The significance of thermal dilepton radiation at intermediate invariant
masses (1GeV<M<3GeV) in ultrarelativistic heavy-ion collisions is investigated.
At CERN-SpS energies, a consistent explanation of the excess observed by NA50
can be given. At RHIC energies the thermal signal is dominated by early
emission indicative for QGP formation. Chemical under-saturation effects and
the competition with open-charm contributions are addressed.Comment: Invited talk at the International Workshop XXVIII on Gross Properties
  of Nuclei and Nuclear Excitations, 'Hadrons in Dense Matter', Hirschegg
  (Austria), Jan. 16-22, 2000; 8 pages LaTeX including 11 eps/ps-figure

Rapp, Ralf

English

arXiv

The significance of thermal dilepton radiation at intermediate invariant masses (1GeV<M<3GeV) in ultrarelativistic heavy-ion collisions is investigated. At CERN-SpS energies, a consistent explanation of the excess observed by NA50 can be given. At RHIC energies the thermal signal is dominated by early emission indicative for QGP formation. Chemical under-saturation effects and the competition with open-charm contributions are addressed.The significance of thermal dilepton radiation at intermediate invariant masses (1GeV<M<3GeV) in ultrarelativistic heavy-ion collisions is investigated. At CERN-SpS energies, a consistent explanation of the excess observed by NA50 can be given. At RHIC energies the thermal signal is dominated by early emission indicative for QGP formation. Chemical under-saturation effects and the competition with open-charm contributions are addressed

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INTERMEDIATE-MASS DILEPTONSAT THE CERN-SPS AND RHICRALF RAPPDepartment of Physics and AstronomySUNY Stony Brook, New York 11794-3800, USAAbstractThe signicance of thermal dilepton radiation at intermediate invariantmasses (1 GeV < M < 3 GeV) in ultrarelativistic heavy-ion collisionsis investigated. At CERN-SpS energies, a consistent explanation of theexcess observed by NA50 can be given. At RHIC energies the thermalsignal is dominated by early emission indicative for QGP formation.Chemical under-saturation eects and the competition with open-charmcontributions are addressed.1 IntroductionDue to their penetrating nature dilepton probes are among the most promisingobservables to access the high temperature/density zones formed in the earlyphases of (ultra-) relativistic heavy-ion collisions (URHIC’s). In the low-massregion (LMR, M  1 GeV) dilepton emission is governed by the light vectormesons , ! and  attaching the main interest to their medium modicationsand possible signatures for the restoration of chiral symmetry in strongly in-teracting matter. In the high-mass region (HMR, M  3 GeV), the focus ison the dissolution of the heavy quarkonium bound states (J=Ψ, ) to detectthe onset of deconnement. In this talk we will address the intermediate-massregion (IMR) between the  and J=Ψ (1 GeV  M  3 GeV). Here, thethermal dilepton production rate is essentially structureless and can be ratherwell approximated by perturbative qq ! l+l− annihilation for both hadronicand quark-gluon phases (as can be inferred from the well-known total crosssection (e+e− ! hadrons) above M ’ 1.5 GeV). With nal-state hadrondecays being concentrated in the LMR, the main competitors with thermalradiation from an interacting reball are primordial processes, most notablyDrell-Yan (DY) annihilation and the simultaneous decays of associatedly pro-duced open-charm (or bottom) mesons, e.g., D ! l−X and D ! l+X. Anexcess over these from proton-proton collision extrapolated sources has longbeen proposed as a suitable signal for the early high-temperature phases inURHIC’s [1]. Since the expected temperatures T  M in the IMR, the ther-mal signal might be suciently sensitive to reflect the initial temperature andlifetime of a possibly formed Quark-Gluon Plasma (QGP).In the following we will investigate these issues in the context of data fromthe CERN-SpS (Sect. 2) and then apply our current understanding to assessupcoming measurements at RHIC (Sect. 3). We nish with some concludingremarks in Sect. 4.2 I-M Dileptons at the SpS2.1 Experimental Results and Previous Theoretical AnalysesAt the CERN-SpS I-M dilepton spectra have been measured by the NA38/50and HELIOS-3 collaborations. Both have found a signicant excess of a factor 2 in central A-A collisions over open-charm and Drell-Yan sources scaled upfrom p-A systems.Fig. 1 shows a comparison of the HELIOS-3 data with transport calcu-lations of Li and Gale [3]: apparently the additional yield from in-mediumhadronic annihilation processes satisfactorily explains the data (left panel);note that the prevailing channels, a1 and !, are of ’4-pion type’ (rightpanel). Within the hadronic transport framework, QGP formation could notbe explicitly addressed. In the context of the NA50 data [4, 5] other possibili-ties for the origin of the additional yield have been elaborated:(i) the NA50 collaboration pointed out that an enhancement of the open-charm contribution by a factor of  3 gives a good account of the datain central Pb(158 AGeV)+Pb. From the theoretical side, however, suchan eect is dicult to justify;(ii) Lin and Wang investigated whether a broadening of transverse-momen-tum distributions due to a (strong) rescattering of charm quarks in mat-ter might enrich the yield within the NA50 acceptance [6]. The resultingincrease amounts to about 20% [5];(iii) Spieles et al. [7] evaluated ’secondary’ Drell-Yan processes (e.g., N !l+l−X) arising in the later stages of the collision and found a 10% en-hancement of the primordial Drell-Yan around M ’ 2 GeV;(iv) thermal radiation from an equilibrated expanding reball [8, 9].In the following, we will pursue the last item in more detail.Figure 1: Left panel: HELIOS-3 dimuon data [2] from central S+W compared to the'standard' background (consisting of Drell-Yan and open charm) and the additionalyield from secondary hadronic annihilation processes evaluated within a transportmodel [3]; right panel: decomposition of the secondary reactions [3].2.2 Drell-Yan Annihilation and NA50 AcceptanceTo enable a comparison of our nal results with NA50 data we need to deter-mine their normalization and acceptance corrections. To this end we use theprimordial Drell-Yan contribution to achieve this. For central A-A collisionsit is given bydNAADYdMdy(b = 0) =34R20A4=3dNNDYdMdy; (1)which we also employ for slightly non-central ones with an accordingly reducedA = Npart=2. Exploiting the fact that the high-mass tail (M  4 GeV) of thedata is entirely saturated by DY-pairs we obtain the overall normalizationwhich will also be applied to the thermal production. We furthermore use thecalculated DY-spectrum to test our approximate acceptance: in addition togeometric cuts [10] on the single-muon tracks imposed by the NA50 spectrom-eter set-up, the muons experience substantial absorption when traversing thehadron absorber. The latter can be roughly represented by a lower energy cut-o which is determined [9] by requiring to reproduce the DY-results of NA50detector simulations, cf. Fig. 2.2.3 Thermal Rates, Space-Time Evolution and SpectraBased on the assumption that an interacting reball formed in heavy-ion colli-sions is in local thermal equilibrium (in the ’comoving’ frame of expansion), theevaluation of the thermal dilepton yield requires two ingredients: productionrates and the time evolution of volume/temperature. In the IMR the formerturns out to be given in a rather model-independent way by the result fromperturbative QCD for the qq annihilation process,d8N thermd4xd4q=244fB(q0; T )Xq=u;d;s(eq)2 + O(s) (2)for both QGP and hadron gas (HG) phases. This is a direct consequenceof the well-known ’duality’ threshold located around 1.5 GeV in the inverseprocess of e+e− ! hadrons annihilation. It is further corroborated by ex-plicit hadronic rate calculations as evidenced from the compilation displayedin Fig. 3 [3]. s-corrections may be as large as 20-30%, whereas higher ordertemperature/density eects are smaller being of order O(T=M), O(q=M).For the space-time evolution of central A-A collisions we employ an ex-panding thermal reball model [11, 12] which is based on an ideal-QGP andresonance-hadron-gas equation of state. Entropy and baryon-number conser-vation x a trajectory in the T -N plane with the ratio s=nB chosen in accordwith experimental information on chemical freezeout at the SpS [13], cf. leftpanel of Fig. 4. Pion- and kaon-number conservation ensure the correct parti-cle abundances at thermal freezeout towards which nite chemical potentials0.0 1.0 2.0 3.0 4.0 5.0 6.0M [GeV]100101102103dNµµ/dM [1/100MeV]NA50sim. (NA50)Ecut=9GeVEcut=12GeVEcut=15GeVDrell−Yan PairsFigure 2: DY-calculations comparedto NA50 simulations (dotted line) anddata [4, 5] in central Pb(158AGeV)+Pb.Figure 3: Compilation [3] of various ap-proaches to assess the thermal dileptonproduction rate in the IMR.0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4µN [GeV]0.000.050.100.150.200.25T [GeV]chem. f.o.RHICSpS−160therm. f.o.SpSAGSSISQGPHG0 5 10 15 20t [fm/c]0.100.150.200.250.30T [GeV]RHIC: s/nB=250SpS:  s/nB=26HGQGPMixFigure 4: Space-time description of central heavy-ion reactions at SpS and RHICenergies within an expanding thermal reball model., K; K build up. A time scale is introduced through a hydro-type volumeexpansion which yields realistic nal flow velocities and transverse sizes [11, 9].A QGP-HG mixed phase is constructed from standard entropy balancing re-sulting in a temperature evolution shown in the right panel of Fig. 4.The thermal dilepton spectra are then computed asdN thermdM=tfoZ0dt VFB(t)ZMd3qq0d8Nd4xd4q(M; q; T )he=Ti4Acc(M; qt; y) (3)including the experimental acceptance as determined above. Note the explicitappearance of the pion-fugacity factor to the 4-th power to appropriately ac-count for o-equilibrium eects in 4-pion-type annihilation processes which0 1 2 3 4 5 6M [GeV]100101102103dNµµ/dM [1/100MeV]NA50charmDrell−YanthermaltotalQGPCentralPb+Pb(158AGeV)0.0 1.0 2.0 3.0 4.0qt [GeV]100101102103dNµµ/dq t  [1/100MeV]NA50charmDrell−YanthermaltotalCentral Pb+Pb(158AGeV)1.5<M<2.5GeVFigure 5: Dimuon invariant-mass (left panel) and transverse-momentum (rightpanel) spectra confronted with NA50 data from central Pb(158 AGeV)+Pb col-lisions. In addition to the calculated thermal and DY contributions the open-charmyield as arising from simulations by NA50 [5] has been included.dominate in the IMR (see right panel of Fig. 1). The nal results of our calcu-lation are displayed in Fig. 5: the experimentally observed excess is reasonablywell reproduced by thermal radiation in both invariant-mass and transverse-momentum projections (very similar conclusions have been reached in ref. [8]).The contribution from the QGP part of the evolution constitutes a rathermoderate fraction of  20%.3 I-M Dileptons at RHICThe same approach as described in the preceding section is now applied to cen-tral Au+Au collisions atps=200 AGeV. For deniteness the charged particlemultiplicity at midrapidity has been xed at hNchi=800 with an entropy perbaryon of s=nB=260. The resulting IMR dilepton spectra are summarized in1.0 1.5 2.0 2.5 3.0 3.5 4.0M [GeV]10−710−610−510−410−310−210−1dN/dM [GeV−1 ]Hadron GasQGP, Ti=360MeVQGP, Ti=280MeVDrell−YanDY+QGP+HGb=1fm|y|<0.35<Nch>=800Au+Au  s1/2=200AGeVFigure 6: Dilepton spectra in central Au+Au at RHIC from equilibrated hadronicand quark-gluon matter as well as DY annihilation.Fig. 6: up to M’ 1.5 GeV the hadron gas radiation dominates; in contrast toSpS conditions, the QGP contribution dominates around 2 GeV before DY an-nihilation takes over. Not shown is the yield from open-charm decays, which infact could completely outshine the spectrum by a factor of 10 or so [14]. If, how-ever, charm quarks undergo appreciable energy loss (dE=dx’−1-2 GeV/fm)when propagating through hot/dense matter they might thermalize entailinga suppression of their contribution above M=1.5 GeV by factors of 100 [15].Another complication at RHIC energies concerns the chemical under-satu-ration of gluon and especially quark densities in the early stages as predictedin various parton-based models [16]: albeit thermalized, the parton distribu-tions are characterized by fugacities i=ni(T )=neqi (T )<1 (i=q,q,g). Naivelyone would expect a substantial reduction of dilepton production in the qqchannel as the rate is proportional to qq. On the other hand, at given en-tropy (or energy) density, an under-saturated QGP has a larger temperaturethan in chemical equilibrium which in turn enhances the thermal emission.Using a parameterization of recent hydrodynamic evolution results [17] (seealso ref. [18]) we have recalculated the plasma contribution starting at thesame initial entropy density as in the equilibrium scenario. The magnitude ofthe pertinent QGP signal in the nal spectrum turns out to be quite similarwith a somewhat harder slope for the o-equilibrium calculation (see left panelof Fig. 7), i.e., the reduction in the fugacities is largely compensated by theincrease in initial temperature.0.0 1.0 2.0 3.0 4.0 5.0τ [fm/c]0.00.20.40.60.81.0n/neqτ0=0.25fm/c, ε0=61GeV/fm−3gluonsanti−/quarks1.0 1.5 2.0 2.5 3.0 3.5 4.0M [GeV]10−710−610−510−410−310−210−1dN/dM [GeV−1 ]Hadron GasQGP, Tieq=360MeVQGP, Tioff=660MeVDrell−YanDY+QGPoff+HGb=1fm|y|<0.35<Nch>=800Au+Au  s1/2=200AGeVFigure 7: Left panel: evolution of parton fugacities in the QGP phase at RHICaccording to ref. [17]; right panel: resulting dilepton spectrum (long-dashed line)compared to equilibrium-QGP (at equal initial entropy density), HG and DY yields.4 Conclusions and OutlookBased on a thermal reball model coupled with ’standard’ dilepton productionrates we have shown that the excess observed in central Pb(158AGeV)+Pb byNA50 in the IMR can be explained by thermal radiation. The contributionfrom early phases indicative for a QGP is moderate; however, our results cor-roborate the present understanding of the conditions probed at the CERN-SpSbeing consistent with low-mass dilepton spectra, chemical freezeout analyses,etc., indicating that one is indeed producing QCD matter in the vicinity of theexpected HG-QGP phase boundary.The extrapolation of this approach to RHIC suggests that the plasmaradiation exceeds HG- and DY-sources around M ’ 2 GeV. Chemical o-equilibrium eects do not seem to alter this conclusion as long as comparableinitial energy densities are reached. A big question mark is attached to theopen-charm contribution, i.e., whether energy loss eects signicantly redis-tribute the associated dilepton yields. Experimental input on these issues iseagerly awaited.AcknowledgmentI thank E. Shuryak and B. Ka¨mpfer for productive discussion. This work issupported in part by the A.-v.-Humboldt foundation (Feodor-Lynen program)and the US-DOE under grant no. DE-FG02-88ER40388.References[1] E.V. Shuryak, Phys. Rep. 61 (1980) 71.[2] N. Masera et al. (HELIOS-3 collaboration), Nucl. Phys. A590 (1995) 93c.[3] G.Q. Li and C. Gale, Phys. Rev. C58 (1998) 2914.[4] E. Scomparin et al. (NA50 collaboration), J. Phys. G25 (1999) 235.[5] P. Bordalo et al. (NA50 collaboration), Nucl. Phys. A661 (1999) 538.[6] Z. Lin and X.-N. Wang, Phys. Lett. B444 (1998) 245.[7] C. Spieles et al., Eur. Phys. J. C5 (1998) 349.[8] K. Gallmeister, B. Ka¨mpfer and O.P. Pavlenko, hep-ph/9908269; see alsothese proceedings.[9] R. Rapp and E. Shuryak, hep-ph/9909348.[10] E. Scomparin, private communication (1999).[11] R. Rapp and J. Wambach, Eur. Phys. J. A6 (1999) 415.[12] R. Rapp and J. Wambach, hep-ph/9909229, to appear in Adv. Nucl. Phys..[13] P. Braun-Munzinger and J. Stachel, Nucl. Phys. A638 (1998) 3c.[14] S. Gavin, P.L. McGaughey, P.V. Ruuskanen and R. Vogt, Phys. Rev. C54(1996) 2606.[15] E. Shuryak, Phys. Rev. C55 (1997) 961.[16] B. Mu¨ller, M.G. Mustafa and D.K. Srivastava, Heavy Ion Phys. 5 (1997)387; K.J. Eskola and K. Kajantie, Z. Phys. C75 (1997) 515.[17] D.M. Elliott and D.H. Rischke, nucl-th/9908004.[18] B. Ka¨mpfer, O.P. Pavlenko, A. Peshier and G. So, Phys. Rev. C52(1995) 2704.

Intermediate-Mass Dileptons at the CERN-SpS and RHIC

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