The transverse mass spectra of Omega, J/psi and psi' in Pb+Pb collisions at 158 AGeV are studied within a hydrodynamical model of the quark gluon plasma expansion and hadronization. The model reproduces the existing data with the common hadronization parameters: temperature T=T_H = 170 MeV and average collective transverse velocity v_T = 0.2

Bugaev, Kyrill A.

Gazdzicki, Marek

Gorenstein, Mark I.

English

Gaździcki, Marek

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:hep-ph/0112197 v2   1 Mar 2002Ω, J/ψ and ψ′ Production in Nuclear Collisionsand Quark Gluon Plasma HadronizationM. I. Gorenstein a,b, K. A. Bugaev a,c and M. Ga´ zdzicki da Bogolyubov Institute for Theoretical Physics, Kiev, Ukraineb Institut f¨ ur Theoretische Physik, Universit¨ at Frankfurt, Germanyc Gesellschaft f¨ ur Schwerionenforschung (GSI), Darmstadt, Germanyd Institut f¨ ur Kernphysik, Universit¨ at Frankfurt, GermanyAbstractThe transverse mass spectra of Ω, J/ψ and ψ′ in Pb+Pb collisions at 158 A GeV arestudied within a hydrodynamical model of the quark gluon plasma expansion andhadronization. The model reproduces the existing data with the common hadroniza-tion parameters: temperature T = TH ∼ = 170 MeV and average collective transversevelocity vT ∼ = 0.2.The possibility of observing the quark gluon plasma (QGP) in nucleus-nucleus (A+A)collisions motivated an extensive experimental program. Rich experimental results onhadron spectra and multiplicities are now available for a broad range of collision energyand for various colliding systems [1]. The anomalies observed [2] in the energy dependenceof pion and strangeness production indicate [3] that in central collisions of heavy nucleithe threshold for QGP creation during the early stage of the reaction is in the region oflow CERN SPS energies (≈ 40 A GeV).The equilibrium hadron gas (HG) model describes remarkably well the hadron mul-tiplicities measured in A+A collisions at top SPS [4] and RHIC [5] energies, where thecreation of QGP is expected. The extracted hadronization temperature parameter is sim-ilar for both energies TH = 170±10 MeV. This is close to an estimate of the temperatureTC for the QGP–HG transition obtained in Lattice QCD simulations at zero baryonicdensity (see e.g. [6]). One may therefore argue that the QGP created in high energyheavy ion collisions hadronizes into an (approximately) locally equilibrated HG and thechemical composition of this HG is weakly aﬀected by rescattering during the expansionof the hadronic system [7].In our previous paper [8] we formulated the hypothesis that the kinetic freeze–out ofJ/ψ and ψ′ mesons takes place directly at hadronization and that those mesons there-fore carry information on the ﬂow velocity of strongly interacting matter just after thetransition to the HG. Based on the measured J/ψ and ψ′ spectra in Pb+Pb collisionsat 158 A GeV [9] and using the hypothesis of the statistical production of charmoniaat hadronization [10, 11, 12] we extracted a mean transverse collective ﬂow velocity ofhadronizing matter: vT ∼ = 0.2.1The eﬀect of the rescattering in the hadronic phase was recently studied within a“hydro + cascade” approach [13, 14]. A+A collisions are considered there to proceed inthree stages: hydrodynamic QGP expansion (“hydro”), transition from QGP to HG andthe stage of hadronic rescattering and resonance decays (“cascade”). The change from“hydro” to “cascade” modelling takes place at T = TC, where the spectrum of hadronsleaving the surface of the QGP–HG transition is taken as input for the subsequent cascadecalculations. The results of Refs. [13, 14] suggest that the transverse momentum (pT)spectrum of Ω may be weakly aﬀected during the cascade stage even for central Pb+Pbcollisions at the top SPS energy. This is because of the small hadronic cross section andlarge mass of the Ω hyperon [15]. The corresponding calculations for charmonia are notyet performed within this model.Thus we are faced with an intriguing problem: if the above considerations for charmo-nia [8] and Ω [13, 14] are correct, their pT spectra should be simultaneously reproducedusing the same hydrodynamic parameters, TH and vT. In this letter we demonstrate thatsuch a description is indeed possible. The transverse mass mT (mT =qp2T + m2, wherem is a particle rest mass) spectra around midrapidity in Pb+Pb at the SPS (158 A GeV)were recently measured for Ω by WA97 Collaboration [16, 17] and for J/ψ and ψ′ byNA50 Collaboration [9]. These spectra will be the subject of the present analysis.Assuming kinetic freeze–out of matter at constant temperature T, the transverse massspectrum of i-th hadron species (with mass mi) in cylindrically symmetric and longitudi-nally boost invariant ﬂuid expansion can be approximated as [18]:dNimTdmT∝ mTZ R0rdr K1 mT coshyTT!I0 pT sinhyTT!, (1)where yT = tanh−1 vT is the transverse ﬂuid rapidity, R is the transverse system size, K1and I0 are the modiﬁed Bessel functions. The spectrum (1) is obtained under assumptionthat the freeze-out occurs at constant longitudinal proper time τ =√t2 − z2, where t isthe time and z is the longitudinal coordinate. Thus the freeze–out time t is independentof the transverse coordinate r [18]. The analysis of the numerical calculations of Ref. [14]shows that the latter is approximately fulﬁlled. The quality of the approximation madegets better for considered here heavy particles and small transverse ﬂow velocities becausea possible deviation from Eq. (1) is proportional to p2TvT/(2mTT) and thus it decreaseswith increasing particle mass at constant pT.In order to calculate (1) the function yT(r) has to be given. A linear ﬂow proﬁle,yT(r) = ymaxT   r/R, is often assumed in phenomenological ﬁts [18]. The numerical cal-culations of Ref. [14] justify this assumption. For heavy hadrons analysed in this workthe condition mi >> T is always satisﬁed and, therefore, the asymptotic form for largearguments of K1(x) ∼ x−1/2 exp(−x) can be used in Eq. (1). At SPS energies typicalvalues of vT are small (v2T << 1) and consequently coshyT ∼ = 1 + 12v2T and sinhyT ∼ = vT.The experimental mT–spectra are usually parametrised by a function1:dNimTdmT∝√mT exp −mTT ∗i!, (2)1 It corresponds formally to neglecting the transverse ﬂow (vT ≡ 0 in Eq. (1)), but introducing insteadan “eﬀective” temperature.2where the inverse slope T ∗i is extracted from the ﬁt to the data. However, when Eq. (2)is considered as an approximation of Eq. (1), the inverse slopes T ∗i should depend onboth mi and pT. The limiting cases of T ∗i behaviour at low and high pT can be easilystudied using the small and large argument asymptotic of the modiﬁed Bessel function I0in Eq. (1):T∗i (pT → 0) =T1 −12 v2T (mi/T − 1)≈ T +12mi v2T , (3)T∗i (pT → ∞) ≡ T∗ =T1 − vmaxT + 12 (vmaxT )2 , (4)where the average velocity vT in Eq. (3) is deﬁned as v2T =R R0 rdrv2T(r)/R R0 rdr. Themaximum velocity vmaxT in Eq. (4) is related to vT as v2T = (vmaxT )2/2 provided a linearﬂow proﬁle is assumed, vT(r) = vmaxT   r/R. Note that T ∗ in Eq. (4) is equivalent to thewell known “blue shifted” temperature, T[(1 + vmaxT )/(1 − vmaxT )]1/2 (see e.g. [14, 18]),calculated for (vmaxT )2 << 1. The shape of the “high–pT” tail (pT >> mi) of the mTdistribution (1) is “universal”, i.e. T ∗ given by Eq. (4) is independent of particle massmi. On the other hand, the inverse slopes T ∗i (3) at “low–pT” are strongly dependent onmi. Two remarks are appropriate here. First, for heavy particles like Ω and J/ψ the term12miv2T/T in Eq. (3) is not small compared to one thus the second (approximate) equalityin this equation is violated. Second, a condition of the validity of Eq. (3), pTvT << T, istoo restrictive for heavy hadrons, e.g. for T ∼ = 170 MeV and vT ∼ = 0.2 discussed below itleads to mT − mi << 0.3/mi GeV2/c4. This means that Eq. (3) is valid for the values ofmT − mi which are much smaller than 0.2 GeV/c2 for Ω and than 0.1 GeV/c2 for J/ψ.Summarising: (a) none of the asymptotic regimes (3) or (4) can be clearly seen in theexperimental mT spectra, i.e. neither “low–pT” (mT−mi << 0.3/mi GeV2/c4) nor “high–pT” (mT −mi >> mi) approximations are useful ones (at least for studying the availablemT spectra of Ω and charmonia); (b) ﬁtting the experimental mT spectrum of i–th hadronspecies by Eq. (2) one ﬁnds in fact the “average inverse slopes” which depend not onlyon particle mass mi, but also on the mT −mi interval covered in a given experiment (seealso Ref. [14], where T ∗i have been discussed separately for mT − mi < 0.6 GeV/c2 andfor 0.6 GeV/c2 < mT − mi < 1.6 GeV/c2).For small values of vT relevant for our discussion a good approximation of Eq. (1)at mT − mi < mi can be obtained by substituting the vT distribution in Eq. (1) by itsaverage value vT and by using large argument K1 asymptotic:dNimTdmT∝√mT exp −mT(1 + 12v2T)T!I0￿pTvTT￿. (5)We checked numerically that the values of the parameter vT extracted from the ﬁts (seebelow) to Eqs. (1) and (5) assuming a linear velocity proﬁle diﬀer by about 5%.We turn now to the test of our hypothesis of the kinetic freeze–out of J/ψ, ψ′ andΩ occurring directly at hadronization i.e. at T = TH = 170 MeV. The mT–spectraof these hadrons are measured around midrapidity [9, 16] for Pb+Pb collisions at 158A GeV. The ﬁt to these data performed using Eq. (5) with T = TH = 170 MeV yields3vT = 0.194 ± 0.017 and χ2/dof = 1.3. The value of vT varies by ∓0.016 when THis changed within its uncertainty ±10 MeV. Note that T and vT parameters are anti–correlated. A surprisingly good agreement (see Fig. 1) of our model with the data onmT–spectra serves as a strong support of the hypothesis of statistical nature of J/ψ andψ′ production [10] and their kinetic freeze–out occurring directly at hadronization [8].The dependence of the J/ψ and ψ′ transverse mass spectrum on the centrality (quan-tiﬁed by the neutral transverse energy ET) of Pb+Pb collisions at 158 A GeV was alsomeasured by NA50 Collaboration [9]. An increase of  pT  and  p2T  from peripheral colli-sions to the most central collisions can be explained, within our approach, by an increaseof the model parameter vT with ET. Note that the increase of mean ﬂow velocity andconsequently an increase of  pT  and  p2T  with a centrality of the collision as well as an in-crease of  pT  and  p2T  with particle mass mi are characteristic features of hydrodynamics.In contrast to J/ψ and ψ′ mesons the mT–spectra of the Drell–Yan pairs (dileptons withinvariant mass M > 4.2 GeV/c2) do not show this type of hydrodynamical behaviour.The values of  pT  and  p2T  [9] for the Drell–Yan pairs are smaller than those for J/ψand ψ′ and do not change signiﬁcantly with ET.The kinetic freeze–out parameters of pions were extracted from the analysis of single–and two–pion spectra measured for central Pb+Pb collisions at 158 A GeV by the NA49Collaboration [19, 20, 21]. The results are: Tf ∼ = 120 MeV and vT ∼ = 0.55, i.e. theyare very diﬀerent than those obtained here from the analysis of heavy hadron spectra.In fact we checked that the parameters obtained for pions lead to the mT spectra ofheavy hadrons which strongly disagree with the data. A decrease of temperature and anincrease of transverse ﬂow velocity with time is a general property of expanding systems.The diﬀerent kinetic freeze–out times of heavy hadrons and pions allow us to follow theexpansion history of the hadron gas phase created in Pb+Pb collisions at 158 A GeV.The freeze–out points of heavy hadrons and pions extracted from the data are plotted inFig. 2 deﬁning the path of the expanding hadron system in the T − vT plane.In conclusion, the mT–spectra of Ω, J/ψ and ψ′ produced in Pb+Pb collisions at158 A GeV are analysed within the hydrodynamical model of the QGP expansion andhadronization. The spectra are in agreement with the hypothesis of kinetic freeze–out ofthese heavy hadrons occurring directly after the transition from the quark gluon plasmato the hadron gas. A mean collective transverse ﬂow of hadronizing matter of vT ∼ = 0.2 isextracted from the ﬁt to the spectra using temperature TH ∼ =170 MeV ﬁxed by the analysisof hadron multiplicities [4]. This result together with a previously obtained parametersof pion freeze–out (Tf ∼ = 120 MeV and vT ∼ = 0.55) allow for the ﬁrst time to establish thehistory of the expanding hadron matter created in nuclear collisions.In the RHIC energy range the temperature parameter is approximately the sameT = TH ∼ = 170 MeV [5], whereas the transverse hydrodynamic ﬂow at T = TH is expectedto be stronger. The model predictions for the mT–spectra of Ω and charmonia at theRHIC energies will be presented elsewhere.AcknowledgementsWe are thankful to P. Bordalo, O. Drapier, R. Fini, R. Litava and D. R¨ ohrich forproviding us with the numerical data of NA50 [9] and WA97 [16]. The authors are4thankful to L. Bravina, A. Dumitru, D.H. Rischke, H. Stroebele, D. Teaney and Nu Xufor useful discussions. M.I.G. is thankful to the Humboldt Foundation for the ﬁnancialsupport. The research described in this publication was made possible in part by Award #UP1-2119 of the U.S. Civilian Research and Development Foundation for the IndependentStates of the Former Soviet Union (CRDF) and INTAS grant 00-00366.References[1] For recent review see Proceedings of 15th International Conference on Ultrarelativis-tic Nucleus-Nucleus Collisions (QM2001), Stony Brook, New York, 15-20 Jan 2001.[2] T. Kollegger et al. (NA49 Collab.), Proceedings of 6th International Conference onStrange Quarks in Matter: 2001: A Flavorspace Odyssey (SQM2001), Frankfurt,Germany, 25-29 Sept 2001, nucl-ex/0201019.[3] M. Ga´ zdzicki and M. I. Gorenstein, Acta Phys. Polon. B30, 2705 (1999).[4] J. Cleymans and H. Satz, Z. Phys. C57, 135 (1993),J. Sollfrank, M. Ga´ zdzicki, U. Heinz and J. Rafelski, Z. Phys. C61, 659 (1994),P. Braun-Munzinger, I. Heppe and J. Stachel, Phys. Lett. B465, 15 (1999),G. D. Yen and M. I. Gorenstein, Phys. Rev. C59, 2788 (1999),F. Becattini et al., Phys. Rev. C64, 024901 (2001).[5] N. Xu and M. Kaneta, Nucl. Phys. A698, 306 (2002),P. Braun-Munzinger et al., Phys. Lett. B518, 41 (2001),W. Florkowski, W. Broniowski and M. Michalec, Acta Phys. Pol. B33 761 (2002).[6] M. Oevers et al., Nucl. Phys. Proc. Suppl. 73, 465 (1999),F. Karsch, Nucl. Phys. Proc. Suppl. 83-84, 14 (2000).[7] R. Stock, Phys. Lett. B456, 277 (1999).[8] K. A. Bugaev, M. Ga´ zdzicki and M. I. Gorenstein, Phys. Lett. B523, 255 (2001),K. A. Bugaev, nucl-th/0112016.[9] M. C. Abreu et al. (NA50 Collab.), Phys. Lett. B499, 85 (2001).[10] M. Ga´ zdzicki and M. I. Gorenstein, Phys. Rev. Lett. 83, 4009 (1999).[11] P. Braun-Munzinger and J. Stachel, Phys. Lett. B490, 196 (2000).[12] M. I. Gorenstein et al., Phys. Lett. B498, 277 (2001), J. Phys G27, L47 (2001),Phys. Lett. B524, 265 (2002), hep-ph/0110269,A. P. Kostyuk, M. I. Gorenstein and W. Greiner 2001 Phys. Lett. B519, 207 (2001),M. I. Gorenstein et al., hep-ph/0012292.[13] S. Bass and A. Dumitru, Phys. Rev. C61, 064909 (2000).[14] D. Teaney, J. Lauret and E. V. Shuryak, nucl-th/0110037.5[15] H. van Hecke and H. Sorge, Nucl. Phys. A661, 493 (1999).[16] F. Antinori et al. (WA97 Collab.), J. Phys. G27, 375 (2001).[17] E. Anderson et al. (WA97 Collab.), Phys. Lett. B433, 209 (1998).[18] E. Schnedermann, J. Sollfrank and U. Heinz, Phys. Rev. C48, 2462 (1993).[19] B. K¨ ampfer, hep-ph/9612336, B. K¨ ampfer et al., J. Phys. G23, 2001 (1997).[20] H. Appelshauser et al. (NA49 Collab.), Eur. Phys. J. C2, 661 (1998).[21] U. A. Wiedemenn and U. Heinz, Phys. Rep. 319, 145 (1999) and references therein.60 1 2 3 mT−m (GeV/c2)10−810−610−410−210 010−1010−12 dN/(mTdmT) (a.u.)Ω−J/ψΩ+ψ’Pb + Pb at 158 A GeVFigure 1: The transverse mass spectra of Ω− (triangles down) and Ω+ (triangles up) [16]as well as J/ψ (circles) and ψ′ (squares) [9] produced in Pb+Pb collisions at 158 A GeV.The solid lines indicate a prediction of model (5) assuming kinetic freeze–out of heavyhadrons directly after hadronization of expanding quark gluon plasma. The freeze–outparameters are: T = 170 MeV and vT = 0.194.70.0 0.2 0.4 0.6 0.8  vT100120140160180200 T (MeV)Pb + Pb at 158 A GeV−QGPΩ  J/ψ  ψ’FREEZE−OUTFREEZE−OUT→  EXPANSION  →πFigure 2: The expansion history of strongly interacting matter created in Pb+Pb colli-sions at 158 A GeV. The points indicate the temperature T and the mean transverse ﬂowvelocity vT of matter at the time of Ω, J/ψ and ψ′ freeze–out (upper point) and at thetime of pion kinetic freeze–out (lower point).8

and references therein.

For recent review see

Ω, J/ψ and ψ′ production in nuclear collisions and quark gluon plasma hadronization

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.345.2027

Omega, J/psi and psi' production in nuclear collisions and quark gluon plasma hadronization

Abstract

Similar works

Full text

Available Versions

Hochschulschriftenserver - Universität Frankfurt am Main