Di-electron production from vector mesons with medium modifications in heavy ion collisions
Hao-jie Xu, Hong-fang Chen, Xin Dong, Qun Wang, Yi-fei Zhang
aa r X i v : . [ nu c l - t h ] J a n Di-electron production from vector mesons with medium modifications in heavy ioncollisions
Hao-jie Xu, Hong-fang Chen, Xin Dong, Qun Wang, and Yi-fei Zhang Department of Modern Physics, University of Science and Technology of China, Anhui 230026, People’s Republic of China Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
We reproduce the di-electron spectra in the low and intermediate mass regions in most centralAu+Au collisions by the STAR Collaboration incorporation of the STAR detector acceptance. Wealso compare our results with PHENIX data constrained by the PHENIX acceptance. We includethe medium modifications of vector mesons from scatterings of vector mesons by mesons and baryonsin the thermal medium. The freezeout contributions from vector mesons are also taken into account.The space-time evolution is described by a 2+1 dimensional ideal hydrodynamic model. The back-grounds from semi-leptonic decays of charm hadrons are simulated by the PYTHIA event generatorand corrected by the nuclear modification factor of electrons from charm decays. It is difficultto extract the thermal contributions from those from charm decays in the invariant mass spectraalone and in the current detector acceptances. Other observables such as transverse momenta andcollective flows may provide additional tools to tag these sources.
I. INTRODUCTION
The electromagnetic probes such as photons and dilep-tons are expected to provide clean signatures for thequark gluon plasma (QGP) in heavy ion collisions due totheir instant emissions once produced [1–7]. These ther-mal photons and dileptons contain undistorted informa-tion about the space-time trace of the new state of matterformed in such collisions. The invariant mass spectrumis usually divided into the low, intermediate and highmass regions (LMR, IMR and HMR), based on the no-tion that each region is dominated by different sources ofdileptons. In the LMR, M . M & GeV,dileptons are dominated by the Drell-Yan process andquarkonium decays. In the IMR, . M . GeV, itwas argued that dileptons from semi-leptonic decays ofcorrelated open charm hadrons are dominant [14].The medium modifications of the ρ meson spectralfunctions are successful in describing the di-muon en-hancement in the LMR of the NA60 experiment at theSPS energy [11, 12, 15]. The PHENIX and STAR col-laborations also observed such an enhancement in the di-electron spectra at the RHIC energy [16, 17]. The ther-mal quark-antiquark annihilation in the QGP phase is ex-pected to give a measurable signal in the IMR for the de-confinement phase transition at RHIC energy [18]. How-ever, in this mass region, the di-lepton yield from semi-leptonic decays of open charm mesons increases rapidlywith the collisional energy. The single leptons from opencharm mesons and their dynamic correlations are ex-pected to undergo medium modifications. The questionis: to what extent the di-leptons from charm hadronswith medium modifications mix up with the thermal con-tributions from the QGP in the IMR. Another issue isthat the dilepton spectra measured by the STAR andPHENIX collaborations are very different in the LMR.It is worthwhile to to look at this disagreement closely by using the Monte Carlo simulation incorporating thedifferent acceptances of STAR and PHENIX detectors.In this paper, we try to reproduce the data of di-electron invariant mass spectra in the LMR and IMR incentral Au+Au collisions at 200 GeV. We will include themedium modifications of the vector mesons and charmhadrons. The acceptances of STAR and PHENIX de-tectors are incorporated in our calculation. We will usea 2+1 dimension ideal hydrodynamic model to give thespace-time evolution of the fireball, where the parametersare determined by fitting the data of transverse momentaof long life hadrons (pions, Kaons and protons). Thespectra of charm hadrons ( D , D ± , D s and Λ c ) are givenby a simulation of the PYTHIA event generator. We ne-glect the Dalitz decay channel for π : π → e + e − γ butinclude those for η and ω : η → e + e − γ and ω → e + e − π .The contribution from pion’s Dalitz decay is mainly be-low m π and irrelevant to our current range of the invari-ant mass. II. PARAMETERS IN HYDRODYNAMICMODEL
We use a 2+1 dimensional ideal hydrodynamic model[18] to give the space-time evolution of the medium cre-ated in heavy ion collisions. We choose two types of theEquation of state (EOS) [19–22], S95P-CE (CE) withcomplete chemical equilibrium to very low temperaturesand a wide range of phase transition temperatures from184MeV to 220MeV, and S95P-PCE (PCE) with partialchemical equilibrium below chemical freezeout temper-ature T chem = 165 MeV [43]. After kinetic freeze-out,we use the Cooper-Frye formula [23, 24] to obtain themomentum spectra for each hadron species
E dN i d p = dN i dyp T dp T dφ = g i (2 π ) ˆ T f d Σ µ p µ n i ( x, u · p ) , (1) set EoS T chem [MeV] T f [MeV] e f [GeV / fm ] S1 S95P-CE - 136 0.12S2 S95P-PCE 165 136 0.275S3 S95P-PCE 165 106 0.12Table I: Parameter sets. We choose most central collisionswith b = 2 . fm. The initial conditions are chosen to be: τ = 0 . fm , e = 45 GeV/ fm ( T =395 MeV). where Σ µ denotes the normal vector of the freezeout hy-persurface, T f is the kinetic freeze-out temperature onthe freezeout hypersurface, n i is the phase space distri-bution function for the baryon/meson species i which canbe Fermi-Dirac/Bose-Einstein distribution and g i is itsdegeneracy factor, and p T denotes the transverse mo-mentum.Beside the EOS, there are some free parameters whichshould be fixed in the hydrodynamical model, such asequilibration time τ , the initial energy density e (orinitial temperature T ) and the kinetic freeze-out energydensity e f (or T f ). At the RHIC energy √ s NN = 200 GeV for Au+Au collisions [25, 26], we constrain theseparameters with STAR and PHENIX data for the rapid-ity densities of multiplicities, dN i /dy , and the p T spec-tra for long-life hadrons (pions, koans and protons). Thedistribution of the initial energy density is determined bythe Glauber model with 5% of the contribution from bi-nary collisions. We focus on most central collisions withimpact parameter b = 2 . fm throughout the paper andassume a system with vanishing net baryon number.To make a comparison, we choose the same initial con-ditions for two EOS ( τ = 0 . fm , e = 45 GeV/ fm (or T =395 MeV)), but freeze-out conditions are differ-ent due to different relations between the energy densityand temperature. The same initial conditions imply thatthe entropy densities are chosen to be the same for thesetwo EOS. We choose T f = 136 MeV ( e f = 0 . GeV/ fm )for CE and roughly reproduce the p T spectra for the pi-ons and kaons, as shown in Fig. (1(a)). But the protonyield is under-estimated. For PCE, we choose the kineticfreeze-out occurs at either the same energy density or thesame temperature as CE, i.e. ( e f , T f ) = ( .
12 GeV / fm ,106 MeV) or ( .
275 GeV / fm , 136 MeV). The p T spectrawith PCE are shown in Fig. (1(b)). The parameter setsare listed in Tab. (I).The PCE scenario has a feature compared to the CEone [19]: dN i /dy and p T spectra in the low p T range( p T < GeV) are almost independent of T f . However,the high T f will reduce the dilepton production rate byshortening the evolution time. So we can regard T f asa tuning parameter to the dilepton production rate fromthe in-medium vector meson decay.We give a few comments about the yields of vectormesons, whose multiplicity ratios, ρ/π , ω/π and φ/π , aregiven in Tab. (II). Most of the decays of the ω and φ mesons take place after the kinetic freeze-out. The yieldsof ω and φ are in good agreement with the data and will (GeV) T p0 0.5 1 1.5 2 2.5 ) - ( G e V T dp T ) d y p π d N / ( -3 -2 -1 (a)S95P-CE b = 2.4fm Centrality 0-5% b=2.4fm + π PHENIX /5 + PHENIX KPHENIX p/25 (GeV) T p0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ) - ( G e V T dp T ) d y p π d N / ( -3 -2 -1 (b)S95P-PCE b = 2.4fm Centrality 0-5% b=2.4fm + π PHENIX /5 + PHENIX KPHENIX p/25
Figure 1: (Color online) Transverse momentum spectra for π + (black-dashed), K + (red-dash-dot-dot-dotted) and p (green-dotted) for central collisions with centrality 0-5%. The dataare from the PHENIX collaboration [26]. (a) S95P-CE and(b) S95P-PCE EOS are used. In (b), the differences between T f = 106 MeV (thick lines) and T f =
136 MeV (thin lines) inthe low p T range are small. contribute to the dilepton rate. We see that the ratio ρ/π at the freeze-out is smaller than the data, but we notethat most of the ρ mesons decay in the thermal mediumearlier than the kinetic freeze-out whose contribution tothe dilepton production dominates the dilepton spectra.Hereafter we will use the parameter set S3 of PCE as adefault choice unless stated explictly. The comparisonwill be made with other parameter sets. III. DILEPTON EMISSIONS IN HEAVY IONCOLLISIONS
In the thermalized medium, hadron gas (HG) or quarkgluon plasma (QGP), the dilepton production rate per sets π + p ρ/π ω/π φ/π S1 . . . × − . × − . × − S2 . . . × − . × − . × − S3 . . . × − . × − . × − PHENIX . . . × − . × − . × − STAR
327 34 . . × − - . × − Table II: Rapidity densities dN i /dy for meson/proton yieldsin most central collisions with b = 2 . fm. The PHENIX dataare taken from Ref. [16, 26], where they only have the π + data in most central collisions and their ρ data are from thefragmentation model. The STAR data are from Ref. [27, 28]. unit volume is given by dN ll d xd p = − α π M n B ( p · u ) (cid:18) m l M (cid:19) × r − m l M ImΠ R ( p, T ) . (2)Here m l is the lepton mass, α = e / π is the finestructure constant with the electric charge e for lep-tons, p = ( p , p ) = p + p is the dilepton 4-momentumand M = p p , n B = 1 / (cid:0) e p · u/T − (cid:1) ( T and u arethe local temperature and fluid velocity respectively)is the Bose distribution function, Π Rµν is the retardedphoton polarization tensor from the quark or hadronicloop, and Π R = Π Rµµ . For the partonic phase, Π R given by the Born term reflects the lowest order process q ¯ q → γ ∗ → l + l − . For the hadronic phase, Π R is furtherrelated to the retarded vector-meson propagator D RV with V = ρ, ω, φ via ImΠ R = − (cid:0) e m V /g V (cid:1) Im D RV , where g V is the photon-vector-meson coupling constant in the vec-tor meson dominance model, and m V is the vector-mesonmass. The retarded vector meson propagator is Im D RV = ImΠ RV (cid:0) p − m V + ReΠ RV (cid:1) + (cid:0) ImΠ RV (cid:1) , (3)where Π R is the contraction of the retarded vector mesonpolarization tensor.We use the hadronic many body effective theory [29]to calculate in-medium ρ spectral functions by scatter-ing with surrounding mesons. Though we assume a netbaryon free system at RHIC energy, the effective chemi-cal potentials in the PCE scenario will give a considerablenumber of baryons [30], and we assume that there areequal number of anti-baryons which give the same con-tribution as the baryons to the ρ spectral functions. Toinclude the baryonic (including anti-baryonic) contribu-tions, we use the empirical scattering amplitude method[31] which agrees with the hadronic many body effectivetheory [32]. Here we only consider the coupling of the ρ meson with baryonic resonances in the medium and setthe momentum q = 300 MeV for the ρ meson in-mediumpropagator. The in-medium ρ meson spectral functionswith and without baryonic contributions are shown in ) M (GeV/c0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 ) - ( G e V ρ I m D T (MeV)vac120150180
Figure 2: The imaginary parts of the in-medium ρ mesonpropagators (or in-medium spectral functions) with (thicklines) and without (thin lines) baryonic contributions. Thechemical potentials in PCE EOS are used. Fig. (2) at different temperatures but at a fixed mo-mentum q = 300 MeV. The differences between with andwithout baryonic contributions are larger at low temper-atures than at high temperatures.Since the collision rate in a meson gas around the tran-sition temperature indicates a large broadening of φ me-son spectra due to binary collisions [33], we include thiseffect via a schematic estimate as follows (with T = 150 MeV), Γ φ coll ≃ (22 MeV) (cid:18) TT (cid:19) . (4)In Fig. (3(a)) we show the invariant mass spectra ofthermal di-electrons at the RHIC energy 200 GeV formost central Au+Au collisions. Beside the ρ compo-nent (red-dotted line) in the hadronic phase in an earlystudy [18], we include the in-medium ω (magenta-short-dashed line) and φ (light-brown-dash-dotted line) contri-butions to thermal di-electrons. The thermal di-electronsare dominated by the in-medium ρ mesons, while the ω contribution is submerged under the broadened ρ spec-tra. The thermal spectra with the CE EOS (green-dash-dotted-dotted line) has also been shown. The productionrate in the PCE scenario is larger in the invariant massrange below free ρ mass than in the CE one, though thetemperatures with PCE are lower. This is because thechemical potentials in the PCE scenario lead to a largerbroadening of the ρ spectral function and an enhance-ment factor e µ π /T compared with the CE scenario. Theenhancement at low masses in the PCE scenario is moreobvious at lower T f . We will come back to this issuelater. These two EOS have the same partonic contribu-tions because their differences only occur in the hadronicphase.The dilepton emission rate from the freezeout vector ) M (GeV/c0 0.2 0.4 0.6 0.8 1 1.2 ) - d N / d M d y ( G e V -4 -3 -2 -1 S95P-PCE b = 2.4fm (a)
PartonicHadronicS95P-CETotal ) M (GeV/c0 0.2 0.4 0.6 0.8 1 1.2 ) - d N / d M d y ( G e V -5 -4 -3 -2 -1 S95P-PCE b = 2.4fm (b) - e + e →ρ - e + e →ω - e + e →φ S95P-CETotal
Figure 3: (Color online) (a) The invariant mass spectra ofthermal di-electrons in full phase space. In the partonicphase, the main source is q ¯ q → γ ∗ → e + e − (magenta-long-dashed line). In the hadronic phase, the total contribution isthe blue-dashed line, where the contribution from the ρ me-son (red-dotted line) dominates, and those from the ω and φ mesons are shown in magenta-short-dashed and brown-dash-dotted lines respectively. (b) The invariant mass spectra ofdi-electrons for vector mesons ρ , ω and φ at the freezeout. meson is given by dN fol ¯ l d p = α (cid:18) eg (cid:19) m V Γ V dN foV d p . (5)where Γ V is the total decay width of the vector mesons.The vector meson momentum spectra at thermal freeze-out can be expressed by the extended Cooper-Frye for-mula [5] dN foV d p = g ρs π ˆ T f d Σ µ p µ Im D V n B ( p · u ) . (6)Since the lifetimes of ω and φ are much longer than thetime scale of the freezeout process, we treat these con-tributions as in vacuum and neglect the medium effect.The imaginary parts of the ω and φ propagators can begiven by the Breit-Wigner formula, Im D foω,φ = − m V Γ V ( M − m V ) + m V Γ V . (7) ) M (GeV/c0 0.2 0.4 0.6 0.8 1 1.2 1.4 ) - d N / d M d y ( G e V -5 -4 -3 -2 -1 S95P-PCE b = 2.4fm
PartonicIn-MediumFreezeOutS95P-CETotal
Figure 4: (Color online) The cocktail mixture of the partonic,in-medium and freezeout hadronic sources for di-electrons.The partonic, in-medium and freezeout hadronic contribu-tions are in magenta-long-dashed, red-dotted, and blue-dash-dotted lines, respectively. The total contribution is in theblack-solid line.
But most of the ρ mesons decay in the medium due toits short lifetime, so we include the medium effect in the ρ meson propagator. In Fig.(3(b)) are shown the invari-ant mass spectra of di-electrons from the freezeout vectormesons, where the sharp peaks of the ω and φ mesonscan be seen compared to a much broader bump of the ρ meson.In Fig. (4) we sum over all sources we have considered.The full mass spectra have two sharp peaks of the ω and φ mesons at the freezeout same as in vacuum due totheir long lifetime. For comparison the in-medium spec-tra are also shown where only a much lower peak fromthe φ meson is visible, indicating clear medium effects.Subtracting these sharp peaks of ω and φ , the broad-ened spectrum of the in-medium ρ meson can be seen.The partonic contribution dominates over the hadronicone when M > . GeV/ c . These continuum-like IMRdileptons may provide a direct probe to the deconfine-ment phase transition in high energy heavy ion collisions.The different EOS give the similar structure but slightlydifferent magnitude. It seems that the low mass enhance-ment favors the PCE scenario, we will come back to thispoint with details later in the following section. IV. COMPARISON WITH DATA
Different from the SPS energy, the charm quarks havea considerable production rate at the RHIC energy. Sothere is a large background from semi-leptonic decays ofthe charm hadrons. In this section we will estimate thisbackground and compare our dilepton results with thedata.We use the event generator PYTHIA [34] (version6.416 with CTEQ5L PDF) to simulate the background ) M (GeV/c0 0.5 1 1.5 2 2.5 3 3.5 4 / G e V ) I N P H E N I X ACC EP T ANC E ( c ee ) d N / d m ev t ( / N -10 -9 -8 -7 -6 -5 > 0.2 GeV/c eT p|y| < 0.35 (a) PHENIX DATAPHENIX PYTHIA(PYTHIA) - e + e → cc (GeV) T p0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 e AA R -1
101 (b)
Fitting FunctionPHENIX 0-10%
Figure 5: (Color online) The semi-leptonic decays of charmhadrons. (a) The re-scaled di-electron cross section fromcharm hadrons of semi-leptonic decays in p+p collisions byPYTHIA. The data are taken from the PHENIX collabora-tion [14]. (b) The nuclear modification factor for nonphotonicelectrons in central Au+Au collisions from the PHENIX col-laboration [36]. The fitting function is given in Eq.(8). from semi-leptonic decays of the charm hadrons ( D , D ± , D s and Λ c ). The PHENIX collaboration also tuned theparameters of PYTHIA [35] to fit the charm hadron dataat SPS and FNAL and single electron data at ISR. Theparameter dependences such as intrinsic k T and the par-ton distribution functions are also addressed in Ref. [14].In our paper, we do not consider the fluctuations fromthese parameter.In p+p collisions, the dilepton yield in the mass range[1.1,2.5] GeV/ c is dominated by semi-leptonic decays ofcharm hadrons. In the PHENIX acceptance the inte-grated yield of di-electrons per event from heavy-flavordecays in that range is (4 . ± . ± . × − [14].With the branch ratio for charm quarks to electrons [37]and the correction for the geometrical acceptance, therapidity density of c ¯ c pairs can be estimated [14]. Weuse the PYTHIA event generator with the PHENIX ac-ceptance to reproduce the spectra from charm hadroncontribution, see Fig. (5(a)). It can be seen that ourresults from PYTHIA (black-dashed line) are consistent with those given by PHENIX (red-dotted line). We ob-tain the cross section of c ¯ c pairs σ c ¯ c = 0 . mb.For Au+Au collisions, we use the renormalized crosssection in pp collisions and scale it by the mean number ofbinary collisions. We choose N coll = 950 for most centralcollisions. The charm quarks are mostly generated inthe pre-equilibrium stage. In medium the p T spectra ofthe charm quarks as well as the angular correlation ofthe c ¯ c pairs could be modified due to its interaction withthe thermalized partrons. The medium modifications ofheavy flavors have been widely studied in, e.g., Ref. [38,39]. To include the medium modifications in a simpleway, we parametrize the nuclear modification factor ofthe single electron in the form, R eAA ( p T ) = min [1 . , exp ( a/p T + b )] , (8)where a = 1 . and b = − . , see Fig. (5(b)) for thefitting function and experimental data. Note that wehave neglected the Υ contribution here. To get a realis-tic p T distribution for electrons, we use the original p T spectra obtained by PYTHIA and multiply them with R eAA ( p T ) . Using the Monte Carlo method, we samplethe momentum spectra in accordance with the result-ing p T spectra for electrons and positrons respectively.In each event we randomly choose from the sample themomenta of one electron and one positron and combinethem to a di-electron pair, from which the invariant massand total transverse momentum of the pair can be deter-mined. The modified invariant mass spectra by R eAA ( p T ) are found to be narrower than without such a modifica-tion as shown in Fig. (6(a)).With the STAR acceptance (transverse momentum p T > . GeV/c and pseudorapidity | η e | < for an indi-vidual electron, rapidity | y ee | < for a pair of electrons)and p T resolution, we compute the di-electron spectra inmost central collisions and compare them with the STARpreliminary data of 0-10% centrality, see Fig. (6(a)). Wealso included the Dalitz decay channels for η [40] and ω : η → e + e − γ and ω → e + e − π . The η contribution can beeasily deducted as a background in the experiment dueto its very long lifetime (about . × fm/c), whichleads to its decay outside the freezeout scope.The cooktail sum including the in-medium ρ mesonscan roughly reproduce the di-electron spectra in theLMR, see Fig. (6(a)). In Fig. (6(b)), we show the totaldi-electron spectra (thick lines), the contributions fromthe open charm (green-dashed line) and the in-medium ρ (thin lines) in the range M ∈ [0 , . GeV/ c . We foundthat the ρ meson contributions (thin black-solid line) aresubmerged under the open charm one. This indicatesthat the charm backgrounds play an important role in thedilepton spectra at the RHIC energy. As we discussed inSect. (II) we can tune T f to a lower value (e.g. 90 MeVin red-dashed line) to increase the contribution from thein-medium ρ mesons. The cocktail sum (thick red-dashedline) with the in-medium ρ contribution (thin red-dashedline) for T f = 90 MeV is also shown. This seems to givea better fit to the data. Though the lower T f gives larger ) M (GeV/c0.5 1 1.5 2 2.5 3 )( S T A R A CC EP T . ) - d N / d M d y ( G e V -4 -3 -2 -1 S95P-PCE b = 2.4 fm (a)
PartonicFreezeOutIn-MediumCharm ) AA Charm(w/o R ω , η Dalitz STAR Preliminary 0-10%Total ) M (GeV/c0.2 0.4 0.6 0.8 1 1.2 )( S T A R A CC EP T . ) - d N / d M d y ( G e V -4 -3 -2 -1 S95P-PCE b = 2.4 fm (b) = 106 MeV f T = 90 MeV f T cutoff T w/o pCharm ) AA Charm(w/o R ) M (GeV/c1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 )( S T A R A CC EP T . ) - d N / d M d y ( G e V -4 -3 S95P-PCE b = 2.4 fm (c) = 0.4 fm τ = 0.1 fm τ Charm ) AA Charm(w/o R
Figure 6: (Color online) The invariant mass spectra and thecomparison with STAR preliminary data [17] in most cen-tral (0-10%) Au+Au collisions with the STAR acceptance.The cocktail sums are in thick lines. See the text for de-tailed illustrations. (a) The results in M = [0 . , GeV. (b)The results in M = [0 . , . GeV. The thin-balck/thin-red-long-dashed line denotes the contribution from the in-medium ρ decays for T f = ρ decays without the p T cutoff for T f =
90 MeV. (c) The resultsin M = [1 . , GeV. The thin-balck/thin-red-long-dashed linedenotes the QGP contribution for τ = broadenings of the ρ spectra and low mass enhancements,the ρ meson contribution is still smaller than the opencharm one. This is because: (1) The nuclear modificationfactor enhances the charm contribution in the LMR; (2)Most of the low mass di-electrons from the in-medium ρ mesons have low p T , which are beyond the capabilityof the detectors and can not be measured. To supportthe point (2), we calculate the in-medium ρ meson con-tribution incorporated by the STAR acceptance exceptthe p T cutoff for electrons and positrons. The result isshown in the thin red-dashed-dotted-dotted line in Fig.(6(b)). We can see a strong enhancement below the free ρ mass.With the nuclear modification factor for charmhadrons, we can roughly reproduce the di-electron spec-tra in the IMR, see Fig. (6(c)). One can see that thethermal contributions from the QGP phase (thin black-solid and red-dashed lines) are much smaller than thecorrelated charm decays (blue-dashed and green-dashed-dotted-dotted lines). Now we try to look at if it is pos-sible to increase the QGP thermal contributions in theIMR by the tuning parameters. We know that the ther-mal rate from the QGP is proportional to T Aτ where A is the transverse area [18]. To this end, in our model,we can tune the equilibration time and entropy density(initial energy density) with the constraint s τ = con-stant to keep the multiplicity rapidity density unchanged.The dilepton emission rates do not change much for dif-ferent τ . But for an earlier equilibration time, e.g. τ = 0 . fm (thin red-dashed line), the partonic con-tribution is enhanced in the IMR, since the early equili-bration time gives larger space-time volume of high tem-peratures, whose di-electron emissions mostly contributeto the IMR. But there is still a large gap between thecontributions from charm hadrons and from the QGP.In addition, to lower the transition temperature will in-crease the space-time volume of the QGP phase and thendilepton rates from thermal partons. But this enhance-ment is almost in the LMR and will not significantly in-fluence the IMR. So it seems that it is very difficult toextract the thermal sources from the backgrounds fromcharm hadron decays in the invariant mass spectra alone.Additional observables such as p T spectra and collectiveflows [18, 41] are also needed.We show in Fig. (7) the results with the PHENIX ac-ceptance [16]. We see that the charm backgrounds stillout-perform the in-medium ρ . The acceptance geome-try pushes the charm hadron contributions toward theLMR. Using our cocktail sources, there is still a large un-expected excess of di-electrons in the LMR as reportedby the PHENIX collaboration. V. SUMMARY AND CONCLUSION
We investigate the di-electron low and intermediatemass spectra from the vector and charm hadrons in mostcentral heavy ion collisions at ultra-relativistic energies. ) M (GeV/c0.5 1 1.5 2 2.5 3 )( P H E N I X A CC EP T . ) - d N / d M ( G e V -6 -5 -4 -3 -2 -1 S95P-PCE b = 2.4 fm
PartonicFreezeOutIn-MediumCharm ω , η Dalitz PHENIX 0-10%Total
Figure 7: (Color online) Comparison with PHENIX data [16]in most central (0-10%) Au+Au collisions with the PHENIXacceptance.
The space-time history of the fireball is provided by a 2+1dimension ideal hydrodynamic model, whose parametersare fixed by fitting the transverse momentum spectra oflong-life hadrons, i.e., pions, kaons and protons. Twotypes of equations of state are used. The medium ef-fects of vector mesons from scatterings of vector mesonsby mesons and baryons in the medium are considered.The di-electron emissions from in-medium vector mesondecays can be evaluated via the imaginary parts of thevector meson propagators which are functions of space-time through the temperature. Due to their longer livesthan the time scale of the freezeout process, most of the ω and φ mesons may decay at the thermal freezeout, giv-ing two sharp peaks in di-electron mass spectra. Thecontribution from the charm hadrons is modeled by thePYTHIA simulation of the proton-proton collisions and modified by the binary collision number and the nuclearmodification factor for electrons.The cocktail sum over all above sources and the par-tonic phase incorporated with the acceptances of theSTAR detector is compared to the STAR preliminarydata. The hadronic many body effective theory with abroadening rho meson spectral function can describe theSTAR di-electron data in the LMR. With a parametrizednuclear modification factor for electrons from charmhadron decays, we can roughly reproduce the di-electronspectra in the IMR, though we still lack enough knowl-edge about open charm decays in medium, such as themodification from the dynamical correlation of c ¯ c pairs.In conclusion, we find: (1) The detector acceptanceespecially the transverse momentum cutoff significantlysuppresses the contribution from the in-medium ρ me-son in the mass region below the ρ mass; (2) With thecurrent set of parameters and detector acceptances, thebackgrounds from charm hadrons dominate in the lowand intermediate mass regions. Therefore it is impos-sible to extract the thermal sources of dileptons withthe invariant mass spectra alone if the backgrounds fromcharm hadrons are not removed. Other observables suchas transverse momenta and collective flows may provideadditional tools to tag these sources. Future STAR pro-grams such as the Heavy Flavor Tracker [42] and theMuon Telescope Detecctor are expected to improve thecapability of identifying the backgrounds from charm de-cays and extracting the thermal souces.Acknowledgement: QW is supported in part by the Na-tional Natural Science Foundation of China (NSFC) withgrant No. 10735040. YFZ is supported in part by the Na-tional Natural Science Foundation of China (NSFC) withgrant No. 10805046. [1] L. D. McLerran and T. Toimela, Phys. Rev. D31 , 545(1985).[2] K. Kajantie, J. I. Kapusta, L. D. McLerran, andA. Mekjian, Phys. Rev.
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