The growing consensus that a strongly-coupled quark-gluon plasma (sQGP) has been observed at the SPS and RHIC experiments suggests a different framework for examining heavy quark dynamics. We present both semi-analytical treatment of Fokker-Planck (FP) evolution in pedagogical examples and numerical Langevin simulations of evolving charm quark-antiquark pairs on top of a hydrodynamically expanding fireball. In this way, we may conclude that the survival probability of bound charmonia states is greater than previously estimated, as the spatial equilibration of pairs proceeds through a ``slowly dissolving lump'' stage related to the pair interaction.
Parameterizing the charm and anticharm quark momentum distributions by the Tsallis distribution, we study the nonequilibrium effect on the charmonium production rate in a quark-gluon plasma up to the next-to-leading order in perturbative QCD. We find that nonequilibrium charm and anticharm quarks suppress the charmonium production rate compared to that from equilibrated ones. We further show that the suppression factor calculated with the charm quark relaxation time, which has been frequently used in the literature, is close to our results.
We employ a time-dependent Schrödinger equation to study the evolution of a $c\bar c$ dipole in a quark-gluon plasma (QGP). Medium effects on the heavy-quark potential in the QGP are found to significantly affect the timescales of the internal evolution of the dipole. Color-screening can enhance the overlap of the expanding wavepackage with excited states at high temperature, while it is reduced at lower temperatures where the dipole favors the formation of the charmonium ground state. We investigate the consequences of this mechanism on the double ratio of charmonium nuclear modification fact…
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…
The available data on $J/Ψ$ photoproduction are analyzed in terms of pomeron exchange, two gluon exchange and photon-gluon fusion models. Allowing the pomeron-quark interaction to be flavour dependent and introducing the soft and hard pomerons it is possible to reproduce the data at $\sqrt{s}{>}$10 GeV and small $|t|$. The two gluon exchange calculations indicate strong sensitivity to the gluon distribution function. The results obtained with the most modern MRST2001 and DL PDF reproduce the forward $J/Ψ$ photoproduction cross section at $\sqrt{s}{>}$10 GeV. The calculations with the photon-gl…
We study electromagnetic field effect on charmonium gluon-dissociation in quark-gluon plasma. With the effective Hamiltonian derived from QCD multipole expansion under an external electromagnetic field, we first solve the two-body Schrödinger equation for a pair of charm quarks with mean field potentials for color and electromagnetic interactions and obtain the charmonium binding energies and wave functions, and then calculate the gluon-dissociation cross-section and decay width by taking the color electric and magnetic dipole interactions as perturbations above the mean field and employing Fe…
We update our previous work of a Langevin-with-interaction model for charmonium in heavy-ion collisions, by considering the effect due to recombination. We determine the contribution to J/psi yields from charm-anticharm pairs whose constituent quarks originate from two different hard processes. Like the surviving J/psi states, the recombinant J/psi also undergo both a stochastic interaction, determined by a hydrodynamical simulation of the heavy-ion collision, and an interaction determined by the heavy quark-antiquark potentials measured on the lattice for appropriate temperatures. From the re…
In relativistic heavy ion collisions, also the bremsstrahlung of gluons in the fragmentation regions of the nuclei suppresses the produced charmonium states. In the energy range of the SPS, the radiation of semi-hard gluons occurs in the Bethe-Heitler regime and the density of gluons and therefore the suppression goes like $(AB)^{1\over3}$, where $A$ and $B$ are the nucleon numbers of the projectile and target nuclei. In contrast, the suppression via collisions with nucleons is proportional to $(A^{1\over3} + B^{1\over3})$. Parameter free perturbative QCD calculations are in a good agreement w…
We review the statistical hadronization picture for charmonium production in ultra-relativistic nuclear collisions. Our starting point is a brief reminder of the status of the thermal model description of hadron production at high energy. Within this framework an excellent account is achieved of all data for hadrons built of (u,d,s) valence quarks using temperature, baryo-chemical potential and volume as thermal parameters. The large charm quark mass brings in a new (non-thermal) scale which is explicitely taken into account by fixing the total number of charm quarks produced in the collision.…
We have investigated the charmonium survival probability, in a high baryon density parton plasma, expected to be produced in nuclear collisions at FAIR. Charmonia are assumed to undergo complete dissociation by color screening, if the in-medium Debye radius becomes comparable to the spatial size of the corresponding bound state. Results indicate a non-trivial dependence of the suppression pattern on the plasma evolution dynamics. A much larger magnitude of suppression is foreseen induced by cold nuclear matter compared to that due to plasma screening.
Charmonium directed flows are studied based on transport model coupled with the realistic three dimensional expansions of the bulk medium. The non-central symmetric nucleus-nucleus collisions can generate the rotating quark-gluon plasma (QGP) with symmetry-breaking longitudinal distributions. In $\sqrt{s_{NN}}=200$ GeV Au-Au semi-central collisions, charmonium are primordially produced in the initial hard process, they are mainly dissociated by the initial tilted source with high temperatures and then move out of the bulk medium to keep the early information of the medium. Charmonia are less a…
We study the effect of thermal charm production on charmonium regeneration in high energy nuclear collisions. By solving the kinetic equations for charm quark and charmonium distributions in Pb+Pb collisions, we calculate the global and differential nuclear modification factors $R_{AA}(N_{part})$ and $R{AA}(p_t)$ for $J/Ψ$s. Due to the thermal charm production in hot medium, the charmonium production source changes from the initially created charm quarks at SPS, RHIC and LHC to the thermally produced charm quarks at Future Circular Collider (FCC), and the $J/Ψ$ suppression ($R_{AA}<1$) observe…
In ultra-relativistic heavy-ion collisions, the strong electric field can be produced by the colliding nuclei. The magnitude of the electric field $E$ is on the order of $eE\sim m_π^2$ at the early stage of the collision. In quark gluon plasma (QGP), such a strong electric field can have a significant impact on the evolution of charmonia. We employ the time-dependent Schrödinger equation to study the evolution of charmonium states in the strong electric field generated by the moving charges. The electric field can result in transitions between charmonium states with different angular momenta. …
Starting from an earlier representation of the independent dimension 6 gluon operators in terms of color electric and magnetic fields, we estimate their changes near the critical temperature $T_c$ using the temperature dependence of the dimension 4 electric and magnetic condensates extracted from pure gauge theory on the lattice. We then improve the previous QCD sum rules for the $J/ψ$ mass near $T_c$ based on dimension 4 operators, by including the contribution of the dimension 6 operators to the OPE. We find an enhanced stability in the sum rule and confirm that the $J/ψ$ will undergo an abr…
In the first part of the talk, we briefly review the problem of parton-energy loss and thermalization at the Relativistic Heavy-Ion Collider and discuss how heavy quarks (charm and bottom) can help to resolve the existing experimental and theoretical puzzles. The second part of the talk is devoted to the properties of heavy quarkonia in the (strongly interacting) Quark-Gluon Plasma (sQGP) and their consequences for observables in heavy-ion collisions.
We investigate mass shifts of charmonia driven by change of the gluon condensate below but near transition temperatures at finite baryonic chemical potential. Extending previous prescription on the relation between gluon condensates and thermodynamic quantities, we model the gluon condensates of hadronic matter at finite temperature and baryonic chemical potential such that the scalar gluon condensate fits with the latest lattice QCD data. By making use of the QCD sum rule and the second order Stark effect, we find that the smoother transition in the full QCD can lead to moderate mass shifts o…
We study the charmonium coherent photoproduction and hadroproduction consistently with modifications from both cold and hot nuclear matters. The strong electromagnetic fields from fast moving nucleus interact with the other target nucleus, producing abundant charmonium in the extremely low transverse momentum region $p_T<0.1$ GeV/c. This results in significative enhancement of $J/ψ$ nuclear modification factor in semi-central and peripheral collisions. In the middle $p_T$ region such as $p_T<3\sim 5$ GeV/c, $J/ψ$ final yield is dominated by the combination process of single charm and anti-char…
The evaluation of quarkonium regeneration in ultrarelativistic heavy-ion collisions (URHICs) requires the knowledge of the heavy-quark phase space distributions in the expanding quark-gluon plasma (QGP) fireball. We employ a semi-classical charmonium transport approach where regeneration processes explicitly account for the time-dependent spectra of charm quarks via Langevin simulations of their diffusion. The inelastic charmonium rates and charm-quark transport coefficients are computed from the same charm-medium interaction. The latter is modeled by perturbative rates, augmented with a $K$-f…
All measured Feynman x_f distributions of the ratio, R, of j_psi production in nuclei relative to production on protons fall off with x_f. They show [2] that absorption of charmonium cannot be the only source of j_psi suppression and that energy loss of the constituents of the incident proton prior to the j_psi production, because of the exponential sqrt(s) dependence of the charmonium cross section, should not be neglected. Including the effects of initial state energy loss we find that the latest measured Pb-Pb j_psi cross sections do not provide any evidence for deconfinement.
We suggest the variation of charmonium suppression with Feynman x_F in heavy ion collisions as a novel and sensitive probe for the properties of the matter created in such reactions. In contrast to the proton-nucleus case where nuclear suppression is weakest at small x_F, final state interactions with the comoving matter create a minimum at x_F=0, which is especially deep and narrow if a quark-gluon plasma is formed. While a particularly strong effect is predicted at SPS, at the higher RHIC energy it overlaps with the expected sharp variation with x_F of nuclear effects and needs comparison wi…
We study vacuum masses of charmonia and the charm-quark diffusion coefficient in the quark-gluon plasma based on the spectral representation for meson correlators. To calculate the correlators, we solve the quark gap equation and the inhomogeneous Bethe-Salpeter equation in the rainbow-ladder approximation. It is found that the ground-state masses of charmonia in the pseudoscalar, scalar, and vector channels can be well described. For $1.5\,T_c<T<3.0\,T_c$, the value of the diffusion coefficient $D$ is comparable with that obtained by lattice QCD and experiments: $3.4<2πTD<5.9$. Relating the d…
We study the properties of charmonium in a strongly coupled QCD-like plasma at finite momentum. As a basis for this study, a "bottom-up" holographic model is used which has been previously shown to reproduce charmonium phenomenology in vacuum and give a reasonable dissociation temperature at zero momentum. The finite momentum spectral functions are presented and found to be consistent with recent lattice results. The in-medium dispersion relation and momentum dependence of decay width of J/Psi have also been studied. We find no signature of a subluminal limiting velocity from the dispersion re…
Charmonium production in heavy-ion collisions is investigated within a kinetic theory framework incorporating in-medium properties of open- and hidden-charm states in line with recent QCD lattice calculations. A continuously decreasing open-charm threshold across the phase boundary of hadronic and quark-gluon matter is found to have important implications for the equilibrium abundance of charmonium states. The survival of $J/ψ$ resonance states above the transition temperature enables their recreation also in the Quark-Gluon Plasma. Including effects of chemical and thermal off-equilibrium, we…
We follow Quark-gluon transport theory and analyse singularities of the ultra-relativistic and spherical expanding quark-gluon plasma. Within the linearized QCD oscillations and instabilities of the ultra-relativistic and spherical symmetric expanding quark-gluon plasma near global thermodynamical equilibrium are investigated in dependence on a chemical potential mu(T) of non-strange light quarks and antiquarks, a strange quark mass m_s, a temperature T and a hydrodynamical velocity $u$. We calculate the chromoelectric permeability tensor for the quark-gluon plasma at rest and ultra-relativist…
In this short review we summarize experimental information and theoretical results for the low-energy dissociation cross sections of charmonia by light hadrons. These cross sections are required for the simulation of charmonium absorption through collisions with comovers in heavy ion collisions, which competes with quark-gluon plasma production as a charmonium-suppression mechanism. If the cross sections are sufficiently large these dissociation reactions may be misinterpreted as an effect of quark-gluon plasma production. Theoretical predictions for these RHIC-related processes have used vari…
A selfconsistent calculation of heavy-quark (HQ) and quarkonium properties in the Quark-Gluon Plasma (QGP) is conducted to quantify flavor transport and color screening in the medium. The main tool is a thermodynamic $T$-matrix approach to compute HQ and quarkonium spectral functions in both scattering and bound-state regimes. The $T$-matrix, in turn, is employed to calculate HQ selfenergies which are implemented into spectral functions beyond the quasiparticle approximation. Charmonium spectral functions are used to evaluate eulcidean-time correlation functions which are compared to results f…
An elementary introduction to the physics of quark-gluon plasma is given. We start with a sketchy presentation of the Quantum Chromodynamics which is the fundamental theory of strong interactions. The structure of hadrons built up of quarks and gluons is briefly discussed with a special emphasis on the confinement hypothesis. Then, we explain what is the quark-gluon plasma and consider why and when the hadrons can dissolve liberating the quarks and gluons. The heavy-ion collisions at high-energies, which provide a unique opportunity to get a droplet of the quark-gluon plasma in the terrestrial…
Pressure isotropization of an equilibrating quark-gluon plasma produced in relativistic heavy ion collisions is studied within the framework of a multi-phase transport model (AMPT). The time evolution of the bulk properties of the quark-gluon plasma is found to depend on its expansion dynamics and hadronization scheme as well as the scattering cross sections among quarks and gluons. It is further found that the pressure isotropy of the produced quark-gluon plasma can only be achieved temporarily, indicating that there is only partial thermalization during the time evolution of the quark-gluon …
The present article is the follow-up of our work Bottomonium suppression in quasi-particle model, where we have extended the study for charmonium states using quasi-particle model in terms of quasi-gluons and quasi quarks/antiquarks as a equation of state. By employing medium modification to a heavy quark potential thermodynamic observables {\em viz.} pressure, energy density, speed of sound etc. have been calculated which nicely fit with the lattice equation of state for gluon, massless and as well {\em massive} flavored plasma. For obtaining the thermodynamic observables we employed the deby…
We investigate how charmonium hadroproduction at fixed-target energies can be used to constrain the gluon distribution in pions. Using nonrelativistic QCD (NRQCD) formulation, the $J/ψ$ and $ψ(2S)$ cross sections as a function of longitudinal momentum fraction $x_F$ from pions and protons colliding with light targets, as well as the $ψ(2S)$ to $J/ψ$ cross section ratios, are included in the analysis. The color-octet long-distance matrix elements are found to have a pronounced dependence on the pion parton distribution functions (PDFs). This study shows that the $x_F$ differential cross section…
We have developed a hydrodynamic model to study sequential melting of charmonium states in an expanding QGP medium. According to the initial fluid temperature profile, $J/ψ$'s are randomly distributed in the transverse plane. As the fluid evolve in time, the free streaming $J/ψ$'s are suppressed if the local fluid temperature exceed a critical temperature. PHENIX data on the centrality dependence of $J/ψ$ suppression in Au+Au collisions at mid-rapidity are explained by sequential melting of the charmonium states, $χ_c$, $ψ\prime$ and $J/ψ$, in the expanding medium. The critical temperatures $T…
We calculate rapidity and transverse momentum distributions of charmonium formed in high energy heavy ion collsions from incoherent recombination of charm quarks. The results are very sensitive to the corresponding distributions of the charm quarks, and thus can serve as a probe of the state of matter produced in the heavy ion collision. At one extreme we generate a set of charm pair momenta directly from pQCD amplitudes, which are appropriate if one can neglect interaction of the quarks with the medium. At the other extreme we generate momenta of charm quarks in thermal equilibrium with the e…
Using the two-component model that includes charmonium production from initial nucleon-nucleon hard scattering and regeneration in the produced quark-gluon plasma, we study $J/ψ$ production in heavy ion collisions at SPS, RHIC and LHC. For the expansion dynamics of produced hot dense matter, we use a schematic viscous hydrodynamic model with the specific shear viscosity taken, respectively, to be twice and ten times the lower bound of $1/4π$ suggested by the Ads/CFT correspondence in the quark-gluon plasma and in the hadron gas. For the initial dissociation and the subsequent thermal decay of …
The production of charmonium in heavy-ion collisions is investigated based on Boltzmann-type transport model for charmonium evolution and langevin equation for charm quark evolution. Charmonium suppression and regeneration in both quark-gluon plasma (QGP) and hadron phase are considered. Charm quarks are far from thermalization, and regeneration of charmonium in QGP and hadron gas is neglectable at SPS and FAIR. At peripheral collisions, charmonium suppression with hadron gas explains the experimental data well. But at central collisions, additional suppression from deconfined matter (QGP) is …
Heavy quark and charmonium production as well as their space-time evolution are studied in transport simulations of heavy-ion collisions at RHIC and LHC. In the partonic transport model Boltzmann Approach of MultiParton Scatterings (BAMPS) heavy quarks can be produced in initial hard parton scatterings or during the evolution of the quark-gluon plasma. Subsequently, they interact with the medium via binary scatterings with a running coupling and a more precise Debye screening which is derived from hard thermal loop calculations, participate in the flow and lose energy. We present results of th…
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…
We show that the extensively studied equation of state (EOS) of strongly coupled QED plasma fits the recent lattice EOS data of gluon plasma remarkably well, with appropriate modifications to take account of color degrees of freedom and running coupling constant. Hence we conclude that the quark gluon plasma near the critical temperature is a strongly coupled color-Coulombic plasma.
Contrary to almost standard opinion that the X(3872) resonance is the D^{*0}\bar D^0+c.c. molecule or the qc\bar q\bar c four-quark state, we discuss the scenario where the X(3872)resonance is the c\bar c = χ_{c1}(2P) charmonium which "sits on" the D^{*0}\bar D^0 threshold. We explain the shift of the mass of the X(3872) resonance with respect to the prediction of a potential model for the mass of the χ_{c1}(2P) charmonium by the contribution of the virtual D^*\bar D+c.c. intermediate states into the self energy of the X(3872) resonance. This allows us to estimate the coupling constant of the …
By considering the Debye screening and damping rate of gluons, the viscosity coefficient of the quark-gluon plasma was evaluated via real-time finite temperature QCD in the relaxation time approximation at finite temperature and chemical potential . The results show that both the damping rate and the chemical potential cause considerable enhancements to the viscosity coefficient of hot dense quark-gluon plasma.
We study the radiative correction to $p_T$-broadening of a fast quark in a quark-gluon plasma beyond the soft gluon approximation. We find that the radiative processes can suppress considerably $p_T$-broadening. This differs dramatically from previous calculations to logarithmic accuracy in the soft gluon approximation, predicting a considerable enhancement of $p_T$-broadening.
Chromodynamic fluctuations in the collisionless quark-gluon plasma are found as a solution of the initial value linearized problem. The stable and unstable plasmas are discussed.
Brief review of the hadronic probes that are used to diagnose the quark-gluon plasma produced in relativistic heavy ion collisions and interrogate its properties. Emphasis is placed on probes that have significantly impacted our understanding of the nature of the quark-gluon plasma and confirmed its formation.
We study a smooth crossover transition in the gas of quark-gluon bags. The equation of state at high temperature is that of the quark-gluon plasma. However, the system consists of the bags with finite volumes which are defined by the model parameters of the mass-volume bag spectrum. Possible structures in this {\it cluster} quark-gluon plasma are classified.
A calculation of the thermal quark propagator is presented taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator is derived.
We present a calculation of the thermal quark propagator taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator, describing two massive modes, is discussed.
We study the color randomization of two-gluon states produced after splitting of a primary fast gluon in the quark-gluon plasma. We find that for the LHC conditions the color randomization of the $gg$ pairs is rather slow. At jet energies $E=100$ and $500$ GeV, for typical jet path length in the plasma in central Pb+Pb collisions, the $SU(3)$-multiplet averaged color Casimir of the $gg$ pair differs considerably from its value $2N_c$ for a fully randomized $gg$ state. Our calculations of the energy dependence for generation of the nearly collinear decuplet $gg$ states, that can lead to the bar…
The implications of a numerical error in the photon production rate on the direct photon spectrum of a chemically non-equilibrated quark-gluon plasma are discussed.
The density of states and energy spectrum of the gluon radiation are calculated for the color current of an expanding hydrodynamic skyrmion in the quark gluon plasma with a semiclassical method. Results are compared with those in literatures.
The quark-gluon plasma, possibly created in ultrarelativistic heavy-ion collisions, is a strongly interacting many-body parton system. By comparison with strongly coupled electromagnetic plasmas (classical and non-relativistic) it is concluded that the quark-gluon plasma could be in the liquid phase. As an example for a strongly coupled plasma, complex plasmas, which show liquid and even solid phases, are discussed briefly. Furthermore, methods based on correlation functions for confirming and investigating the quark-gluon-plasma liquid are presented. Finally, consequences of the strong coupli…
We study the behavior of the scalar glueball inside a Quark Gluon Plasma. We follow the fireball from the plasma phase to the hadronic phase and observe that an interesting phenomenon might occur which could have experimental consequences as a signature of Quark Gluon Plasma.
Initially produced quark-gluon matter at RHIC and LHC does not have a temperature. A quark-gluon plasma has a high temperature. From this quark-gluon matter to the quark-gluon plasma is the early thermalization or the rapid creation of temperature. Elastic three-parton scattering plays a key role in the process. The temperature originates from the two-parton scattering, the three-parton scattering, the four-parton scattering and so forth in quark-gluon matter.
Using a temperature-dependent potential obtained from lattice gauge calculations, we study the stability of heavy quarkonia in the quark-gluon plasma. We find that only the Upsilon(1S) and the eta_b(1S) are bound in the quark-gluon plasma, and have a small binding energy. The quark-gluon plasma may be revealed by an Upsilon(1S) dilepton peak with an invariant mass close to twice the current b quark mass, which is lower than the Upsilon(1S) mass in free space. The quarkonia Upsilon(1S) and eta_b(1S) can dissociate by collision with quarks and gluons in the quark-gluon plasma. We evaluate the di…
We suggest a new mechanism for the energy loss of fast heavy quarks in quark-gluon plasma. This mechanism is based on pion production caused by the anomalous chromomagnetic quark-gluon-pion interaction induced by strong topological fluctuations of the gluon fields represented by instantons. We found that this mechanism gives a considerable contribution to the collisional energy loss of a heavy quark in quark-gluon plasma, which shows a nontrivial role of nonperturbative phenomena in strongly interacting quark-gluon plasma.
