We study the production of charmonia and charmed hadrons for nucleus-nucleus
collisions at SPS, RHIC, and LHC energies within the framework of the
statistical hadronization model. Results from this model are compared to the
observed centrality dependence of J/psi production at SPS energy. We further
provide predictions for the centrality dependence of the production of open and
hidden charm mesons at RHIC and LHC.Comment: Contribution to Quark Matter 2002, 4 pages, 3 figures; revised
  version including charmed hyperons (omitted in v1

A. Andronic

Braun-Munzinger

Gallmeister

Gorenstein

Grandchamp

J. Stachel

K. Redlich

Matsui

P. Braun-Munzinger

Rapp

Thews

Vogt

English

arXiv

Crossref

Statistical hadronization of charm at SPS, RHIC and LHC

Andronic, Anton

Braun-Munzinger, P.

Redlich, K.

Stachel, J.

GSI Repository

We study the production of charmonia and charmed hadrons for nucleus-nucleus collisions at SPS, RHIC, and LHC energies within the framework of the statistical hadronization model. Results from this model are compared to the observed centrality dependence of J/psi production at SPS energy. We further provide predictions for the centrality dependence of the production of open and hidden charm mesons at RHIC and LHC

Andronic, A

Braun-Munzinger, P

Redlich, Krzysztof

Stachel, J

CERN Document Server

1Statistical hadronization of charm at SPS, RHIC and LHCA. Andronica, P. Braun-Munzingera, K. Redlichb, J. Stachelca GSI Darmstadt, Germany, b University of Wroclaw, Poland, c University of Heidel-berg, GermanyWe study the production of charmonia and charmed hadrons for nucleus-nucleus colli-sions at SPS, RHIC, and LHC energies within the framework of the statistical hadroniza-tion model. Results from this model are compared to the observed centrality dependenceof J/ψ production at SPS energy. We further provide predictions for the centrality de-pendence of the production of open and hidden charm mesons at RHIC and LHC.1. IntroductionThe original idea of statistical hadronization of charm quarks [1,2] has sparked anintense activity in this eld [3,4]. Initial interest focussed on the available SPS data onJ/ψ production. As we show below, these data can be well described, but only assumingan enhanced charm cross section compared to pQCD calculations. However, the largestdierences between results from the statistical coalescence scenario (or a similar model[5]) and more conventional models are expected at collider energies. For example, in theSatz-Matsui approach [6], one would expect very strong suppression compared to directproduction of J/ψ mesons (up to a factor of 20 [7]) for central Au-Au collision at RHICenergy. In the present approach this suppression is overcome by statistical recombinationof J/ψ mesons from dierent cc pairs, so that much larger yields are expected. Wetherefore focus in this note on predictions for open and hidden charm mesons at RHICand LHC energy, with emphasis on the centrality dependence of rapidity densities.2. Model descriptionThe model assumes that all charm quarks are produced in primary hard collisionsand equilibrate in quark-gluon plasma (QGP); in particular, no J/ψ is preformed in QGP(complete screening). All charmed hadrons (open and hidden) are formed at freeze-out (atSPS and beyond, freeze-out is at the phase boundary [8]) according to the statistical laws.Taking into account the measured dependence of the ratio ψ0/ψ on centrality, the modelis valid for not too small number of participants, Npart. The total number of thermallyproduced open charm hadrons, N thoc is related to the number of directly produced cc pairs,Ndircc¯ as (neglecting charmonia): Ndircc¯ =12gcNthoc I1(gcNthoc )/I0(gcNthoc ), from which the charmenhancement factor gc is extracted. In are the modied Bessel functions. The yield ofa given species X is then NX = gcNthX I1(gcNthX )/I0(gcNthX ) for open charm mesons andhyperons and NX = g2cNthX for charmonia (see ref. [1,2] for more details).2The inputs for the above procedure are: i) the total charged particles yields (or rapiditydensities), which are taken from experiments at SPS [9,10] and RHIC [11] and extrapolatedfor LHC; and ii) Ndircc¯ , which is taken from next-to-leading order (NLO) perturbative QCD(pQCD) calculations for pp [12] (the yield from MRST HO parton distributions wasused here) and scaled to AA via the nuclear overlap function. A constant temperatureof 170 MeV and the baryonic chemical potential µb according to parametrization µb =1270/(1 +√sNN/4.3) [13] have been used for the calculations.3. ResultsWe rst compare predictions of the model to 4pi-integrated J/ψ data at the SPS (NA50data [14] replotted as outlined in [2]). The dierences between this calculation and that of[2] are due to the inclusion in the present version of the complete set of charmed mesons(open and hidden) and baryons as well as due to updated values of the inputs (volume andopen charm cross section) as outlined above. In Fig. 1 we present the comparison for twovalues of Ndircc¯ : from NLO calculations [12] and scaled up by a factor of 2. Note that theobserved centrality dependence is well reproduced using the NLO cross sections for charmproduction scaled by the nuclear overlap function. To explain the overall magnitude ofthe data a Ndircc¯ increase by a factor of 2 compared to NLO calculations is needed.We mention in this context that the observed enhancement of the dilepton yield atintermediate masses has been interpreted by NA50 as possible indication for an anomalousincrease in the charm cross section [15]. If we include into our calculations the suggestedenhancement as a function of Npart [15], the J/ψ data are underpredicted by about 20%and the Npart dependence is flatter (see Fig. 1). However, the NA50 suggestion of charmenhancement is controversial, and other explanations exist of the observed enhancementin terms of thermal radiation [16,17].00.050.10.150.20.250.30.3550 100 150 200 250 300 350 400Npart105  x N J/ψ / NpartNA50 data Nccdir   for Npart=3500.273 (2xNLO)NA50 enhancement0.137 (NLO)Figure 1. The centrality de-pendence of J/ψ productionat SPS. Model predictions arecompared to NA50 data (4pi-integrated). Two curves forthe model correspond to valuesof Ndircc¯ from NLO calculations[12] (0.137, leading to gc=0.93)and scaled up by a factor of 2.The dotted curve is obtainedwhen considering a charm en-hancement as suggested byNA50 [15]. For central colli-sions (Npart=350) we use in thecalculations V=3070 fm3 andN thoc=0.82.3We turn now to predictions for collider energies. For comparison we include in thisstudy also results at SPS energy. The input parameters for these calculations for centralcollisions (Npart=350) are presented in Table 1. Notice that from now on we focus onrapidity densities, which are the relevant observables at the colliders. The results arecompiled in Table 2 for a selection of hadrons with open and hidden charm. All predictedyields increase strongly with energy, reflecting the increasing charm cross section and theconcomitant importance of statistical recombination. Also ratios of open charm hadronsevolve with increasing energy, reflecting the corresponding decrease in charm chemicalpotential.Table 1Input parameters for model calcula-tions at SPS, RHIC and LHC .Table 2Results of model calculations at SPS, RHIC andLHC for Npart=350.√sNN (GeV) 17.3 200 5500√sNN (GeV) 17.3 200 5500T (MeV) 170 170 170 dND+/dy 0.012 0.455 4.07µb (MeV) 253 27 1 dND−/dy 0.020 0.474 4.04dNch/dy 430 730 2000 dND0/dy 0.026 1.00 8.92V∆y=1 (fm3) 861 1663 4564 dNΛc/dy 0.017 0.173 1.32dNdircc¯ /dy 0.064 1.92 16.8 dNJ/ψ/dy 3.65·10−4 0.013 0.296gc 2.22 9.37 26.5 dNψ0/dy 1.37·10−5 5.03·10−4 0.01100.10.20.30.40.50.60.70.80.9150 100 150 200 250 300 350 400Npart103  x (dNJ/ψ /dy) / NpartSPSx100RHICx10LHCFigure 2. Centrality dependence of J/ψ ra-pidity density at SPS, RHIC and LHC.00.20.40.60.811.21.450 100 150 200 250 300 350 400Npart100 x (dND+ /dy) / NpartSPSx100RHICx5LHCFigure 3. Centrality dependence of D+ ra-pidity density at SPS, RHIC and LHC.Predictions for the centrality dependence of J/ψ production are presented in Fig. 2. Inaddition to the dramatic change in magnitude (note the scale-up by factors of 10 and 1004for RHIC and SPS energy, respectively) the results exhibit a striking change in centralitydependence, reflecting the transition from a canonical to a grand-canonical regime (see[2] for more details). The preliminary PHENIX results on J/ψ production at RHIC [18]agree, within the still large error bars, with our predictions. A stringent test of thepresent model can only be made when high statistics J/ψ data are available. Anotherimportant issue in this respect is the accuracy of the charm cross section, for which sofar only indirect measurements are available [19]. In any case, very large suppressionfactors as predicted, e.g., by [7] seem not supported by the data. In Fig. 3 we present thepredicted centrality dependence of charged D+-meson production for the three energies.The expected approximate scaling of the ratio D+/Npart like N1/3part (dashed lines in Fig. 3)is only roughly fullled due to departures of the nuclear overlap function from the simpleN4/3part dependence.4. ConclusionsWe have demonstrated that the statistical coalescence approach yields a good descrip-tion of the measured centrality dependence of J/ψ production at SPS energy, albeit witha charm cross section increased by a factor of 2 compared to current NLO calculation.Rapidity densities for open and hidden charm mesons are predicted to increase stronglywith energy, with striking changes in centrality dependence. First RHIC data on J/ψ pro-duction support the current predictions, although the errors are too large to make rmconclusions. The statistical coalescence implies travel of charm quarks over signicantdistances in QGP. If the model predictions will describe consistently precision data thiswould be a clear signal for the presence of a deconned phase.REFERENCES1. P. Braun-Munzinger and J. Stachel, Phys. Lett. B490 (2000) 196.2. P. Braun-Munzinger and J. Stachel, Nucl. Phys. A690 (2001) 119c.3. M. Gorenstein et al., Phys. Lett. B509 (2001) 277; hep-ph/0012292.4. L. Grandchamp and R. Rapp, Phys. Lett. B523 (2001) 60; hep-ph/0205305.5. R.L. Thews, M. Schroedter and J. Rafelski, Phys. Rev. C63 (2001) 054905.6. T. Matsui and H. Satz, Phys. Lett. B178 (1986) 416;7. R. Vogt (p. 250c) in S.A. Bass et al., Nucl. Phys. A661 (1990) 205c.8. P. Braun-Munzinger and J. Stachel, J. Phys. G28 (2002) 1971.9. NA49 collaboration, nucl-ex/0205002.10. NA50 collaboration, Phys. Lett. B530 (2002) 33.11. PHOBOS collaboration, Phys. Rev. Lett. 88 (2002) 022302.12. R. Vogt, hep-ph/0203151; hep-ph/0111271.13. P. Braun-Munzinger et al., Nucl. Phys. A697 (2002) 902.14. NA50 collaboration, Phys. Lett. B450 (1999) 456; Phys. Lett. B477 (2000) 28.15. NA50 collaboration, Nucl. Phys. A698 (2002) 539c.16. R. Rapp and E. Shuryak, Phys. Lett. B473 (2000) 13.17. K. Gallmeister, B. Ka¨mpfer and O.P. Pavlenko, Phys. Lett. B473 (2000) 20.18. J. Nagle, PHENIX collaboration, these proceedings.19. R. Averbeck, PHENIX collaboration, these proceedings.

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Statistical hadronization of charm at SPS, RHIC and LHC

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