We study quarkonium spectral functions at high temperatures using potential model with complex potential. The real part of the potential is constrained by the lattice QCD data on static quark anti-quark correlation functions, while the imaginary part of the potential is taken from perturbative calculations. We find that the imaginary part of the potential has significant effect on quarkonium spectral functions, in particular, it leas to the dissolution of the 1S charmonium and excited bottomonium states at temperatures about 250 MeV and melting of the ground state bottomonium at temperatures slightly above 450 MeV.
We study quarkonium correlators and spectral functions at zero and finite temperature using the anisotropic Fermilab lattice formulation with anisotropy xi=2 and 4. To control cutoff effects we use several different lattice spacings. The spectral functions were extracted from lattice correlators with Maximum Entropy Method based on a new algorithm. We find evidence for the survival of 1S quarkonium states in the deconfined medium till relatively high temperatures as well as for dissolution of 1P quarkonium states right above the deconfinement temperature.
We discuss the behavior of charmonia and bottomonia correlators and spectral functions above the deconfinement temperature and determine melting temperatures for different mesonic states.
We discuss recent progress in the study of in-medium heavy quarkonium using first-principles lattice QCD calculations and effective field theory. In particular our focus lies on real-time information carried by QCD spectral functions and we report on a novel strategy for their extraction from Euclidean-time simulations. Combining an effective description for heavy quarks with finite temperature lattice QCD we compute in-medium spectra providing insight in heavy quarkonium melting in a static thermal medium. On the other hand we use spectral information to extract the complex in-medium potentia…
By making use of the finite-temperature real-time static potential that was introduced and computed to leading non-trivial order in Hard Thermal Loop resummed perturbation theory in recent work, and solving numerically a Schrödinger-type equation, we estimate the quarkonium (in practice, bottomonium) contribution to the spectral function of the electromagnetic current in hot QCD. The spectral function shows a single resonance peak which becomes wider and then disappears as the temperature is increased beyond 450 MeV or so. This behaviour can be compared with recently attempted lattice reconstr…
In this talk I summarize the progress achieved in recent years on the understanding of quarkonium properties at finite temperature. Theoretical studies from potential models, lattice QCD, and effective field theories are discussed. I also highlight a bridge from spectral functions to experiment.
We discuss the temperature-dependence of S-wave quarkonium spectral functions in a nonrelativistic Green's function approach and compare these to lattice QCD results.
I discuss quarkonium spectral functions at finite temperature reconstructed using the Maximum Entropy Method. I show in particular that the J/psi survives in the deconfined phase up to 1.5Tc
The bound states of a heavy quark and antiquark ($c\bar{c}, b\bar{b}$) are ideal probes to explore the quark-gluon plasma created in relativistic heavy-ion collisions at the RHIC and LHC. Not only have they become experimentally accessible with high precision but also efficient tools, so called effective field theories (EFT) have been developed to treat them theoretically. Here we present recent progress in understanding the in-medium behavior of heavy-quarkonium with the help of EFT's combined with non-perturbative and first principles simulations in lattice QCD. In particular we discuss comp…
In statistical QCD, the thermal properties of the quark-gluon plasma can be determined by studying the in-medium behaviour of heavy quark bound states. The results can be applied to quarkonium production in high energy nuclear collisions, if these indeed form a fully equilibrated QGP. Modifications could arise if an initial charm excess persists in the collision evolution and causes quarkonium regeneration at hadronization.
We study quarkonium correlators and spectral functions at zero and finite temperature in QCD with only heavy quarks using potential models combined with perturbative QCD. First, we show that this approach can describe the quarkonium correlation function at zero temperature. Using a class of screened potentials based on lattice calculations of the static quark-antiquark free energy we calculate spectral functions at finite temperature. We find that all quarkonium states, with the exception of the $1S$ bottomonium, dissolve in the deconfined phase at temperatures smaller than $1.5T_c$, in contra…
The vector channel spectral function at zero spatial momentum is calculated at next-to-leading order in thermal QCD for any quark mass. It corresponds to the imaginary part of the massive quark contribution to the photon polarization tensor. The spectrum shows a well defined transport peak in contrast to both the heavy quark limit studied previously, where the low frequency domain is exponentially suppressed at this order and the naive massless case where it vanishes at leading order and diverges at next-to-leading order. From our general expressions, the massless limit can be taken and we sho…
The pseudoscalar correlator is an ideal lattice probe for thermal modifications to quarkonium spectra, given that it is not compromised by a contribution from a large transport peak. We construct a perturbative spectral function incorporating resummed thermal effects around the threshold and vacuum asymptotics above the threshold, and compare the corresponding imaginary-time correlators with continuum-extrapolated lattice data for quenched SU(3) at several temperatures. Modest differences are observed, which may originate from non-perturbative mass shifts or renormalization factors, however no…
We present the final results of our high statistics study on the properties of bottomonium and charmonium at finite temperature. We focus on the temperature range around the crossover transition $150\leq T\leq 410$MeV, relevant for current heavy ion collision experiments. The QCD medium degrees of freedom which consist of dynamical u,d, and s quarks and gluons are captured by realistic state-of-the art ($m_π\approx 161$MeV) lattice QCD simulations of the HotQCD collaboration. For the heavy quarks we deploy the non-relativistic effective field theory of QCD, NRQCD. The in-medium properties of q…
We present the final results from a multi-year study of the in-medium spectral properties of heavy quarkonium bound states on the lattice. In this work we combine high statistics $N_f=2+1$ ensembles from the HotQCD collaboration with the effective theory NRQCD and improved Bayesian spectral reconstruction methods. We corroborate with high precision the hierarchical in-medium modification of quarkonium states with respect to their vacuum binding energy and provide updated values on melting temperatures. In particular we are able to understand previous disagreements between different Bayesian me…
In the limit of a high temperature T and a large quark-mass M, implying a small gauge coupling g, the heavy quark contribution to the spectral function of the electromagnetic current can be computed systematically in the weak-coupling expansion. We argue that the scale hierarchy relevant for addressing the disappearance ("melting") of the resonance peak from the spectral function reads M >> T > g^2 M > gT >> g^4 M, and review how the heavy scales can be integrated out one-by-one, to construct a set of effective field theories describing the low-energy dynamics. The parametric behaviour of the …
We calculate quarkonium spectral functions in a quark-gluon plasma using a potential model based on full QCD lattice calculations of the free energy of static quark-antiquark pair. We estimate the binding energy and the thermal width of different quarkonium states. The estimated upper limit for the dissociation temperatures is considerably lower than the ones suggested in the recent literature.
In this paper we report our results on quarkonium spectral functions in the vector channel obtained from quenched lattice QCD simulations at $T\in[0.75, 2.25]~T_c$. The calculations have been performed on very large and fine isotropic lattices where both charm and bottom quarks can be treated relativistically. The spectral functions are reconstructed using the Maximum Entropy Method. We study the dissociation of quarkonium states from the temperature dependence of the spectral functions and estimate heavy quark diffusion coefficients using the low-frequency behavior of the vector spectral func…
We extend our lattice QCD potential based study arXiv:1509.07366 (JHEP 1512 (2015) 101) of the in-medium properties of heavy quark bound states to P-wave bottomonium and charmonium. Similar to the behavior found in the S-wave channel their spectra show a characteristic broadening, as well as mass shifts to lower energy with increasing temperature. In contrast to the S-wave states, finite angular momentum leads to the survival of spectral peaks even at temperatures, where the continuum threshold reaches below the bound state remnant mass. We elaborate on the ensuing challenges in defining quark…
We report on recent theory progress in understanding the production of heavy quarkonium in heavy-ion collisions based on the in-medium heavy-quark potential extracted from lattice QCD simulations. On the one hand, the proper in-medium potential allows us to study the spectral properties of heavy quarkonium in thermal equilibrium, from which we estimate the $ψ^\prime$ to $J/ψ$ ratio in heavy-ion collisions. On the other hand, the potential provides a central ingredient in the description of the real-time evolution of heavy-quarkonium formulated in the open-quantum-systems framework.
We present the finite temperature spectra of both bottomonium and charmonium, obtained from a consistent lattice QCD based potential picture. Starting point is the complex in-medium potential extracted on full QCD lattices with dynamical u,d and s quarks, generated by the HotQCD collaboration. Using the generalized Gauss law approach, vetted in a previous study on quenched QCD, we fit ${\rm Re}[V]$ with a single temperature dependent parameter $m_D$, the Debye screening mass, and confirm the up to now tentative values of ${\rm Im}[V]$. The obtained analytic expression for the complex potential…
We elaborate on the fact that quarkonium in hot QCD should not be thought of as a stationary bound state in a temperature-dependent real potential, but as a short-lived transient, with an exponentially decaying wave function. The reason is the existence of an imaginary part in the pertinent static potential, signalling the ``disappearance'', due to inelastic scatterings with hard particles in the plasma, of the off-shell gluons that bind the quarks together. By solving the corresponding Schrödinger equation, we estimate numerically the near-threshold spectral functions in scalar, pseudoscalar,…
We investigate the properties of heavy quarkonia at finite temperature in detail using QCD sum rules. Extending previous analyses, we take into account a temperature dependent effective continuum threshold and derive constraints on the mass, the width, and the varying effective continuum threshold. We find that at least one of these quantities of a charmonium changes abruptly in the vicinity of the phase transition. We also calculate the ratio of the imaginary time correlator to its reconstructed one, $G/G_{\text{rec}}$, by constructing a model spectral function and compare it to the correspon…
We build a "bottom-up" holographic model of charmonium by matching the essential spectral data. We argue that this data must include not only the masses but also the decay constants of the J/psi and psi' mesons. Relative to the "soft-wall" models for light mesons, such a matching requires two new features in the holographic potential: an overall upward shift as well as a narrow "dip" near the holographic boundary. We calculate the spectral function as well as the position of the complex singularities (quasinormal frequencies) of the retarded correlator of the charm current at finite temperatur…
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…
A semi-spectral Chebyshev method for solving numerically singular integral equations is presented and applied in the quarkonium bound-state problem in momentum space. The integrals containing both, logarithmic and Cauchy singular kernels, can be evaluated without subtractions by dedicated automatic quadratures. By introducing a Chebyshev mesh and using the Nystrom algorithm the singular integral equation is converted into an algebraic eigenvalue problem that can be solved by standard methods. The proposed scheme is very simple to use, is easy in programming and highly accurate.
We reconsider a plasma with an anisotropy imposed on the momentum distribution of the system and study the real time static potential for quarkonia. The distribution function is normalised so as to preserve the particle number in an ideal gas, as required in the Keldysh-Schwinger formalism. In contrast to recent findings without this normalisation, a weak anisotropy does not lead to an increase in the melting temperature for bound states. To test for the maximal effect, we also investigate a gluonic medium in the limit of an asymptotically strong anisotropy. The spectral function of quarkonium…
We explore the in-medium properties of heavy-quarkonium states at finite baryo-chemical potential and finite transverse momentum based on a modern complex-valued potential model. Our starting point is a novel, rigorous derivation of the generalized Gauss law for in-medium quarkonium, combining the non-perturbative physics of the vacuum bound state with a weak coupling description of the medium degrees of freedom. Its relation to previous models in the literature is discussed. We show that our approach is able to reproduce the complex lattice QCD heavy quark potential even in the non-perturbati…
Complex heavy-quarkonium potential in an anisotropic collisional quark-gluon plasma
School of Physical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute（国立科学教育研究中心物理科学学院，霍米·巴巴国立学院成员）；Department of Physics and Institute of Physics and Applied Physics, Yonsei University（延世大学物理系及物理与应用物理研究所）
We have studied the dissociation of heavy quarkonium states in a hot QCD medium by investigating the medium modifications to a heavy quark potential. Our model shows that in-medium modification causes the screening of the charge in contrast to the screening of the range of the potential. We have then employed the medium-modified potential to estimate the dissociation pattern of the charmonium and bottomonium states and also explore how the pattern changes as we go from the perturbative to nonperturbative domain in the Debye mass. The results are in good agreement with the other current theoret…
We present an improved analytic parametrisation of the complex in-medium heavy quark potential derived rigorously from the generalised Gauss law. To this end we combine in a self-consistent manner a non-perturbative vacuum potential with a weak-coupling description of the QCD medium. The resulting Gauss-law parametrisation is able to reproduce full lattice QCD data by using only a single temperature dependent parameter, the Debye mass $m_D$. Using this parametrisation we model the in-medium potential at finite baryo-chemical potential, which allows us to estimate the $Ψ^\prime$/$J/Ψ$ ratio in …
In this article, we take the tensor currents $\bar{Q}(x)σ_{μν}Q(x)$ to interpolate the $P$-wave spin-singlet heavy quarkonium states $h_Q$, and study the masses and decay constants with the Borel sum rules and moments sum rules. The masses and decay constants from the Borel sum rules and moments sum rules are consistent with each other, the masses are also consistent with the experimental data. We can take the decay constants as basic input parameters and study other phenomenological quantities with the three-point correlation functions via the QCD sum rules. The heavy quarkonium states $h_Q$ …
We report here on recent progress in the determination of S-wave and P-wave heavy-quarkonium states at finite temperature. Our results are based on the combination of effective field theories with numerical lattice QCD simulations. These non-perturbative tools allow us to compute the heavy-quarkonium in-medium spectral functions, from which we in turn determine the melting temperatures of individual states and estimate phenomenologically relevant observables, such as the $ψ^\prime$ to J/$ψ$ ratio in heavy-ion collisions.
The current status of transport coefficients in relativistic field theories at high temperature is reviewed. I contrast weak coupling results obtained using kinetic theory/diagrammatic techniques with strong coupling results obtained using gauge/gravity duality, and describe the recent developments in extracting transport coefficients and spectral functions from lattice QCD simulations. The fate of quarkonium at high temperature as seen from the lattice is briefly mentioned as well.
We study the evolution of heavy quarkonium states with temperature in a Quark Gluon Plasma (QGP) by evaluating the in-medium Q-\bar{Q} T-matrix within a reduced Bethe-Salpeter equation in both S- and P-wave channels. The underlying interaction kernel is extracted from recent finite-temperature QCD lattice calculations of the singlet free energy of a Q-\bar{Q} pair. The bound states are found to gradually move above the Q-\bar{Q} threshold after which they rapidly dissolve in the hot system. The T-matrix approach is particularly suited to investigate these mechanisms as it provides a unified tr…
Recent investigations show that the thermal spectral function of heavy $ {b \bar b } $ and $ {c \bar c} $ vector mesons can be described using holography. These studies consider a bottom up model that captures the heavy flavour spectroscopy of masses and decay constants in the vacuum and is consistently extended to finite temperature. The corresponding spectral functions provide a picture of the dissociation process in terms of the decrease of the quasi-state peaks with temperature. Another related tool that provides important information about the thermal behaviour is the analysis of the quas…
We have studied the quasi-free dissociation of quarkonia through a complex potential which is obtained by correcting both the perturbative and nonperturbative terms of the $Q \bar Q$ potential at T=0 through the dielectric function in real-time formalism. The presence of confining nonperturbative term even above the transition temperature makes the real-part of the potential more stronger and thus makes the quarkonia more bound and also enhances the (magnitude) imaginary-part which, in turn contributes more to the thermal width, compared to the medium-contribution of the perturbative term alon…
The Schroedinger equation for the charmonium and bottomonium states at finite temperature is solved by employing an effective temperature dependent potential given by a linear combination of the color singlet free and internal energies obtained on the lattice from the Polyakov loop correlation functions. The melting temperatures and other properties of the quarkonium states are evaluated. The consistency of the potential model approach with the available lattice data on the quarkonium temporal correlators and spectral functions is explored.
We study the behavior of the complex potential between a heavy quark and its antiquark, which are in relative motion with respect to a hot and dense medium. The heavy quark-antiquark complex potential is obtained by correcting both the Coulombic and the linear terms in the Cornell potential through a dielectric function estimated within the real-time formalism using the hard thermal loop approximation. We show the variation of both the real and the imaginary parts of the potential for different values of velocities when the bound state ($ Q\bar{Q}$ pair) is aligned in the direction parallel as…
The analytical exact iteration method (AEIM) have been used to calculate the N-dimensional radial schrodinger equation with the real part of complex-valued potential and it is generalized to the finite value of anisotropy (ξ), temperature and baryonic chemical potential. In N-dimensional space the energy eigen values have been calculated for any states (n,l). The present results have been used to study the properties of quarkonium states (i.e, the binding energy and mass spectra in the N-dimensional space). The influences of anisotropy (ξ) on the dissociation temperature(TD) has been also calc…
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…
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）
In these lecture notes we will discuss recent progress in extracting spectral and transport properties from lattice QCD. We will focus on results of probes of the thermal QCD medium as well as transport coefficients which are important ingredients for hydrodynamic and transport models that describe the evolution of the produced medium. These include electromagnetic probes, like the rates of emitted photons and dileptons, quarkonium spectral functions as well as transport coefficients like the electrical conductivity or heavy flavor diffusion coefficients of the quark gluon plasma (QGP). All th…
