We calculate the inclusive J/Psi production in heavy ion collisions including the effects of gluon saturation in the wave functions of the colliding nuclei. We argue that the dominant production mechanism in proton--nucleus and nucleus--nucleus collisions for heavy nuclei is different from the one in hadron-hadron interactions. We find that the rapidity distribution of primary J/Psi production is more peaked around midrapidity than the analogous distribution in elementary pp collisions. We discuss the consequences of this fact on the experimentally observed J/Psi suppression in Au-Au collisions at RHIC energies.
We derive the formulae for the cross section of J/Psi production in high energy pA and AA collisions taking into account the gluon saturation/color glass condensate effects. We then perform the numerical calculations of the corresponding nuclear modification factors and find a good agreement between our calculations and the experimental data on J/Psi production in dA collisions. We also observe that cold nuclear modification effects alone cannot describe the data on J/Psi production in AA collisions. Additional final state suppression (at RHIC) and enhancement (at LHC) mechanisms are required …
Using a nonrelativistic potential model, we calculate the cross section for the leading-order gluon dissociation of J/psi by including the full gluon wave function. We find that the resulting cross section as a function of gluon energy is reduced by about a factor of three at its maximum value compared to that calculated in the dipole approximation that is usually adopted in theoretical studies. The effect of the reduced cross section on the J/psi dissociation width at finite temperature is also discussed.
Our approach to low-x deep inelastic scattering based on the ell-perp factorization of perturbative QCD (the color-dipole picture) yields parameter-free absolute predictions for J/Psi production. The connection of J/Psi production to the low-x saturation scale and to the gluon structure function is clarified.
We consider a novel mechanism for J/Psi production in nuclear collisions arising due to the high density of gluons. We calculate the resulting J/Psi production cross section as a function of rapidity and centrality. We evaluate the nuclear modification factor and show that the rapidity distribution of the produced J/Psi's is significantly more narrow in AA collisions due to the gluon saturation effects. Our results indicate that gluon saturation in the colliding nuclei is a significant source of J/Psi suppression that can be disentangled from the quark-gluon plasma effects.
We investigate possible mass shift and width broadening of J/psi in hot gluonic matter using QCD sum rule. Input values of gluon condensates at finite temperature are extracted from lattice QCD data for the energy density and pressure. Although stability of the moment ratio is achieved only up to T/Tc ~ 1.05, the gluon condensates cause a decrease of the moment ratio, which results in change of spectral properties. Using the Breit-Wigner form for the phenomenological side, we find that mass shift of J/psi just above Tc can reach maximally 200 MeV and width can broaden to dozens of MeV.
We explore the effects of shadowing on inclusive J/psi and Upsilon(1S) production at AFTER@LHC. We also present the rates as a function of p_T and rapidity for p+Pb and Pb+p collisions in the proposed AFTER@LHC rapidity acceptance.
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.
It is shown that the study of the ω-ρinterference pattern in the J/psi -> (rho+omega)eta -> pi+pi-eta decay provides evidence for the large (nearly 90 degrees) relative phase between the isovector one-photon and three-gluon decay amplitudes.
The only experimental information on the parton distribution of kaons was obtained from the scarce kaon-induced Drell-Yan cross section data. From these data, evidence for a valence $u$ quark distribution of kaon softer than that of pion was found. We study the feasibility to extract kaon's valence quark distribution via the existing kaon-induced J/psi production data. We compare the NA3 data on the K- / pi- and K+ / pi+ ratios for J/psi production on a platinum target with theoretical calculations based on the color-evaporation model. We show that the NA3 data on J/psi production provide an i…
The gluon-exchange contribution to $J/ψ$-nucleon scattering is shown to yield a sizeable scattering length of about -0.25 fm, which is consistent with the sparse available data. Hadronic corrections to gluon exchange which are generated by $ρπ$ and $D\bar D$ intermediate states of the $J/ψ$ are shown to be negligible. We also propose a new method to study $J/ψ$-nucleon elastic scattering in the reaction $π^+ d\to J/ψp p$.
We estimate the survival probability of $J/ψ$ in relativistic heavy-ion collisions, using both short-distance QCD and nuclear absorption mechanism. The suppression is found to be almost 100 percent for a thermally equilibrating quark-gluon plasma. The measurement of such a huge suppression of $J/ψ$ may suggest the existence of a deconfined partonic medium, possibly a thermalised quark-gluon plasma, at RHIC.
Two decades ago Matsui and Satz suggested that Debye screening in the quark-gluon plasma would result in J/psi suppression in heavy ion collisions. Much has happened in the subsequent years, and the picture of quark-gluon plasma at present is rapidly evolving - what does it imply for the J/psi suppression? What are the recent RHIC and SPS results trying to tell us? What else has to be done? This talk is an attempt to address these questions.
Exclusive J/psi production, gamma* p -> J/psi p, offers a unique opportunity to determine the gluon density of the proton in the small x domain. We use the available HERA data to determine the gluon distribution in the region 10^{-4} <~ x <~ 10^{-2} and 2 <~ Q^2 <~ 10 GeV^2, where the uncertainty on the gluon extracted from the global parton analyses is large. The gluon density is found to be approximately flat at the lower scale; it is compared with those of recent global analyses.
It is argued that the search of the J/psi --> f0(980)omega and J/psi --> a0(980)rho decays and the more precise definition of B(J/psi --> f0(980)phi) are the urgent purposes in the J/ψspectroscopy. It is shown that the study of the omega-rho0 interference pattern in the J/psi --> (ρ^0+ω)eta --> pi+pi-eta decay provides evidence for the large (nearly pi/2) relative phase between the isovector one-photon and three-gluon decay amplitudes .
We consider a contribution to J/psi hadroproduction in which the meson production is mediated by three-gluon partonic state, with two gluons coming from the target and one gluon from the projectile. This mechanism involves double gluon density and thus it enters at a non-leading twist, but it is enhanced at large energies due to large double gluon density at small x. The three-gluon contribution to J/psi hadroproduction is calculated within perturbative QCD in the k_T factorization framework, and it is found to provide a significant correction to the standard leading twist cross-section at the…
The nonlinear effect of gluon depletion in the collision of large nuclei can be large. It is due to multiple scatterings among comoving partons initiated by primary scattering of partons in the colliding nuclei. The effect can give rise to substantial suppression of $J/ψ$ production in very large nuclei, even if the linear depletion effect is insignificant for the collisions of nuclei of smaller sizes. This mechanism offers a natural explanation of the enhanced suppression in the Pb-Pb data recently observed by NA50.
Presented here is a study of the large p_T J/psi production in hard diffractive process by the pomeron exchange at the Fermilab Tevatron. We find that this process (p\bar p \to p+J/psi+X) can be used to probe the gluon content of the pomeron and to measure the gluon fraction of the pomeron. And the diffractive direct J/psi production can also provide another crucial test for the color-octet fragmentation mechanism. Using the renormalised pomeron flux factor D\approx 1/9, the single diffractive J/psi production cross section at large p_T (\geq 8GeV) is found to be of order of 0.01 nb, and the r…
We show that, contrary to recent claims, the $J/ψ$ suppression resulting from its interaction with comovers does not saturate at large transverse energy $E_T$. On the contrary, it shows a characteristic structure - change of curvature near the knee of the $E_T$ distribution - which is due to the $E_T$ (or multiplicity) fluctuation, and agrees with recent experimental results.
We investigate photo-production of vector mesons J/Psi and Psi(2s), based on both HERA and LHC data, using 2 fits of unintegrated gluon distributions. The latter are subject to non-linear Balitsky-Kovchegov evolution (Kutak-Sapeta gluon; KS) and linear next-to-leading order Balitsky-Kuraev-Fadin-Lipatov evolution (Hentschinski-Sabio Vera-Salas; HSS gluon) respectively. Apart from extending previous studies to the case of radially excited charmonium Psi(2s), we further use an improved set of charmonium wave functions and provide an estimate of the uncertainties associated with the HSS gluon. Wh…
We point out that dissociation of J/Psi by partons (mostly gluons) present in the intermediate stage of heavy-ion collisions can explain J/Psi suppression observed recently by the NA-50 Collaboration at the CERN-SPS in Pb-Pb interactions. Suppression by intermediate stage gluons represents an additional multiplicative factor to that given by Gerschel-Hufner mechanism. The agreement with data on J/Psi suppression both in light- ions induced nuclear collisions and in Pb-Pb interactions requires that the life-time of intermediate gluons increases with nucleon numbers of colliding nuclei. In our m…
New, more precise data on diffractive J/psi photoproduction and on exclusive J/psi production in the process pp -> p + J/psi + p at the LHC allow a better constraint on the low-x gluon distribution in the domain of relatively low scales Q^2 ~ 2-6 GeV^2. We account for the `skewed' effect and for the real part of the amplitude, as well as for the absorptive corrections in the case of the exclusive process pp -> p + J/psi + p. The predictions for exclusive J/psi production at \sqrt{s}=8 and 14 TeV and for exclusive Upsilon(1S) production at 7, 8 and 14 TeV are also given. We present results at l…
The modifications induced in the calculation of the cross section of the diffractive process gamma gamma -> J/Psi J/Psi when the gluon propagator is changed are analyzed. Instead of the usual perturbative gluon propagator, alternative forms obtained using non-perturbative methods like Dyson-Schwinger equations are used to consider in a more consistent way the contributions of the infrared region. The result shows a reduction in the differential cross-section for low momentum transfer once compared with the perturbative result, to be confirmed with future experimental results from TESLA.
The depletion of gluons as the parton flux traverses a nucleus in a heavy-ion collision can influence the production rate of heavy-quark states. Thus the suppression of $J/ψ$ can be due to gluon depletion in the initial state in addition to nuclear and hadronic absorption in the final state. A formalism is developed to describe the depletion effect. It is shown that, without constraints from other experimental facts beside the $J/ψ$ suppression data in $pA$ and $AB$ collisions, it is not possible to determine the relative importance of depletion vs absorption. Possible relevance to the enhance…
We update our previous studies of nuclear-matter effects on J/Psi production in proton-nucleus for the recent LHC pPb runs at sqrt(s_NN)=5 TeV. We have analysed the effects of the modification of the gluon PDFs in nucleus, using an exact kinematics for a 2->2 process, namely g+g->J/Psi+g as expected from LO pQCD. This allows to constrain the transverse-momentum while computing the nuclear modification factor for different rapidities, unlike with the usual simplified kinematics. Owing to the absence of measurement in pp collisions at the same sqrt(s_NN) and owing to the expected significant unc…
The eta(1760) may be significantly produced in J/Psi radiative decay. We deduce from experimental data that its branching ratio to two gluons is bounded, 0.4 +- 0.3 < BR(eta(1760) -> gg) < 0.9 +- 0.3, consistent with gluonic admixture. Moreover, the expectation that there should be an isoscalar analogue of the gluonic (hybrid) meson candidate pi(1800) is argued to reinforce hybrid admixture in eta(1760). Two-gluon coupling of hybrids is estimated in a spectator model to be considerably larger than that of quarkonium. In addition, the two-photon coupling of eta(1760) is estimated to be 1.4 +- 0…
Prompt gluons are an additional source for charmonium suppression in nuclear collisions, in particular for nucleus-nucleus collisions. These gluons are radiated as bremsstrahlung in N-N collisions and interact inelastically with the charmonium states while the nuclei still overlap. The spectra and mean number <n_g> of the prompt gluons are calculated perturbatively and the gluon-Psi inelastic cross section is estimated. The integrated cross sections for AB --> J/Psi (Psi')X for p-A and A-B collisions and the dependence on transverse energy for S-U and Pb-Pb can be described quantitatively with…
We review the search for the quark-gluon plasma using the signal of the suppression of J/psi production in high-energy heavy-ion collisions. Recent observations of anomalous J/psi suppression in high-energy Pb-Pb collisions observed by the NA50 Collaboration are examined and compared with earlier results from pA and nucleus-nucleus collisions with heavy ions of smaller mass numbers. The anomalous suppression of J/psi production in Pb-Pb collisions can be explained as due to the occurrence of a new phase of strong J/psi absorption, which sets in when the number of nucleon-nucleon collisions at …
To study the stability of heavy quarkonia in quark-gluon plasma, we use a color-singlet Q-Qbar potential determined previously to be a well-defined linear combination of the free energy F_1 and the internal energy U_1. Using the lattice gauge results of Kaczmarek et al., the dissociation temperatures of J/psi and chi_b in quenched QCD are found to be 1.62Tc and 1.18Tc respectively, in good agreement with spectral function analyses. The dissociation temperature of J/psi in full QCD with 2 flavors is 1.42Tc. Thus, the presence of dynamical quarks in full QCD lowers the dissociation temperature o…
The NA50 Collaboration has recently observed a strong suppression of J/Psi production in Pb-Pb collisions at 158 Gev/n. We show that this recent observation finds a quantitative explanation in a model which relates the suppression mechanism to the local energy density, whose value is higher in Pb-Pb collisions than in any other system studied previously. The sensitivity of the phenomenon to small changes in the energy density could be suggestive of quark-gluon plasma formation.
We study coherent and incoherent diffractive hadron production in high energy quarkonium--heavy nucleus collisions as a probe of the gluon saturation regime of QCD. Taking this process as a model for pA collisions, we argue that the coherent diffractive gluon production, in which the target nucleus states intact, exhibits a remarkable sensitivity to the energy, rapidity and atomic number dependence. The incoherent diffractive gluon production is less sensitive to the details of the low-x dynamics but can serve as a probe of fluctuations in the color glass condensate. As a quantitative measure …
We summarize what is known about the transverse spatial distribution of gluons in the nucleon and its x-dependence from exclusive J/psi photo/electroproduction in e-p fixed-target and collider experiments (HERA H1 and ZEUS). This information can be used to predict the impact parameter dependence of the cross section for certain hard QCD processes (dijet production) in pbar-p and p-p collisions at the Tevatron and LHC.
Cold nuclear matter effects on J/psi production in proton-nucleus and nucleus-nucleus collisions are evaluated taking into account the specific J/psi production kinematics at the partonic level, the shadowing of the initial parton distributions and the absorption in the nuclear matter. We consider two different parton processes for the c-cbar pair production: one with collinear gluons and a recoiling gluon in the final state and the other with initial gluons carrying intrinsic transverse momentum. Our results are compared to RHIC observables. The smaller values of the nuclear modification fact…
We calculate the Wilson coefficients of all dimension 6 gluon operators with non zero spin in the correlation function between two heavy vector currents. For the twist-4 part, we first identify the three independent gluon operators, and then proceed with the calculation of the Wilson coefficients using the fixed point gauge. Together with the previous calculation of the Wilson coefficients for the dimension 6 scalar gluon operators by Nikolaev and Radyushkin, our result completes the list of all the Wilson coefficients of dimension 6 gluon operators in the correlation function between heavy ve…
Diffractive production of J/Psi particles by virtual photons on a proton target is studied with a view towards understanding two important corrections to the leading order result. First, the effect of Fermi motion of the heavy quarks is studied by performing a systematic expansion in the relative velocity, and a simple correction factor is derived. This is considerably less than estimated previously. Second, since the kinematics necessarily requires that non-zero momentum be transferred to the proton, off-forward gluon distributions are probed by the scattering process. To estimate the importa…
The production and space-time evolution of heavy quarks and J/psi in the quark gluon plasma is studied within the partonic transport model Boltzmann Approach to MultiParton Scatterings (BAMPS). This framework allows interactions among all partons: gluons, light quarks and heavy quarks. Heavy quarks, in particular, interact with the rest of the medium via binary scatterings with a running coupling and a more precise Debye screening which is derived from hard thermal loop calculations. We compare our results of the elliptic flow and nuclear modification factor not only to experimental data of he…
The gluon density in nuclei, G^A(x), is poorly constrained at all x from the current DIS and Drell-Yan data. In this paper, we point out that J/psi production measured in proton-nucleus collisions at sqrt(s)=38.8 GeV by the E866 collaboration puts stringent constraints on the x-dependence of the G^W/G^Be ratio in the x=0.02-0.1 range. The E866 data suggest a rather mild x-dependence of G^W/G^Be, and consequently tend to favour DS and HKM sets, rather than the DSg, EKS, and EPS parametrizations which exhibit a large shadowing and anti-shadowing.
The gluon distribution of a nucleon propagating through a nucleus can change depending on how far the penetration depth is. It is a nonperturbative process that we describe by an evolution equation. The kernel of the integral equation is to be determined by a phenomenological study of J/psi suppression in pA collision. The data of E866 on alpha(x_F) shows significant dependence on x_F at large x_F. It presents a feature that has not been explained by any hadronic absorption model. We show that gluon depletion is a simple mechanism that can account for it. The result has far-reaching implicatio…
The experimental results on the pion, strangeness and J/psi production in high energy nuclear collisions are discussed. The anomalous energy dependence of pion and strangeness production is consistent with the hypothesis that a transition to a deconfined phase takes place between the top AGS (15 AGeV) and the SPS (200 AGeV) energies. The J/psi production systematics at the SPS can be understood assuming that the J/psi mesons are created at hadronization according to the available hadronic phase space. This new interpretation of the J/psi data allows one to establish a coherent picture of high …
Color-octet contributions to the associate J/psi+gamma hadroproduction are studied in detail, and found to be negligible, compared to the ordinary color-singlet contribution. Within the color-singlet model the J/psi+gamma production in the leading order is possible only through gluon-gluon fusion process. Therefore, the associate J/psi+gamma hadroproduction remains to be useful as a clean channel to probe the gluon distribution inside proton, to study heavy quarkonia production mechanism, and to find proton's spin structure.
We discuss the potential to constrain the small-$x$ PDFs using the exclusive production of heavy vector mesons. The calculation of $J/ψ$ and $Υ$ photoproduction at NLO in collinear factorisation is described. The different behaviour of the NLO corrections for $J/ψ$ and $Υ$ is highlighted and we outline what might be expected from the inclusion of these processes in a PDF fit.
The upcoming p+Pb run at the LHC will probe the nuclear gluon distribution at very small Bjorken x (from $x \sim 10^{-4}$ at mid-rapidity down to $x \sim 10^{-6}$ in the proton fragmentation region) and will allow to test approaches based on parton saturation. Here, we present the predictions of the KLN model for hadron multiplicities and multiplicity distributions in p+Pb collisions at a center-of-mass energy of 4.4 TeV. We also compare the model to the existing pp, dA and AA data from RHIC and LHC.
We modified the gluon saturation model by rescaling the momentum fraction according to saturation momentum and introduced the Cooper-Frye hydrodynamic evolution to systematically study the pseudo-rapidity distributions of final charged hadrons at different energies and different centralities for Au-Au collisions in relativistic heavy-ion collisions at BNL Relativistic Heavy Ion Collider (RHIC). The features of both gluon saturation and hydrodynamic evolution at different energies and different centralities for Au-Au collisions are investigated in this paper.
We consider the contribution of radially excited 2^3P_{1,2} states to psi^prime production at the Tevatron energy. Production of these states via the conventional gluon fusion mechanism and via gluon and charm quark fragmentation processes is considered. We find that it is possible to account for the data on psi^prime production from the CDF experiment, by taking into account the decays of these 2^3P_{1,2} states into psi^prime.
We examine angular distributions of leptons arising from the decay of J/psi in inclusive hadroproduction. Taking into account feed-down contributions from chi_{1,2}, a flat distribution emerges without fine tuning parameters. Changes in the ratio of direct to total J/psi cross sections would change this distribution significantly. Such angular distributions are, therefore, confirmatory tests of the J/psi suppression signal for the production of a quark-gluon plasma. Related effects are predicted for the Upsilon.
We show that, in the saturation/Color Glass Condensate framework, odd azimuthal harmonics of the two-gluon correlation function with a long-range separation in rapidity are generated by the higher-order saturation corrections in the interactions with the projectile and the target. At the very least, the odd harmonics require three scatterings in the projectile and three scatterings in the target. We derive the leading-order expression for the two-gluon production cross section which generates odd harmonics: the expression includes all-order interactions with the target and three interactions w…
We study the diffractive electroproduction of quarkonia from quark-antiquark-gluon states in the photon wave function. We show that these states contribute to the leading-power and leading-logarithm level. We suggest the measurement of J/psi production via inelastic diffraction to study color-transparency and color-opacity effects in the diffractive gluon distribution.
We consider the J/Psi production in proton (deuteron) -- nucleus collisions at high energies. We argue that the production mechanism in this case is different from that in pp collisions due to gluon saturation in the nucleus and formation of the Color Glass Condensate. At forward rapidities (in the proton fragmentation region), the production of J/Psi is increasingly suppressed both as a function of rapidity and centrality. On the other hand, at backward rapidities at RHIC (in the fragmentation region of the nucleus) the coherent effects lead to a modest enhancement of the production cross sec…
In order to get information about the polarized gluon distribution in a proton, we studied the electroproduction of ψ' in polarized electron and polarized proton collisions in the framework of the NRQCD factorization approach. The value of the cross section dΔσ/ dp_T^2 for color-octet mechanism is about 5 times larger than that for color-singlet one, and it might be another test of the color-octet model if the polarized gluon distribution Δg(x) is well known. Furthermore, we found that this reaction is quite effective for testing the model of gluon polarization by measuring the double spin asy…
We investigate the masses of the lowest c\bar{c} states, the J/psi and eta_c, in nuclear matter using QCD sum rules. Up to dimension four, the differences between the operator product expansions in vacuum and in medium arise from the density-dependent change in the gluon condensate and from a new contribution proportional to the nucleon expectation value of the twist-2 gluon operator. Both terms together give an attractive shift of about 5-10 MeV to the J/psi and eta_c masses in nuclear matter.
We study properties of high energy factorisable gluon densities focusing on saturation effects. In particular we show that the property of saturation of unintegrated gluon density allows for introduction of thermodynamical entropy associated with production of gluons. This is due to the observation that saturation scale acts like a mass of a gluon which related with temperature via thermodynamical relations allows for calculations of entropy. We also show that obtained entropy behaves like multiplicity of produced gluons.
Using a bound-state model of weakly bound gluons for glueballs made of two gluons and a natural generalization of the perturbative QCD formalism for exclusive hadronic processes, we present results for glueball production in radiative J/psi, Upsilon decays into several possible glueball states, including L \not= 0 ones. We perform a detailed phenomenological analysis, presenting results for the more favored experimental candidates and for decay angular distributions.
We study saturation effects in the production of dijets in p-p and p-Pb collisions using the framework of high energy factorization. We focus on central-forward jet configurations, which allow for probing gluon density at low longitudinal momentum fraction. We find significant suppression of the central-forward jet decorrelations in p-Pb compared to p-p, which we attribute to saturation of gluon density in nuclei.
We compute the contributions to large-$p_T$ $J/ψ$ production at HERA coming from fragmentation of gluons and charm quarks. We find that the charm quark fragmentation contribution dominates over the direct production of $J/ψ$ via photon-gluon fusion at large-$p_T$, while the gluon fragmentation is negligibly small over the whole range of $p_T$. An experimental study of $p_T$ distributions of $J/ψ$ at HERA will provide a direct probe of the charm quark fragmentation functions.
We study the charmonium suppression in different evolutions of quark gluon plasma (QGP) based on the transport model. In the colliding energies of Large Hadron Collider, charmonium final yields are dominated by the recombination of charm and anti-charm quarks in the deconfined phase. Heavy quark diffusions depend less on the shear viscosity of the bulk medium, which makes the J/psi nuclear modification factor in the entire pT bin shows weak dependence on the shear viscosity of QGP. However, charmonium with high transverse momentum pT, can only be produced in the early stage of nuclear collisio…
The reaction γγ---> J/Psi J/Psi is discussed assuming dominance of the QCD BFKL pomeron exchange. We give prediction for the cross-section of this process for LEP2 and TESLA energies. We solve the BFKL equation in the non-forward configuration taking into account dominant non-leading effects which come from the requirement that the virtuality of the exchanged gluons along the gluon ladder is controlled by their transverse momentum squared. We compare our results with those corresponding to the simple two gluon exchange mechanism and with the BFKL pomeron exchange in the leading logarithmic app…
We extract the pole positions, hadronic and gamma-gamma widths of sigma and f_0(980, from pi-pi and gamma-gamma scattering data using an improved analytic K-matrix model. Our results favour a large gluon component for the sigma and a \bar ss or/and gluon component for the f_0(980) but neither a large four-quark nor a molecule component. Gluonium sigma_B production from J/psi, phi radiative and D_s semi-leptonic decays are also discussed.
Using the color-singlet free energy F_1 and total internal energy U_1 obtained by Kaczmarek et al. for a static quark Q and an antiquark Qbar in quenched QCD, we study the binding energies and wave functions of heavy quarkonia in a quark-gluon plasma. By minimizing the grand potential in a simplified schematic model, we find that the proper color-singlet Q-Qbar potential can be obtained from the total internal energy U_1 by subtracting the gluon internal energy contributions. We carry out this subtraction in the local energy-density approximation in which the gluon energy density can be relate…
