Quarkonium suppression in relativistic heavy ion collisions has been studied experimentally for decades to probe the properties of the quark-gluon plasma. For this purpose, complete theoretical understanding of the time evolution of quarkonium inside the quark-gluon plasma is needed but challenging. Here I review recent progress in applying the open quantum system framework to describe the real-time dynamics of quarkonium, with a focus on the gauge-invariant chromoelectric field correlators of the plasma that control the dynamics.
A model for the production of quarkonium states in the midrapidity region at RHIC and LHC energy range is presented which explores well understood properties of QCD only. An increase of the quarkonium hadronisation time with the initial energy leads to a gradual change of the most important phenomena from fixed target- to collider-energies. We evaluate nuclear effects in the quarkonium production due to medium modification of the momentum distribution of the heavy quarks produced in the hard interactions, i.e. due to the broadening of the transverse momentum distribution. Other nuclear effects…
Heavy quarkonium suppression was proposed long ago as a signal of the formation of a deconfined phase in heavy ion collisions. Originally the mechanism responsible for this suppression was thought to be color screening. However perturbative computations and recent lattice studies suggest the existence of an imaginary part of the potential which could have a more important role for suppression than screening. In this work we review some general aspects of effective field theories for heavy quarkonium in the medium and discuss the physical phenomena behind the imaginary part of the potential and…
Many prior studies of in-medium quarkonium suppression have implicitly made use of an adiabatic approximation in which it was assumed that the heavy quark potential is a slowly varying function of time. In the adiabatic limit, one can separately determine the in-medium breakup rate and the medium time evolution, folding these together only at the end of the calculation. In this paper, we relax this assumption by solving the 3d Schrodinger equation in real-time in order to compute quarkonium suppression dynamically. We compare results obtained using the adiabatic approximation with real-time ca…
The effects of parton energy loss in cold nuclear matter on heavy-quarkonium suppression in p-A collisions are studied. It is shown from first principles that at large quarkonium energy E and small production angle in the nucleus rest frame, the medium-induced energy loss scales as E. Using this result, a phenomenological model depending on a single free parameter is able to reproduce J/psi and Upsilon suppression data in a broad xF-range and at various center-of-mass energies. These results strongly support energy loss as the dominant effect in heavy-quarkonium suppression in p-A collisions. …
The effect of parton energy loss in cold nuclear matter on the suppression of quarkonia (J/psi, Upsilon) in heavy-ion collisions is investigated, by extrapolating a model based on coherent radiative energy loss recently shown to describe successfully J/psi and Upsilon suppression in proton-nucleus collisions. Model predictions in heavy-ion collisions at RHIC (Au-Au, Cu-Cu, and Cu-Au) and LHC (Pb-Pb) show a sizable suppression arising from the sole effect of energy loss in cold matter. This effect should thus be considered in order to get a reliable baseline for cold nuclear matter effects in q…
Quarkonium production in proton-nucleus collisions is a powerful tool to disentangle cold nuclear matter effects. A model based on coherent energy loss is able to explain the available quarkonium suppression data in a broad range of rapidities, from fixed-target to collider energies, suggesting cold energy loss to be the dominant effect in quarkonium suppression in p-A collisions. This could be further tested in a high-energy fixed-target experiment using a proton or nucleus beam. The nuclear modification factors of J/$ψ$ and $Υ$ as a function of rapidity are computed in p-A collisions at $\sq…
The nuclear suppression of heavy quarkonium production at low transverse momentum in pA collisions in high energy scatterings is investigated in the small-x factorization formalism. A universal suppression is found in the large Nc limit between the two formalisms to describe the heavy quarkonium production: the non-relativistic QCD (NRQCD) and the color-evaporation model (CEM). This provides an important probe to the saturation momentum at small-x in big nucleus. We also comment on the phenomenological applications of our results.
I discuss quarkonium suppression in equilibriated strongly interacting matter. After a brief review of basic features of quarkonium production I discuss the application of recent lattice data on the heavy quark potential to the problem of quarkonium dissociation as well as the problem of direct lattice determination of quarkonium properties in finite temperature lattice QCD.
Heavy quarkonium theory has seen significant progress over the past years. Not only has the community steadily improved the understanding of fully equilibrated quarkonium using first principles lattice QCD studies, but it has taken major steps towards developing a genuine dynamical understanding of quark-antiquark pairs immersed in a hot medium by embracing the paradigm of open quantum systems. We review recent developments, placing an emphasis on quarkonium real-time dynamics.
The suppression of quarkonium production in nucleus-nucleus collisions was originally proposed as a signal of colour deconfinement. Strong ``anomalous" J/ψsuppression in Pb-Pb collisions has been reported at this Conference by the NA50 Collaboration. Is this suppression really anomalous? Can we conclude that the quark-gluon plasma is already discovered? What has to be done next? I address these questions basing on the current theoretical understanding of quarkonium production and new precise experimental information.
We use recent lattice data on the heavy quark potential in order to determine the dissociation temperatures of different quarkonium states in hot strongly interacting matter. Our analysis shows in particular that certain quarkonium states dissociate below the deconfinement point.
Many of the hadron-hadron cross sections required for the study of the dynamics of matter produced in relativistic heavy-ion collisions can be calculated using the quark-interchange model. Here we evaluate the low-energy dissociation cross sections of $J/ψ$, $ψ'$, $χ$, $Υ$, and $Υ'$ in collision with $π$, $ρ$, and $K$, which are important for the interpretation of heavy-quarkonium suppression as a signature for the quark gluon plasma. These comover dissociation processes also contribute to heavy-quarkonium suppression, and must be understood and incorporated in simulations of heavy-ion collisi…
We address the evolution of heavy-quarkonium states in an expanding quark-gluon plasma by implementing effective field theory techniques in the framework of open quantum systems. In this setting we compute the nuclear modification factors for quarkonia that are $S$-wave Coulombic bound states in a strongly-coupled quark-gluon plasma. The calculation is performed at an accuracy that is leading-order in the heavy-quark density expansion and next-to-leading order in the multipole expansion. The quarkonium density-matrix evolution equations can be written in the Lindblad form, and, hence, they acc…
About 40-50 % of the quarkonium ground states J/psi(1S) and Upsilon(1S) produced in hadronic collisions originate from the decay of higher excitations. In a hot medium, these higher states are dissociated at lower temperatures than the more tightly bound ground states, leading to a sequential suppression pattern. Using new finite temperature lattice results, we specify the in-medium potential between heavy quarks and determine the dissociation points of different quarkonium states. On the basis of recent CDF data on bottomonium production, we then obtain first predictions for sequential Upsilo…
Modifications in the production pattern of heavy quark bound states have long been considered to provide sensitive signatures for the thermal properties of dense matter created in heavy ion collisions. The original concept of Matsui and Satz for quarkonium suppression as signature for deconfinement in heavy ion collisions has been challenged recently through lattice studies of spectral functions, which indicate the persistence of heavy quark bound states at temperatures well above the transition, as well as through the refined analysis of hadronization and recombination models, which take into…
The study of heavy quarkonium suppression in heavy-ion collisions represents an important source of information about the properties of the quark-gluon plasma produced in such collisions. In a previous paper, we have considered how to model the evolution of a quarkonium in such a way that the solution of the resulting equations evolves toward the correct thermal equilibrium distribution for an homogeneous and static medium. We found that it is crucial to take into account the energy gap between singlet and octet configurations when the temperature is not much greater than this energy gap. In t…
We introduce a framework called Heavy Quarkonium Quantum Dynamics (HQQD) which can be used to compute the dynamical suppression of heavy quarkonia propagating in the quark-gluon plasma using real-time in-medium quantum evolution. Using HQQD we compute large sets of real-time solutions to the Schrödinger equation using a realistic in-medium complex-valued potential. We sample 2 million quarkonia wave packet trajectories and evolve them through the QGP using HQQD to obtain their survival probabilities. The computation is performed using three different HQQD model parameter sets in order to estim…
The geometric clustering of partons in the transverse plane of nuclear collisions leads for increasing A or sqrt(s) to percolation. In the resulting condensate, the partons are deconfined but not yet in thermal equilibrium. We discuss quarkonium dissociation in this precursor of the quark-gluon plasma, with an onset of dissociation when the saturation scale of the parton condensate reaches that of the given quarkonium state.
We study the energy and nuclear A dependence of the hadronic production of heavy quarkonia. We review theoretical ideas which have been put forward, seeking a consistent global picture reconciling the large effects in quarkonia with the small nuclear effects observed in continuum Drell Yan production. The data indicates that shadowing or leading twist modifications of parton distributions can be ruled out as explanations, leaving higher twist energy loss. {}From general principles the maximum allowed energy loss of partons traversing the nuclear medium can be related to the parton transverse m…
A dense parton system is expected to be formed in the early stage of relativistic heavy-ion collisions at RHIC energies and above. The probability of a quark gluon plasma production and the resulting strength of its signatures depends strongly on the initial conditions associated to the distributions of partons in the nuclear wave functions. At very high energies, the growth of parton distributions should saturate, possibly forming a Color Glass Condensate, which is characterized by a bulk momentum scale $Q_s$. As a direct consequence, the possible signatures of the QGP should be $Q_s$-depende…
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 ana…
The entropic approach to dissociation of bound states immersed in strongly coupled systems is developed. In such systems, the excitations of the bound state are often delocalized and characterized by a large entropy, so that the bound state is strongly entangled with the rest of the statistical system. If this entropy $S$ increases with the separation $r$ between the constituents of the bound state, $S = S(r)$, then the resulting entropic force $F = T\ {\partial S}/{\partial r}$ ($T$ is temperature) can drive the dissociation process. As a specific example, we consider the case of heavy quarko…
We perform a comprehensive study of the time evolution of heavy-quarkonium states in an expanding hot QCD medium by implementing effective field theory techniques in the framework of open quantum systems. The formalism incorporates quarkonium production and its subsequent evolution in the fireball including quarkonium dissociation and recombination. We consider a fireball with a local temperature that is much smaller than the inverse size of the quarkonium and much larger than its binding energy. The calculation is performed at an accuracy that is leading-order in the heavy-quark density expan…
Quarkonium suppression is one of the more useful observables to obtain information about the hot medium created in ultrarelativistic heavy-ion collisions. In this manuscript, we discuss a simple way to implement both the initial-state effects and the hot-medium evolution, and to compute the quarkonium nuclear modification factor if the survival probability for a bound state at a given energy density is known. Based on the Glauber model, the temperature of the evolving medium and the centrality dependence of the nuclear modification factor will be analysed.
Color screening versus thermal decay as the mechanism of $Υ$ suppression in high energy nuclear collisions
Tianjin University（天津大学）；Helmholtz Research Academy Hesse for FAIR (HFHF), GSI Helmholtz Center for Heavy Ion Physics, Campus Frankfurt（黑森亥姆霍兹FAIR研究院，GSI重离子物理中心法兰克福校区）；Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität（约翰·沃尔夫冈·歌德大学理论物理研究所）；Yantai University（烟台大学）；Tsinghua University（清华大学）；South Center for Nuclear-Science Theory, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院现代物理研究所核科学理论南方中心）
We calculate the heavy quarkonium energy levels and decay widths in a quark-gluon plasma, whose temperature T and screening mass m_D satisfy the hierarchy m alpha_s >> T >> m alpha_s^2 >> m_D (m being the heavy-quark mass), at order m alpha_s^5. We first sequentially integrate out the scales m, m alpha_s and T, and, next, we carry out the calculations in the resulting effective theory using techniques of integration by regions. A collinear region is identified, which contributes at this order. We also discuss the implications of our results concerning heavy quarkonium suppression in heavy ion …
In this proceedings contribution, I review recent work that aims to provide a more comprehensive and systematic understanding of bottomonium dynamics in the quark-gluon plasma using an open quantum system (OQS) approach that is applied in the framework of the potential non-relativistic QCD (pNRQCD) effective field theory and coupled to realistic hydrodynamical backgrounds that have been tuned to soft hadron observables. I review how the computation of bottomonium suppression can be reduced to solving a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation for the evolution of the b-bbar reduce…
We anticipate new features of quarkonium production in heavy ion collisions at RHIC and LHC energies which differ from a straightforward extrapolation of results at CERN SPS energy. General arguments indicate that one may expect quarkonium formation rates to increase more rapidly with energy and centrality than the production rate of the heavy quarks which they contain. This is due to new formation mechanisms in which independently-produced quarks and antiquarks form a bound quarkonium state. This mechanism will depend quadratically on the total number of initially-produced heavy quark pairs, …
These proceedings are dedicated to Miklos Gyulassy's 70$^{\rm th}$ birthday. In his long and distinguished career he has made seminal contributions to many areas of heavy ion theory, including early papers on quarkonium phenomenology in fixed-target heavy ion experiments. Theoretical and experimental studies of the $J/ψ$ and $Υ$ states have evolved considerably in the past decades, and I describe a recent generalization of non-relativistic Quantum Chromodynamics to include interactions in a generic nuclear medium. NRQCD with Glauber gluons aims to provide a universal microscopic description of…
At RHIC the cross section for c-cbar production will be large enough such that approximately 10 pairs will be produced in each central collision. If a region of deconfined quarks and gluons is subsequently formed, one would expect that the mobility of the charm quarks will enable them to form J/Psi through "off-diagonal" combinations, involving a quark and an antiquark which were originally produced in separate incoherent interactions. We present model estimates of this effect, which indicate that the signal for deconfinement at RHIC may possibly be J/Psi enhancement rather than suppression.
In this proceedings contribution I review recent progress concerning the suppression of bottomonium production in the quark-gluon plasma. Making use of open quantum system methods applied to potential non-relativistic quantum chromodynamics one can show that the dynamics of heavy-quarkonium bound states satisfying the scale hierarchy 1/a_0 >> pi T ~ m_D >> E obey a Lindblad equation whose solution provides the quantum evolution of the heavy-quarkonium reduced density matrix. To solve the resulting Lindblad equation we use a quantum trajectories algorithm which allows one to include all possibl…
Quarkonium suppression in heavy ion collisions is a potential signature of the formation of the quark-gluon plasma. After a very brief review of the J/psi result at CERN, we restrict our discussion to the effects of the high-energy multiple scattering of the quark pair in the colliding nuclei.
Using the open quantum system formalism and effective field theory of QCD, we derive the Boltzmann transport equation of quarkonium inside the quark-gluon plasma. Our derivation illuminates that the success of transport equations in quarkonium phenomenology is closely related to the separation of scales in the problem.
Heavy quarkonium continues to play a central role in the study of nuclear matter under extremes of temperature and density in relativistic heavy-ion collisions. In this talk I report on recent developments in the theoretical description of quarkonium in-medium dynamics using the open-quantum systems approach. Not only does it provide a clear interpretation of the imaginary part of the complex heavy-quark potential but also reveals that a subtle interplay between screening and wavefunction decoherence is responsible for the melting of heavy quarkonium states.
Using the variational method and supersymmetric quantum mechanic we calculate in a approximate way eigenvalues, eigenfunctions and wave functions at origin of Cornell potential. We compare results with numerical solutions for heavy quarkonia $c\bar{c}$, $b\bar{b}$ y $b\bar{c}$.
We study an effect of the off-shellness of the quark and antiquark inside a heavy quarkonium system on IR renormalons contained in the perturbative computations of the quarkonium energy levels. We demonstrate that, when the off-shellness p_Q^2 -m_Q^2 \sim alpha_S^2 m_Q^2 is larger than m_Q Lambda_QCD, renormalons in the energy levels as calculated in perturbative QCD are suppressed by a factor Lambda_QCD/alpha_S^2 m_Q as compared to those in 2 m_pole + V_QCD(r). In this case the residual O(Lambda_QCD^4) renormalon has the same dimension as that of the leading gluon-condensate contribution.
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.
Recent results from proton(deuteron)-nucleus collisions at RHIC and LHC energies have shown an unexpected suppression of excited quarkonium states as compared to their ground states. In particular, stronger suppression of the $ψ(2S)$ relative to the $J/ψ$ has been detected. Similar observations were made at lower energies and were easily explained by nuclear absorption. At higher energies, a similar explanation would violate the Heisenberg principle, since the calculations based on the uncertainty principle lead to a charmonium formation time expected to be larger than the nuclear radius, whic…
We introduce an open-source package called QTraj that solves the Lindblad equation for heavy-quarkonium dynamics using the quantum trajectories algorithm. The package allows users to simulate the suppression of heavy-quarkonium states using externally-supplied input from 3+1D hydrodynamics simulations. The code uses a split-step pseudo-spectral method for updating the wave-function between jumps, which is implemented using the open-source multi-threaded FFTW3 package. This allows one to have manifestly unitary evolution when using real-valued potentials. In this paper, we provide detailed docu…
Two-pion transitions in charmonium and bottomonium are considered with the leading relativistic effects taken into account. The contribution of the chromo- magnetic interaction of the charmed quarks to the amplitude of the decay $ψ(2S) \to ππJ/ψ$ is estimated from the available data. This contribution is enhanced by a factor of three in the decay $η_c(2S) \to ππη_c$ and should produce a noticeable modification of the rate and the spectrum in the latter decay. It is argued that the peculiar observed spectrum in the decay $Υ(3S) \to ππΥ$ arises due to a dynamical suppression of the leading nonre…
Lindblad-driven quarkonium production in heavy-ion collisions
Instituto Galego de Física de Altas Enerxías IGFAE, Universidade de Santiago de Compostela（加利西亚高能物理研究所，圣地亚哥-德孔波斯特拉大学）；Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos, Universitat de Barcelona（量子物理与天体物理系及宇宙科学研究所，巴塞罗那大学）
The measurements of heavy quarkonium suppression at RHIC and LHC urge theory to develop intuitive as well as quantitative methods for the description of $Q\bar{Q}$ melting in the quark-gluon plasma. Here I will present a brief sketch on the effective field theory strategies underlying the definition of the heavy quark static potential and report on two recent advances in the extraction and interpretation of such a potential. On the one side, progress has been made in obtaining its values from lattice QCD, which promises to make possible investigating its real and imaginary part non-perturbativ…
We discuss the quarkonium production as a tool for the study of the Quark Gluon Plasma. In particular, we concentrate on the Cold Nuclear Matter effetcs. We show that quarkonium production is also useful for the study of Quantum Chromodynamics first principles and the nuclear Parton Distribution Functions.
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 …
Substantial anisotropies should occur in the hot expanding QCD plasma produced in relativistic heavy-ion collisions due to non-vanishing shear viscosity. We discuss the form of the real-time, hard thermal loop resummed propagator for static gluons in the presence of such anisotropies and the consequences for quarkonium binding. It has been predicted that the propagator develops an imaginary part due to Landau damping at high temperature. This generates a much larger width of quarkonium states than the Appelquist-Politzer vacuum estimate corresponding to decay into three gluons. We argue that t…
Dissociation of quarkonium in quark-gluon plasma (QGP) is a long standing topic in relativistic heavy-ion collisions because it has been believed to signal one of the fundamental natures of the QGP -- Debye screening due to the liberation of color degrees of freedom. Among recent new theoretical developments is the application of open quantum system framework to quarkonium in the QGP. Open system approach enables us to describe how dynamical as well as static properties of QGP influences the time evolution of quarkonium in a coherent way. Currently, there are several master equations for quark…
We review weakly-bound heavy quarkonium systems using effective field theories of QCD. We concentrate on potential Non-Relativistic QCD, which provides with a well founded connection between QCD and descriptions of the heavy quarkonium dynamics in terms of Schrödinger-like equations. This connection is obtained using standard quantum field theory techniques such as dimensional regularization, which is used throughout, and renormalization. Renormalization group equations naturally follow. Certain effort is made to illustrate how computations are performed and the necessary techniques, providing…
We calculate the transition between a quarkonium state and an unbound heavy quark-antiquark pair through gluo-dissociation and inelastic parton scattering using a partonic picture that interpolates between the formal limits based on potential nonrelativistic QCD (pNRQCD) at different temperatures. While the thermal width increases with momentum and temperature, the quarkonium regeneration is affected by the heavy quark distribution function which depends on the diffusion constant. By solving the Boltzmann equation with the dissociation and regeneration terms, we investigate the medium modifica…
By coupling the Boltzmann transport equations of both quarkonium and open heavy quarks, we investigate their dynamical evolution inside the quark-gluon plasma and study quarkonium production in heavy ion collisions. The Boltzmann transport equation of quarkonium is derived from the open quantum system formalism and effective field theory of QCD by assuming quarkonium interacts weakly with the plasma. The dissociation and recombination terms in the Boltzmann equation are calculated in potential nonrelativistic QCD. It is shown that the combination of quarkonium dissociation, recombination, open…
Broad meson phenomenology in vacuum is discussed in a single model containing scalar, pseudoscalar, vector and axial-vector states both in the non-strange and strange sectors. Emphasis is given to search for quark-antiquark (quarkonium) states in the scalar and axial-vector channels. In particular, the work examines the question whether the scalar quark-antiquark states are found in the energy region below or above 1 GeV in the physical spectrum. Contrarily to the naive expectation, the mentioned states are found in the region above 1 GeV. Additionally, the axial-vector isotriplet state $a_1(1…
