We compute the energy loss of heavy quarkonia in high temperature QCD plasmas and investigate the energy loss effects on quarkonium suppression. Based on the effective vertex derived from the Bethe-Salpeter amplitude for quarkonium, the collisional and radiative energy loss are determined by quarkonium-gluon elastic scattering and the associated gluon-bremsstrahlung, respectively. In the energy regime $E<m_Υ^2/T$ the collisional energy loss is dominant over the radiative one, and the total energy loss increases with the plasma temperature and the initial energy of quarkonium. Our numerical analysis indicates that the medium-induced energy loss of the $Υ$(1S) results in stronger suppression at higher momentum, although the energy loss effects are found to be small compared with the previous estimates of quarkonium dissociation in heavy-ion collisions.
In this paper we review recent progress towards understanding the nature of quarkonia in the quark-gluon plasma. We review the theory necessary to understand the melting of bound states due to color-screening, including lattice results for the heavy quark potential, lattice results on the correlation functions related to the relevant spectral functions, and the emergence of a complex-valued potential in high-temperature quantum chromodynamics. We close with a brief survey of phenomenological models of quarkonium suppression in relativistic heavy ion collisions.
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…
Master equations of the Lindblad type have recently been derived to describe the dynamics of quarkonium states in the quark-gluon plasma. Because their full resolution in three dimensions is very challenging, the equations are often reduced to one dimension. The main ingredient of these equations is the complex potential that describes the binding of the heavy quark-antiquark pairs and their interactions with the medium. In this work, we propose a one-dimensional complex potential parameterized to reproduce at best two key properties -- the temperature-dependent masses of the eigenstates and t…
Using the potential model and thermodynamical quantities obtained in lattice gauge calculations, we determine the spontaneous dissociation temperatures of color-singlet quarkonia and the `quark drip lines' which separate the region of bound $Q\bar Q$ states from the unbound region. The dissociation temperatures of $J/ψ$ and $χ_b$ in quenched QCD are found to be 1.62$T_c$ and $1.18T_c$ respectively, in good agreement with spectral function analyses. The dissociation temperature of $J/ψ$ in full QCD with 2 flavors is found to be 1.42$T_c$. For possible bound quarkonium states with light quarks, …
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 revisit the transport coefficients of heavy quarkonia moving in high-temperature QCD plasmas. The thermal width and mass shift for heavy quarkonia are closely related to the momentum diffusion coefficient and its dispersive counterpart for heavy quarks, respectively. For quarkonium at rest in plasmas the longitudinal gluon part of the color-singlet self-energy diagram is sufficient to determine the leading-order thermal width, whereas the momentum dependence is obtained from the transverse gluon channel. Using the quarkonium-gluon effective vertex based on the dipole interaction of color ch…
The melting of a heavy quark-antiquark bound state depends on the screening phenomena associated with the binding energy, as well as scattering phenomena associated with the imaginary part of the potential. We study the imaginary part of the static potential of heavy quarkonia moving in the strongly coupled plasma. The imaginary potential dependence on the velocity of the traveling bound states is calculated. Non-zero velocity leads to increase of the absolute value of the imaginary potential. The enhancement is stronger when the quarkonia move orthogonal to the quark-gluon plasma maximizing t…
The fate of heavy quarkonia states has been investigated in QCD at high temperature when the plasma has a small momentum space anisotropy within a quasi-particle model. A real time static potential has been obtained from a Hard thermal loop expression for the gluon self-energy, by employing the quasi-parton equilibrium distribution functions extracted from hot QCD equations of state of $O(g^5)$ and $O(g^6\ln(1/g))$. Employing the potential, quarkonia melting has been studied. It is found that the equations of state and the momentum anisotropy cause significant modifications in the screening pr…
The gauge/gravity duality is used to investigate the imaginary part of the heavy quark potential (defined via the rectangular Wilson loop) in strongly coupled plasmas. This quantity can be used to estimate the width of heavy quarkonia in a plasma at strong coupling. In this paper the thermal worldsheet fluctuation method, proposed in [J.Noronha and A.Dumitru, Phys.\ Rev.\ Lett.\ {\bf 103}, 152304 (2009)], is revisited and general conditions for the existence of an imaginary part for the heavy quark potential computed within classical gravity models are obtained. We prove a general result that …
The in-medium physics of heavy quarkonium is an ideal proving ground for our ability to connect knowledge about the fundamental laws of physics to phenomenological predictions. One possible route to take is to attempt a description of heavy quark bound states at finite temperature through a Schroedinger equation with an instantaneous potential. Here we review recent progress in devising a comprehensive approach to define such a potential from first principles QCD and extract its, in general complex, values from non-perturbative lattice QCD simulations. Based on the theory of open quantum syste…
We study the properties of quarkonia inside a bulk-viscous quark gluon plasma. The non-equilibrium nature of the medium is encoded in the deformed distribution functions of thermal quarks and gluons, with which we compute the dielectric permittivity within the hard thermal loop approximation at one-loop. The modified dielectric permittivity is used to calculate the in-medium heavy quark potential, and using the potential we compute spectral functions, which reflect the physical properties of heavy quarkonia. We discuss how the bulk viscous effect influences quantities such as binding energies …
In relativistic heavy ion collisions at RHIC and the LHC, a quark gluon plasma (QGP) is created for a short duration of about 10fm/c. Quarkonia (bound states of $c\bar{c}$ and $b\bar{b}$) are sensitive probes of this phase on length scales comparable to the size of the bound states which are less than 1fm. Observations of quarkonia in these collisions provide us with a lot of information about how the presence of a QGP affects various quarkonium states. This has motivated the development of the theory of heavy quarks and their bound states in a thermal medium, and its application to the phenom…
We summarize results of recent studies of heavy quarkonia correlators and spectral functions at finite temperatures from lattice QCD and systematic T-matrix studies using QCD motivated finite-temperature potentials. We argue that heavy quarkonia dissociation shall occur in the temperature range $1.2 \le T_d/T_c \le 1.5$ by the interplay of both screening and absorption in the strongly correlated plasma medium. We discuss these effects on the quantum mechanical evolution of quarkonia states within a time-dependent harmonic oscillator model with complex oscillator strength and compare the result…
We study the properties of heavy quarkonia in a quark-gluon plasma in the presence of bulk viscous effects. Within the hard thermal loop approximation at one-loop, the dielectric permittivity of quark-gluon plasma is computed, where the bulk viscous effect enters through the deformation of the distribution functions of thermal quarks and gluons. Based on the modified dielectric permittivity, we compute the in-medium heavy quark potential, that includes non-pertubative string-like terms as well as the perturbative Coulombic term. We discuss how the bulk viscous effect modifies the real and imag…
The present article is the follow up work of, Phys.\ Rev.\ D {\bf 94}, 094006 (2016), where we have extended the study of quarkonia dissociation in (momentum) anisotropic hot QCD medium. As evident by the experimentally observed collective flow at RHIC and LHC, the momentum anisotropy is present at almost all the stages after the collision and therefore, it is important to include its effects in the analysis. Employing the in-medium (corrected) potential while considering the anisotropy (both oblate and prolate cases) in the medium, the thermal widths and the binding energies of the heavy quar…
The problem of the evolution of a heavy quarkonium in a medium can be recast as that of a quantum dissipative system. Within the framework of the master-equation approach to open quantum systems, we consider the real-time dynamics of quarkonia. We find that in a plasma at fixed temperature, the populations of the various quarkonium states evolve together, while their momentum distribution satisfies a Fokker-Planck equation.
For heavy quarkonia of moderate energy, we generalize the relevant successful theory, non-relativistic Quantum Chromodynamics (NRQCD), to include interactions in nuclear matter. The new resulting theory, NRQCD with Glauber gluons, provides for the first time a universal microscopic description of the interaction of heavy quarkonia with a strongly interacting medium, consistently applicable to a range of phases, such as cold nuclear matter, dense hadron gas, and quark-gluon plasma. The effective field theory we present in this work is derived from first principles and is an important step forwa…
Recent analyses show that it is possible to produce a strong magnetic field at a very early stage of ultrarelativistic heavy ion collisions (URHIC), therefore, the effect of homogeneity and constant strong magnetic field on the heavy meson spectrum quarkonium is studied which the states are described as charmonium and bottominum in a non-relativistic framework and by Debye screen potential. In particular, a model that takes into account potential isotopes emerging at the level of quark-static potential, as has been observed in recent studies. Investigation is performed with and without regard …
According to the usual application of the sequential-suppression picture to the dynamics of heavy quarkonia in the hot medium formed in ultrarelativistic nuclear collisions, quark-antiquark pairs created in a given bound or unbound state remain in that same state as the medium evolves. We argue that this scenario implicitly assumes an adiabatic evolution of the quarkonia, and we show that the validity of the adiabaticity assumption is questionable.
The imaginary part of the heavy quark-antiquark potential experienced by moving heavy quarkonia in strongly coupled plasmas dual to theories of gravity is computed by considering thermal worldsheet fluctuations of the holographic Nambu-Goto string. General results for a wide class of gravity duals are presented and an explicit formula for $\mathrm{Im} \, V_{Q\bar{Q}}$ is found in the case where the axis of the moving $\bar{Q}Q$ pair has an arbitrary orientation with respect to its velocity in the plasma. These results are applied to the study of heavy quarkonia propagating through a strongly c…
We investigate the Mott effect for heavy quarkonia due to Debye screening of the heavy quark potential in a plasma of massless quarks and antiquarks. The influence of residual color correlation is investigated by coupling the light quark sector to a temporal gauge field driven by the Polyakov loop potential. This leads to an increase of the Mott dissociation temperatures for quarkonia states which stabilizes in particular the excited states, but has marginal effect on the ground states. The temperature dependence of binding energies suggests that the dissciation of the charmonium (bottomonium)…
Quarkonium production has been considered as a tool to study the medium formed in high energy nuclear collisions, assuming that the formation of a hot and dense environment modifies the production pattern observed in elementary collisions. The basic features measured there are the relative fractions of hidden to open heavy flavor and the relative fractions of the different hidden heavy flavor states. Hence the essential question is if and how these quantities are modified in nuclear collisions. We show how the relevant data must be calibrated, i.e., what reference has to be used, in order to d…
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…
We aim to describe the process of dissociation and recombination of quarkonia in the quark-gluon plasma. Therefore we developed a model which allows to observe the time evolution of a system with various numbers of charm-anticharm-quark pairs at different temperatures. The motion of the heavy quarks is realized within a Langevin approach. We use a simplified version of a formalism developed by Blaizot et al. in which an Abelian plasma is considered where the heavy quarks interact over a Coulomb like potential. We have demonstrated, that the system reaches the expected thermal distribution in t…
The N-radial Schrödinger equation is analytically solved by using SUSYQM method, in which the heavy quarkonia potential is introduced at finite temperature and baryon chemical potential. The energy eigenvalue is calculated in the N-dimensional space. The obtained results show that the binding energy strongly decreases with increasing temperature and is slightly sensitive for changing baryon chemical potential up to 0.6 GeV at higher values of temperatures. We employed the nonperturbative corrections to the leading-order of the Debye mass at finite baryon chemical potential. We found that the b…
The problem of quarkonium production in heavy ion collisions presents a set of unique theoretical challenges -- from the relevant production mechanism of $J/ψ$ and $Υ$ to the relative significance of distinct cold and hot nuclear matter effects in the observed attenuation of quarkonia. Inthese proceedings we summarize recent work on the generalization of non-relativistic Quantum Chromodynamics (NRQCD) to include off-shell gluon (Glauber/Coulomb) interactions in strongly interacting matter. This new effective theory provides for the first time a universal microscopic description of the in-mediu…
We develop a framework of coupled transport equations for open heavy flavor and quarkonium states, in order to describe their transport inside the quark-gluon plasma. Our framework is capable of studying simultaneously both open and hidden heavy flavor observables in heavy-ion collision experiments and can account for both, uncorrelated and correlated recombination. Our recombination implementation depends on real-time open heavy quark and antiquark distributions. We carry out consistency tests to show how the interplay among open heavy flavor transport, quarkonium dissociation and recombinati…
Recently a lot of progress has been made in deriving the heavy quark potential within a QCD medium. In this article we have considered heavy quarkonium in a hot quark gluon plasma phase. The heavy-quark potential has been modeled properly for short as well as long distances. The potential at long distances is modeled as a QCD string which is screened at the same scale as the Coloumb field. We have numerically solved the 1+1-dimensional Schrodinger equation for this potential and obtained the eigen wavefunction and binding energy for the $1S$ and $2S$ states of charmonium and bottomonium. Furth…
Emphasizing the possibility of moderate suppression of heavy quarkonium states, we invite some attention towards the issue of real time evolution of quarkonia during the cooling phase of quark gluon plasma(QGP). In this context, we have used time dependent perturbation theory to show that $Υ(1S)$, $Υ(2S)$, $J/Ψ$ can further be dissociated in the medium at a temperature below their dissociation thresholds even though they survive the Debye screening. We have presented and compared the dissociation probabilities and dissociation rates of these states in real and complex valued potential in this …
I address the effect that a temperature dependent potential has on the suppression of heavy quarkonia states in deconfined hadronic matter. I focus on a simple medium: a homogenous, fixed temperature and deconfined system with a finite lifetime (QGP-brick). Assuming that all the interactions of a heavy quark anti-quark ($Q-\bar Q$) pair with the medium can be recast into an in-medium potential, I solve the time dependent Schrödinger equation to evolve the density matrix which describes the hard pair production and its connection to the final distribution of hadrons after the medium disappears.…
Using the chromo-electric dipole coupling Hamiltonian from QCD multipole expansion, we derive the dissociation cross sections of heavy quarkonia by thermal gluons at next-to-leading order (NLO, also known as inelastic parton scattering dissociation) in the Quark-Gluon Plasma (QGP) in the framework of second order quantum mechanical perturbation theory. While suffering divergence (infrared and soft-collinear divergences) in vacuum, the cross sections thus derived become finite in the QGP as rendered by the finite thermal gluon masses. In contrast to the leading order (LO, also known as gluo-dis…
We investigate the real-time evolution of quarkonium bound states in a quark-gluon plasma in one dimension using an improved QCD based stochastic potential model. This model describes the quarkonium dynamics in terms of a Schrödinger equation with an in-medium potential and two noise terms encoding the residual interactions between the heavy quarks and the medium. The probabilities of bound states in a static medium and in a boost-invariantly expanding quark-gluon plasma are discussed. We draw two conclusions from our results: One is that the outcome of the stochastic potential model is qualit…
We present a modified colour screening model for $J/ψ$ suppression in the Quark-Gluon Plasma (QGP) using quasi-particle model (QPM) as equation of state (EOS). Other theoretical ingredients incorporated in the model are feed-down from higher resonances namely, $χ_c$, and $ψ^{'}$, dilated formation time for quarkonia and viscous effects of the QGP medium. Assuming further that the QGP is expanding with Bjorken's hydrodynamical expansion, the present model is used to analyze the centrality dependence of the $J/ψ$ suppression in mid-rapidity region and compare it with the data obtained from SPS, …
The spectroscopic properties of heavy quarkonia are substantially different in the quark-gluon plasma (QGP) that is created in relativistic heavy-ion collisions as compared to the vacuum situation that can be tested in pp collisions at the same center-of-mass energy. In this article, a series of recent works about the dissociation of the Y(nS) and chi_b(nP) states in the hot QGP is summarized. Quarkonia dissociation occurs due to (1) screening of the real quark-antiquark potential, (2) collisional damping through the imaginary part of the potential, and (3) gluon-induced dissociation. In addit…
Quarkonium suppression is one of the most investigated probes of the medium produced in heavy-ion collisions. In this thesis we extend the well-established and successful zero temperature framework of Non-Relativistic (NR) Effective Field Theories (EFTs) (NRQCD, pNRQCD) for the study of heavy quarkonia (production, spectroscopy, decays, ...) to finite temperatures. This is achieved by integrating out in sequence the scales that characterize a NR bound state and those that are typical of a thermal medium, in the possible hierarchies that are relevant for quarkonia in the quark-gluon plasma. Wit…
We study different processes responsible for the modification of quarkonia yields in the medium produced in PbPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV. The quarkonia and heavy flavour cross sections are estimated using the measurements in pp collisions at LHC energies and shadowing corrections are obtained using the EPS09 parametrizations. A kinetic model is used which incorporates quarkonia suppression inside the Quark Gluon Plasma (QGP), suppression due to hadronic comovers, and regeneration from recombination of heavy quark pairs. The quarkonia dissociation cross section due to gluon col…
I review recent applications of the open quantum system framework in the understanding of quarkonium suppression in heavy-ion collisions, which has been used as a probe of the quark-gluon plasma for decades. The derivation of the Lindblad equations for quarkonium in both the quantum Brownian motion and the quantum optical limits and their semiclassical counterparts is explained. The hierarchy of time scales assumed in the derivation is justified from the separation of energy scales in nonrelativistic effective field theories of QCD. Physical implications of the open quantum system approach are…
Measurements made at the LHC have shown that the production of the ${\rm J}/ψ$, $ψ$(2S), $Υ$(1S) and $Υ$(2S) quarkonia is suppressed in Pb-Pb collisions, with respect to the extrapolation of the pp production yields. The $ψ$(2S) and $Υ$(2S) states are more strongly suppressed than the ground states and the level of the suppression changes with the centrality of the collision. We show that the measured patterns can be reproduced by a simple model, where all quarkonia are treated in a unified way, starting from the recent realisation that, in pp collisions, the probability of quarkonium formatio…
In the present work, we have studied heavy quarkonia potential in hot and magnetized quark gluon plasma. Inverse magnetic catalysis (IMC) effect is incorporated within the system through the magnetic field modified Debye mass by modifying the effective quark masses. We have obtained the real and imaginary part of the heavy quark potential in this new scenario. After the evaluation of the binding energy and the decay width we comment about the dissociation temperatures of the heavy quarkonia in presence of magnetic field.
We investigate the Mott effect for heavy quarkonia due to Debye screening of the heavy quark potential in a plasma of massless quarks and antiquarks. The influence of residual color correlation is investigated by coupling the light quark sector to a temporal gauge field driven by the Polyakov loop potential. This leads to an increase of the Mott dissociation temperatures for quarkonia states which stabilizes in particular the excited states, but has marginal effect on the ground states.
We derive an expression for the heavy quark damping rate in hot quark gluon plasma in presence of flow. Here all the bath particles here are out of equilibrium due to the existence of non-zero velocity gradient. The magnetic sector shows similar infrared divergences even after hard thermal loop corrections as one encounters in case of non-viscous plasma. We estimate the first order correction in ($η/s$) for heavy quark damping rate due to the non-zero viscosity of the QCD plasma.
We review the progress achieved in extracting the properties of hot and dense matter from relativistic heavy ion collisions at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory and the large hadron collider (LHC) at CERN. We focus on bulk properties of the medium, in particular the evidence for thermalization, aspects of the equation of state, transport properties, as well as fluctuations and correlations. We also discuss the in-medium properties of hadrons with light and heavy quarks, and measurements of dileptons and quarkonia. This review is dedicated to the memor…
Melting of heavy quarkonia in QGP using deep neural networks
Key Laboratory of Quark and Lepton Physics (MOE) & Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室及粒子物理研究所）；Artificial Intelligence and Computational Physics Research Center, Central China Normal University（华中师范大学人工智能与计算物理研究中心）；Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) & Institute of Modern Physics, Fudan University（复旦大学核物理与离子束应用教育部重点实验室及现代物理研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学的上海理论核物理研究中心）
We extend a previous work on the study of heavy charmonia and bottomonia in a deconfined quark-gluon plasma by considering the Bc family of mesons. With the introduction of this bound state of a charm and a beauty quark, we investigate at finite temperature the behavior of the quarkonium, in an energy region between the ψ and the Υ states.
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 calculate the bound state properties of $J/ψ$ in a hot and dense QCD plasma using phenomenological potentials augmented by inputs from perturbative QCD. The temperature and density region of study will be relevant in future heavy ion collision experiments at FAIR. We find that the effect of baryon density on the dissociation of $J/ψ$ is small in this regime. However we indicate that if there is a critical end point in the QCD phase diagram then strong density fluctuation will dissociate charmonia near hadronization. The measurement of $J/ψ$ suppression can therefore signify the existence of…
We calculate the free energy of a hot gluon plasma to leading order in hard-thermal-loop perturbation theory. Effects associated with screening, gluon quasiparticles, and Landau damping are resummed to all orders. The ultraviolet divergences generated by the hard-thermal-loop propagator corrections can be cancelled by a temperature-independent counterterm. The deviation of the hard-thermal-loop free energy from lattice QCD results for T > 2 T_c has the correct sign and roughly the correct magnitude to be accounted for by next-to-leading order corrections.
We show how hot QCD equations of states can be adapted to make definite predictions for quark-gluon plasma at RHIC. We consider equations of state up to $O(g^5)$ and $O[g^6(ln(1/g)+δ)]$. Our method involves the extraction of equilibrium distribution functions for gluons and quarks from these equations of state by capturing the the interaction effects entirely in the effective chemical potentials. We further utilize these distribution functions to study the screening length in hot QCD and dissociation phenomenon of heavy quarkonia states by combining this understanding with the semi-classical t…
