaya, R. Rapp and J. Wambach,Phys. Rev. C57 (1998) 916.[3] B. Lenkeit, nucl-ex/9910015, Proceedings of the QM’99 conference, Turin(Italy), May 1999.[4] R. Rapp and J. Wambach, Eur. Phys. J. A6 (1999) 415.[5] V. Koch and C. Song, Phys. Rev. C54 (1996) 1903.[6] J. Sollfrank, P. Huovinen, M. Kataja, P. V. Ruuskanen, M. Prakash andR. Venugopalan, Phys. Rev. C55 (1997) 392.[7] R. Rapp, hep-ph/9907342, Proceedings of the QM’99 conference, Turin(Italy), May 1999.[8] C. Gale and J. Kapusta, Phys. Rev. C35 (1987) 2107.

https://escholarship.org/uc/item/7q2716h3

Dileptons from transport and hydrodynamical models

Abstract

Similar works

Full text

Available Versions

eScholarship - University of California

UNT Digital Library