Phenomenology of Heavy Flavors in Ultrarelativistic Heavy-Ion Collisions
aa r X i v : . [ h e p - ph ] J un Phenomenology of Heavy Flavors in Ultrarelativistic Heavy-IonCollisions
A. A. Isayev
Kharkov Institute of Physics and Technology,Academicheskaya Street 1, Kharkov, 61108, UkraineKharkov National University, Svobody Sq., 4, Kharkov, 61077, Ukraine
Abstract
Some recent experimental results obtained in collisions of heavy nuclei ( √ s = 200 GeV) atBNL Relativistic Heavy-Ion Collider (RHIC) are discussed. The probes of dense matter created inheavy-ion collision by quarkonia, D and B mesons containing heavy charm and beauty quarks areconsidered. The centrality, rapidity and transverse momentum dependences of the nuclear modifi-cation factor and elliptic flow coefficient are presented and their possible theoretical interpretationis provided. . INTRODUCTION Lattice QCD (LQCD) calculations predict that at a critical temperature T c ≃
170 MeV,corresponding to an energy density ε c ≃ / fm , nuclear matter undergoes a phase tran-sition to a deconfined state of quarks and gluons, called Quark-Gluon Plasma (QGP). At themodern collider facilities such as CERN supersynchrotron (SPS) (the nucleon-nucleon (NN)centre-of-mass energy for collisions of the heaviest ions is √ s = 17 . √ s = 200 GeV), and Large Hadron Collider (LHC) atCERN ( √ s = 5 . ε c . This makes the QCD phase transition po-tentially realizable within the reach of the laboratory experiments. The objective is then toidentify and to assess suitable QGP signatures, allowing to study the properties of QGP. Tothat end, a variety of observables (probes) can be used [1]-[4]. Further we will be mainlyinterested in heavy-flavour probes of QGP, i.e., utilizing particles having c- and b-quarks.A special role of heavy Q = ( c, b ) quarks as probes of the medium created in heavy-ioncollision (HIC) resides on the fact that their masses ( m c ≈ . , m b ≈ . m Q ≫ T c , Λ QCD = 0 . x , where gluon saturation effects become important. Heavy quarks are useful tools to studygluon saturation, since, due to their large masses, charm and bottom cross sections arecalculable via perturbative QCD and their yield is sensitive to the initial gluon density.The heavy-flavor hadrons we will be interested in include: 1) open charm D = ( c ¯ q ) andopen beauty B = ( b ¯ q ) mesons composed of a heavy quark Q = ( c, b ) and a light antiquark¯ q = (¯ u, ¯ d ). These mesons could be sensitive to the energy density of the medium through themechanism of in-medium energy loss; 2) hidden charm [charmonia=( c ¯ c )] and hidden beauty2bottomonia=( b ¯ b )] mesons (called collectively heavy quarkonia) being the bound states ofthe charm quark-antiquark, or bottom quark-antiquark pairs, respectively. Heavy quarkoniacould be sensitive to the initial temperature of the system through the dissociation due tocolor screening of the color charge that will be discussed later.For detecting heavy flavor hadrons, different decay channels are used. At RHIC, inPHENIX and STAR experiments the measurement of the spectra of open heavy flavorsis based on the measurement of the spectra of heavy flavor (HF) electrons and positrons[( e + + e − ) /
2] from the semileptonic decays like D → K − e + ν e , D + → ¯ K e + ν e , etc. Thesemeasurements are based on the fact that the decay kinematics of HF electrons/positronslargely conserves the spectral properties of the parent particles. Besides, the STAR ex-periment has the capability to directly reconstruct open heavy flavor mesons through thehadronic decay channels like D ( D ) → K ∓ π ± , D + → K − π + π + , etc. At low transverse mo-mentum, the STAR experiment also uses heavy flavor decay muons to provide open heavyflavor measurements. Quarkonia in both STAR and PHENIX experiments are detectedthrough their dilepton decays Q ¯ Q → e + e − (midrapidity), Q ¯ Q → µ + µ − (forward rapidity). II. HEAVY FLAVOR PROBES OF QGP: QUARKONIA
We begin the discussion of heavy flavor probes of QGP with heavy quarkonia. Thequestion we would like to address is: What could happen with quarkonium yields in HIC ifQGP is really formed?Let us note that if the deconfinement phase transition really takes place in a densemedium created in HIC, then a color charge in the QGP will be screened analogously tothe Debye screening of an electric charge in the electromagnetic plasma. As a result ofcolor Debye screening of the heavy quark interaction in QGP, the binding energy of a boundstate decreases and one can expect that this would lead to the suppression of quarkoniumyields in HIC. This idea was first suggested by H. Matsui and H. Satz [6] who predictedthat color Debye screening will result in the suppression of
J/ψ meson ( c ¯ c in the S state, M = 3 .
097 GeV) yields. After that, the
J/ψ suppression was considered as one of thekey probes for the QGP formation in heavy ion collisions.
J/ψ is especially promisingbecause of the large production cross-section and dilepton decay channels which make iteasily detectable. 3owever, soon it was realized that besides melting
J/ψ mesons in QGP due to thescreening of the color charge, there are also a few competing mechanisms which could explainthe suppression of
J/ψ production in heavy-ion collisions. These mechanisms are referredto as cold nuclear matter (CNM) effects. The first CNM effect is the absorption of
J/ψ bynuclear fragments from colliding nuclei. Let us consider, e.g., the proton-nucleus collision.Once produced in the hard primary parton processes,
J/ψ has to cross the length L ofnuclear matter before exiting the nucleus, and, when traversing nuclear matter, it can beabsorbed by forthcoming nucleons of a nucleus. The production cross section of J/ψ in p - A collision can be parameterized as σ J/ψpA = Aσ J/ψpp e − σ J/ψabs ̺L , (1)where σ J/ψpp is the production cross section of
J/ψ in p - p collisions and σ J/ψabs is the nuclearabsorption cross section. From the global fit to the data on charmonium production in p - A collisions the value of σ J/ψabs can be extracted, in particular, at SPS (NA50 experiment) itwas obtained that σ J/ψabs = 4 . ± . R Ai ( x, Q ) = f Ai ( x, Q ) f Ni ( x, Q ) < , i = q v , q sea , g. (2)Here ”i” denotes valence quarks, sea quarks, and gluons, x is the parton momentum fraction, Q is the momentum transfer squared. At high energies, J/ψ s are dominantly producedthrough the gluon fusion, and the
J/ψ yield is therefore sensitive to gluon shadowing. Theunderlying idea explaining the occurrence of gluon shadowing is that the gluon densitystrongly rises at small x to the point where gluon fusion, gg → g , becomes significant.In the case of proton-nucleus and nucleus-nucleus collisions, where nuclei with large massnumber A are involved, the nonlinear effects are enhanced by the larger density of gluonsper unit transverse area of the colliding nuclei. A direct consequence of nuclear shadowingis the reduction of hard-scattering cross sections in the phase-space region characterized bysmall- x incoming partons. For gluons, e.g., shadowing becomes important at x . × − ,and, hence, is relevant for the conditions of RHIC and LHC. Note however that the strength4f the reduction is constrained by the current experimental data only for x & − .Let us consider the J/ψ production at RHIC experiments. The
J/ψ suppression can becharacterized by a ratio called the nuclear modification factor R AB ( p T , y ) = d N ABJ/ψ /dp T dyN coll d N ppJ/ψ /dp T dy , (3)obtained by normalizing the J/ψ yield in A - B nucleus-nucleus collision by the J/ψ yield in p - p collision at the same energy per nucleon pair times the average number of binary inelasticNN collisions. This ratio characterizes the impact of the medium on the particle spectrum.If heavy ion collision is a superposition of independent N coll inelastic NN collisions, then R AB = 1, whereas R AB < R AB >
1) corresponds to the case of the
J/ψ suppression(enhancement). As we discussed already, at first, it is necessary to clarify the role of CNMeffects on
J/ψ production. At RHIC, CNM effects are studied in collisions of light deuteronand heavy gold nuclei, when the energy density reached in the collision is not enough for theformation of QGP. At RHIC energies, shadowing of partons is important and in the modelcalculations is implemented in two shadowing schemes for the nuclear parton distributionfunctions, the EKS model [10] and NDSG model [11]. The
J/ψ break-up cross sectionsobtained for two shadowing schemes from the best fit to data are σ breakup = 2 . +2 . − . mb (EKS)and σ breakup = 2 . +2 . − . mb (NDSG) [12] (in Ref. [12], the term ”break-up cross section” isused instead of the term ”absorption cross section”). Although these values are consistent,within large uncertainties, with the corresponding value obtained at CERN SPS, a recentanalysis [13] shows that, in fact, the level of J/ψ
CNM break-up significantly decreases withthe collision energy.Let us now consider charmonium production in heavy ion collisions at RHIC. Figs. 1,2show the p T -integrated J/ψ nuclear modification factor obtained in Au-Au collisions atRHIC/PHENIX experiment as a function of centrality, parametrized by the number ofparticipating nucleons at mid- and forward rapidities, respectively [12, 14]. The PHENIXdata are shown by boxes. The R AA approaches unity for the peripheral collisions (small N part ) and goes down to approximately 0.2 at most central collisions (large N part ). To see thelevel of the anomalous suppression beyond the cold nuclear matter effects it is necessary toextrapolate the CNM effects obtained in d-Au collisions to Au-Au collisions within the givenshadowing scheme and corresponding J/ψ break-up cross section. The results are shown byblack and red curves with the corresponding error bands. It is seen that
J/ψ production5 umber of Participants Au+Au0 50 100 150 200 250 300 350 400 AA R – global PHENIX Au+Au Data |y|<0.35 (syst mb -2.1+2.3 = 2.8 breakup s EKS Shadowing + mb -2.6+2.2 = 2.6 breakup s NDSG Shadowing +
FIG. 1: (Color online)
J/ψ ’s R AA for Au - Au collisions at midrapidity compared to a band oftheoretical curves for the breakup values found to be consistent with the d - Au data. Both EKSand NDSG shadowing schemes are included. Number of Participants Au+Au0 50 100 150 200 250 300 350 400 AA R – global PHENIX Au+Au Data |y|<1.2-2.2 (syst mb -2.1+2.3 = 2.8 breakup s EKS Shadowing + mb -2.6+2.2 = 2.6 breakup s NDSG Shadowing +
FIG. 2: (Color online) Same as in Fig. 1 but at forward rapidity. is significantly suppressed beyond CNM effects at forward rapidity and suppression is lesspronounced at midrapidity in most central Au-Au collisions.Thus, one can conclude that assuming the conservative cold nuclear matter approachessome level of the anomalous suppression is indeed observed at RHIC which could characterizethe produced medium as hot and deconfined.6 art
N0 50 100 150 200 250 300 350 400 AA R
11% syst. – NA50, Pb+Pb, 0 FIG. 3: (Color online) J/ψ nuclear modification factor for the most energetic SPS (Pb-Pb) andRHIC (Au-Au) collisions, as a function of the number of participants N part . However, not all is still clear. Measurements of the J/ψ suppression by PHENIX col-laboration at RHIC lead to some surprising features. Fig. 3 shows compiled data for thenuclear modification factor obtained in CERN SPS and RHIC PHENIX experiments. Thereare two surprising results in these measurements. First, the mid rapidity suppression inPHENIX (the red boxes) is lower than the forward rapidity suppression (blue boxes) despitethe experimental evidence that the energy density is higher at midrapidity than at forwardrapidity, and, hence, one could expect that at midrapidity J/ψ will be more suppressed dueto higher density of color charges. Secondly, the nuclear modification factor R AA at midra-pidity in PHENIX (red boxes) and SPS (black crosses) are in agreement within error bars,a surprising result considering that the energy density reached at RHIC is larger than theone reached at SPS. This indicates that at RHIC energies additional mechanisms counteringthe suppression, could be operative.Let us consider possible explanations of the above features. 1. Regeneration of J/ψ inthe hot partonic phase from initially uncorrelated c and ¯ c quarks (quark coalescence model).If to compare the J/ψ suppression pattern at RHIC and SPS, J/ψ could be indeed moresuppressed at RHIC than at SPS, but then regenerated during (or at the boundary of) thehot partonic phase from initially uncorrelated c and ¯ c quarks. If to compare the results at7 (GeV/c) T p v -0.3-0.2-0.100.10.20.3 Coalescence at freeze-out (PLB595,202)in transport model (PLB655,126)in fireball (PRL97:232301)+ initial mix (Zhao, Rapp priv. comm.) (PRL97:232301) y Initially produced J/Comovers (Lynnik priv. comm.) PHENIX |y|<0.35 [20,60%] (Preliminary) 3% – Global Syst. [0,5] GeV/c ˛ T p 0.02 – – = -0.10 v 42% of Run-7 FIG. 4: (Color online) J/ψ ’s v at midrapidity for [20 , p T , using42% of 2007 Au + Au statistics, with some theoretical predictions. RHIC (midrapidity vs. forward rapidity), at midrapidity, due to the higher energy density,there are more c and ¯ c quarks to regenerate than at forward rapidity that could explain thestronger suppression at forward rapidity. Note that the total number of initial c ¯ c pairs islarger than 10 in the most central Au-Au collisions. Certainly, if regeneration is important atthe RHIC conditions, it will be even more important at the LHC conditions where more than100 c ¯ c pairs is expected to be produced in the central Pb-Pb collisions. 2. J/ψ productioncould be more suppressed at forward rapidity due to the nuclear shadowing effects, whichcould be more pronounced away from midrapidity [15].One of possible experiments aimed to verify the quark coalescence model is the measure-ment of the J/ψ elliptic flow [16]. The idea is that if charmonia were produced by coalescenceof charm quarks, they should inherit somehow their flow, which is known to be quite largefrom the open heavy flavor measurements (see the next Section), resulting in a higher v than in the case of the direct production of J/ψ in hard collisions. The PHENIX experimentreported a first tentative measurement of J/ψ ’s v in Au-Au collisions [17]. As is seen fromFig. 4, these proof-of-principle measurements at the current level of precision do not allowone to distinguish between models assuming various level of regeneration (and thus ellipticflow) and much larger statistics is probably needed to differentiate between different models.To show the complexity of the problem, let us consider some theoretical models forthe charmonium production, which quite satisfactory describe the RHIC data but whosepredictions for LHC are drastically different. First, in the statistical hadronization model (SHM) [18], it is assumed that: 1. All heavy quarks (charm and bottom) are produced inprimary hard collisions and their total number stays constant until hadronization. 2. Heavyquarks reach thermal equilibrium in the QGP before the chemical freeze-out (hadronization).8 Au+Au 0-20% (N part =280) R AA J / y -2 -1 0 1 2 Au+Au 20-40% (N part =140) y FIG. 5: (Color online) Rapidity dependence of R J/ψAA for two centrality classes in the statisticalhadronization model. The data from the PHENIX experiment (symbols with errors) are comparedto calculations (lines, see text). 3. All quarkonia are produced (nonperturbatively) through the statistical coalescence ofheavy quarks at hadronization. Multiplicities of various hadrons are calculated with thegrand canonical ensemble. The generation of J/ψ proceeds effectively if c, ¯ c quarks are freeto travel over large distances implying deconfinement.Fig. 5 shows the rapidity dependence of the nuclear modification factor, obtained in thismodel and the comparison with the rapidity dependence at PHENIX for two centrality bins.Two theoretical curves correspond to two fitting procedures, with one and two Gaussians ofthe J/ψ data in pp collisions. In both cases, calculations reproduce rather well (consideringthe systematic errors) the R AA data. The model describes the larger suppression away frommidrapidity. The maximum of R AA at midrapidity in this model is due to the enhancedgeneration of charmonium around midrapidity, determined by the rapidity dependence ofthe charm production cross section. The centrality dependence of R AA at y = 0 is shownin Fig. 6. The model reproduces quite well the decreasing trend with centrality seen in theRHIC data. Fig. 6 also shows the prediction of the model for the LHC. At much higherLHC energies, the charm production cross section is expected to be larger by about an orderof magnitude. As a result, a totally opposite trend as a function of centrality is predicted,with R AA exceeding unity for central collisions.Let us consider the comovers interaction model (CIM) [19]. This model does not assumethe deconfinement phase transition. Anomalous suppression of J/ψ (beyond CNM effects)is the result of the final state interaction of the c ¯ c pair with the dense medium producedin the collision (comovers interaction). The model consistently treats the initial and final9 N part R AA J / y ModelLHCRHIC RHIC data FIG. 6: (Color online) Centrality dependence of the R J/ψAA at midrapidity, according to the statisticalhadronization model. state effects. The initial state effects include: 1) nuclear absorption of the pre-resonant c ¯ c pairs by nucleons of the colliding nuclei, 2) consistent treatment of nuclear shadowing forhard production of charmonium. The final state effects include absorption of the c ¯ c pairsby the dense medium created in the collision (interaction with comoving partons or hadronsproduced in the collision). The model does not assume thermodynamic equilibrium and,thus, does not use thermodynamic concepts. The density of charmonium is governed by thedifferential rate equation τ dn J/ψ dτ = − σ co [ n co ( b, s, y ) n J/ψ ( b, s, y ) − (4) − n c ( b, s, y ) n ¯ c ( b, s, y )] , supposing a pure longitudinal expansion of the system and boost invariance. In Eq. (4), n co is the density of comovers, which is found in the dual parton model [20] together with theproper shadowing correction, σ co is the cross section of J/ψ dissociation due to interactionswith comovers, taken such as to reproduce the low energy SPS experimental data (with σ co = 0 . 65 mb). The first term on the right describes dissociation of charmonium due tointeraction with comovers. The second term describes the recombination of charmonium andis proportional to the product of densities of charm quarks and antiquarks. The important10 art N A u + A u R PHENIX (|y|<0.35) - e + e shadowing+ dissociation+ recombination C = 0.59 = 200 GeVs FIG. 7: Results for J/ψ suppression in Au-Au collisions at RHIC at midrapidity in the comoversinteraction model. The solid curve is the final result. The dash-dotted one is the result withoutrecombination ( C = 0). feature of the CIM is that recombination of c -¯ c quarks proceeds only locally, when thedensities of quarks and antiquarks are taken at the same transverse coordinate s . This isdifferent from the recombination in the SHM, where recombining quarks can be separated bylarge distance that implies deconfinement. The effective recombination cross section in theCIM is equal to the dissociation cross section due to the detailed balance. The results for thecentrality dependence of the R AA are shown in Fig. 7. At midrapidity, the experimental dataare well reproduced by full theoretical calculations (solid curve) taking into account nuclearshadowing, dissociation by comovers and recombination from charm quark and antiquarkpairs. The results at forward rapidity, presented in Fig. 8, also well agree with the data, inparticular, the J/ψ suppression at forward rapidity is somewhat larger that the suppressionat midrapidity.Fig. 9 shows the predictions of the model for LHC. The parameter C encodes the recom-bination from c -¯ c pairs and vanishes in the absence of recombination. Although the densityof charm grows substantially from RHIC to LHC, the combined effect of initial-state shad-owing, absorption and comovers dissociation overcomes the effect of parton recombination.This is in sharp contrast with the predictions of the statistical hadronization model where11 art N A u + A u R [1.2,2.2]) ˛ PHENIX (|y| - m + m shadowing+ absorption+ dissociation+ recombination = 200 GeVs FIG. 8: Same as in Fig. 7, but at forward rapidity. The dashed line is the total initial-state effect.The dotted line is the result of shadowing. In Fig. 7, the last two lines coincide. a strong enhancement of the J/ψ yield with increasing centrality was predicted.Thus, the J/ψ suppression is an important characteristic to search for QGP. But if J/ψ anomalous suppression (beyond CNM effects) was observed in HIC, there are a few com-peting mechanisms to explain that: 1. Charmonium is dissociated due to the genuine colorscreening in the deconfined medium. 2. Charmonium is dissociated through interactionswith comoving partons or hadrons in the medium formed in HIC. How to differ these mech-anisms? In comovers interaction model, the anomalous suppression sets in smoothly fromperipheral to central collisions rather than in a sudden way when the corresponding disso-ciation temperature in the deconfined medium is reached. Even at SPS, where the role ofquark recombination is of minor importance, current experimental errors still do not allowto disentangle these two mechanisms. However, even if the color screening mechanism isdominating, it is unclear what is really melted, directly produced J/ψ s or originating fromthe feed-down of less bound charmonium states, χ c ( → J/ψ + X ), ψ ′ ( → J/ψ + X ), whichhave lower dissociation temperatures. At RHIC and LHC conditions, the feed-down from B-meson decays becomes also important. Recombination enhances J/ψ production and muchcomplicates the picture but its effect may be different depending on whether the deconfine-ment phase transition happened or not. It is even possible that after all J/ψ s were melted12 art N P b + P b R = 5500 GeVs shadowingC = 0 - no recombinationC = 2C = 3.5C = 5 FIG. 9: Results for J/ψ suppression in Pb+Pb at LHC ( √ s = 5 . C in the comovers interaction model. The upper line is the suppressiondue to initial-state effects. in QGP they can be statistically regenerated at hadronization. True operative mechanismsof J/ψ production can be established only after studying all important dependences (fromcentrality, rapidity, collision energy √ s ,...) of all relevant observables with sufficient accu-racy. Further we will consider also the J/ψ production in RHIC experiments as a functionof the transverse momentum, but, for the sake of comparison, this will be more illustrativeto do after presenting the respective dependence for open heavy flavor mesons.So far we considered the suppression (or enhancement) patterns for the J/ψ produc-tion. Now let us briefly discuss the perspective for bottomonia. One could expect thatbottomonium production might be easier to understand than charmonium production dueto the following reasons. 1. Since less than one b ¯ b pair is produced in one central Au-Aucollision, the regeneration is negligible at the conditions of RHIC. Besides, only about 5 b ¯ b pairs are expected to be produced in a single central Pb-Pb collision at LHC. Hence,regeneration should play much less role in the beauty sector than in the charm sector. 2.Having higher masses, bottomonia originate from higher momentum partons and will lesssuffer from shadowing effects. 3. The absorption cross section for Υ is by 40 − 50 % smallerthan the corresponding cross section for J/ψ and ψ ′ .13hese features should ease the separation of the anomalous suppression in the Υ’s family. III. HEAVY FLAVOR PROBES OF QGP: OPEN HEAVY FLAVOR MESONS What qualitative effects could one expect to obtain when probing the dense matter byheavy quarks (charm or bottom)? As well known from electrodynamics, the bremsstrahlungoff an accelerated heavy quark Q is suppressed by the large power of its mass ∼ ( m q /m Q ) ascompared to light quarks. Therefore, gluon radiation off heavy quarks (i.e., radiative energyloss) is much suppressed relative to light quarks. Consequently, one could expect a decreaseof high p T suppression and of the elliptic flow coefficient v from light to charm to bottomquarks. Or, that the energy loss and coupling to matter of heavy quarks is smaller than forlight quarks as well as that the thermalization time for heavy quarks is longer than for lightquarks. Due to the above features, one should observe a pattern of gradually increasing R AA when going from the mostly gluon-originated light-flavor hadrons ( h ± and π ) to D to B mesons: R hAA . R DAA . R BAA [21] (gluons lose more energy than quarks since gluonshave a higher color charge). The enhancement above the unity of the heavy-to-light ratio R D/hAA = R DAA /R hAA probes the color charge dependence of the parton energy loss while theratio R B/DAA = R BAA /R DAA probes the mass dependence of the parton energy loss.Let us now consider what the experiment tells us about the open heavy flavor p T sup-pression and elliptic flow. As mentioned earlier, at RHIC, open heavy flavors can be studiedthrough the measurements with the electrons and positrons originating from the semilep-tonic decays of D and B mesons. Fig. 10 shows the nuclear modification factor and ellipticflow coefficient for HF electrons as functions of p T , obtained in central collisions of goldnuclei at RHIC (closed circles) [22]-[25]. In contrast to the above expectations, the resultsfor R HFAA show a strong suppression of HF decay electrons at p T > p T the level of suppression for π . This evidences that produced medium is quitedense for heavy quarks to lose energy as efficiently as light quarks do. The measurement ofelliptic flow gives rather large value for v HF . This means that HF electrons are involved ina collective motion being indicative of the collective flow of their parent particles as well.In Fig. 10, the results of some model considerations are also shown. The best description isprovided by the model assuming the Brownian motion of heavy quarks within the frameworkof Langevin dynamics [26]. Let us consider the basic assumptions of this theory. Firstly,14 A R NN sAu+Au @ 0-10% central (a) Moore &Teaney (III) (cid:237) T) p p [GeV/c] T p H F v (b) minimum bias AA R p > 2 GeV/c T , p v p HF2 v – , e AA R – e FIG. 10: (Color online) Nuclear modification factor (upper panel, central Au-Au) and elliptic flow(lower panel, minimum-bias Au-Au) of non-photonic electrons at RHIC, compared to theory. Theband corresponds to the Langevin simulations based on an expanding fireball with effective heavyquark resonance interactions [26]. the thermal heavy quark momentum p ∼ mT (in nonrelativistic approximation) is muchlarger than the typical momentum transfer Q ∼ T from a thermal medium to a heavyquark. Hence, the motion of a heavy quark in the QGP can be represented as the Brownianmotion, which can be described by using the Langevin equation. Secondly, heavy quarkloses its energy in elastic scattering processes with light partons. Besides, as evidenced fromcalculations of heavy and light meson correlators within LQCD, in QGP the D - and B -meson like resonant states exist up to T < T c . Rescattering on these resonant states playsan important role in thermalizing heavy quarks. Thirdly, in order to get the spectrum of HFelectrons, c - and b -quarks are to be hadronized to D and B mesons via quark coalescence(at low p T ) and fragmentation (at high p T ).The analysis shows that resonance scattering decreases nuclear modification factor R HFAA and increases azimuthal asymmetry v HF . Heavy-light quark coalescence in subsequenthadronization significantly amplifies v HF and increases R HFAA , especially in the p T ≃ R HFAA and v HF is estimated by providing full calcu-15 GeV/c) T Electron p e ) fi e + b fi e / ( c fi b PHENIX |y| <0.35FONLL y=0FONLL error band y=0 =200 GeVs p+p at 90% C.L.90% C.L. FIG. 11: (Color online) Transverse momentum dependence of the relative contribution from Bmesons to the non-photonic electron yields. The solid curve illustrates the fixed-order-plus-next-to-leading-log (FONLL) calculation [28]. lations with c + b quarks and with only c quarks. The result is that the B-meson contributionincreases R HFAA and decreases v HF , and becomes important above p T ≃ b → e ) / [( b → e ) + ( c → e )], obtained in p - p collisions at √ s = 200 GeV andshown in Fig. 11 [27]. Thus, one can conclude, that the combined effect of coalescence ofheavy quarks Q with light quarks q , and of the resonant heavy-quark interaction is essentialin generating strong elliptic flow v HF of up to 10%, together with strong suppression ofheavy flavor electrons with R HFAA about 0.5. IV. CHARMONIUM PRODUCTION AT FINITE TRANSVERSE MOMENTUM Now we can consider the production of J/ψ mesons at finite transverse momentum p T and compare it with the corresponding dependence for open heavy flavor mesons. Fig. 12shows the p T -dependence of J/ψ ’s R AA in 0 − 20% Cu+Cu collisions from PHENIX [29] andSTAR [30], and 0 − 60% Cu+Cu collisions from STAR [30]. The most striking peculiarity isthat the nuclear modification factor for J/ψ increases with p T from the value of about 0.5 atlow p T to the value slightly exceeding unity at high p T > / c. These data indicate thatthere is no J/ψ suppression at high p T in heavy-ion RHIC experiments - the result whichcould be considered as surprising taking into account the strong suppression of heavy flavor16 T (GeV/c) R AA STAR Cu+Cu 0-20%STAR Cu+Cu 0-60%PHENIX Cu+Cu 0-20% AdS/CFT+Hydro2-Componentcharm quarkheavy resonance FIG. 12: (Color online) J/ψ ’s R AA vs. p T , obtained at RHIC experiments and compared withdifferent model calculations. The best description of the data is provided by the two-componentmodel [33] (dotted line). electrons considered in the previous section.For comparison, Fig. 12 also shows the results of the model calculations for the opencharm R AA . The solid line corresponds to the charm quark energy loss because of the elasticscattering and radiative parton processes, with assumed medium gluon density dN g /dy =254 for 0 − 20 % Cu+Cu collisions [31]. The dash-dotted line shows the results of themodel calculations for the D-meson energy loss with dN g /dy = 275 [32], where the D-mesonsuppression is caused by the collisional dissociation in quark-gluon plasma. Both models,which correctly describe open heavy-flavor suppression in Au-Au collisions, predict charmmeson suppression of a factor about 2 at p T > / c, in contrast to the J/ψ ’s R AA .This comparison suggests that high- p T J/ψ production does not dominantly proceed via achannel carrying color, but rather the contribution of the color singlet channel is prevailing.The dotted line in Fig. 12 is the result for the J/ψ ’s R AA ( p T ) in the two-componentmodel [33], which provides quite good qualitative description of the data. Let us considerthe basic assumptions of this model in more detail. First, it assumes that the p T spectra ofcharmonia states (Ψ = J/ψ, χ c , ψ ′ ) consist of two parts, direct and coalescence: dN Ψ p T dp T = dN Ψ p T dp T (cid:12)(cid:12)(cid:12)(cid:12) dir + dN Ψ p T dp T (cid:12)(cid:12)(cid:12)(cid:12) coal . (5)The direct component is associated with hard production of charmonia in primordialN-N collisions, subject to suppression in the subsequent medium evolution due to gluondissociation reactions in QGP and break-up by π and ρ mesons in a hadron gas phase. The17 (GeV/c) T p ( i n c l u s i ve )] Y ] / [ J / Y J / fi [ B Y ]/J/ Y J/ fi [B(pQCD)/(STAR Data) p+p 200 GeV STAR Preliminary FIG. 13: (Color online) Tevatron and STAR data for the ratio of J/ψ from B-meson feed-down toinclusive J/ψ . phase space distribution of different charmonia follows the Boltzmann transport equation,where the nuclear absorption is included in the initial conditions. Besides, the Cronin effect,consisting in multiple scattering of an initial parton on elementary constituents of the facingnucleus and leading to an increased p T in its final state (before fusion to charmonia), isalso taken into account through initial conditions for charmonia momentum distributions.The model consistently treats the leakage effect, i.e., charmonia travelling outside the fire-ball boundary before freeze-out are not subject to dissociation. The leakage effect reducessuppression primarily for high- p T charmonia. The soft component is associated with thecoalescence of c, ¯ c quarks near the QCD phase boundary assuming an approximate thermal-ization up to c -quark momenta of p T ∼ − . / c. The medium evolution is modelledby the isentropically expanding fireball with a cylindrical volume.Although in such a formulation the model is already quite complicated, two additionaleffects should be taken into account in order to reproduce an increasing trend of J/ψ ’s R AA at high p T [33]. These two additional effects are: 1. Finite formation time, required tobuild up the charmonium wave function from a ”pre-hadronic” c -¯ c pair - this effect leads tothe reduction of the charmonia dissociation cross sections. 2. Feed-down from B -mesons, B → J/ψ .Fig. 13 (from Ref. [33]) shows the data from Tevatron [34] and STAR on the B → J/ψ feed-down fraction in elementary p - ¯ p ( p - p ) collisions which is quite considerable at high p T .After including the formation time effects and B-meson feed-down (according to Tevatron18ata) into the two-component model, it is able to reproduce the increasing behavior of J/ψ ’s R AA at high p T . 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