We perform a quark model calculation of the quarkonia $b\overline{b}$ and $c\overline{c}$ spectra using smooth and sudden string breaking potentials. The screening parameter is scale dependent and can be related to an effective running gluon mass that has a finite infrared fixed point. A temperature dependence for the screening mass is motivated by lattice QCD simulations at finite temperature. Qualitatively different results are obtained for quarkonia properties close to a critical value of the deconfining temperature when a smooth or a sudden string breaking potential is used. In particular, with a sudden string breaking potential quarkonia radii remain almost independent of the temperature up to the critical point, only well above the critical point the radii increase significantly. Such a behavior will impact the phenomenology of quarkonia interactions in medium, in particular for scattering dissociation processes.
We study the quarkonia correlators above deconfinement using the potential model with screened temperature-dependent potentials. We find that while the qualitative features of the spectral functions, such as the survival of the 1S state, can be reproduced by potential models, the temperature dependence of the correlators disagree with the recent lattice data.
Here I review the temperature-dependence of heavy quarkonia correlators in potential models with three different screened potentials, and compare these to the results from lattice QCD. None of the potentials investigated yield results consistent with the lattice data, indicating that screening is likely not the mechanism for heavy quarkonia suppression. I also discuss a simple toy model, not based on temperature-dependent screening, that can reproduce the lattice results.
We investigate the quarkonia correlators in QCD with no light quarks within a potential model with different screened potentials. Our results for the temperature dependence of the charmonium and bottomonium correlators are qualitatively consistent with existing and preliminary lattice results. We identify however, a much reacher structure in the correlators than the one seen on the lattice.
Screening effects from sea pairs on the quark-antiquark static potential are analyzed phenomenologically from the light-quark to the heavy-quark meson spectra. From the high excited light-quark meson spectrum a universal form for the screened static potential is proposed. This potential is then succesfully applied to heavy quarkonia. Our results suggest the assignment of X(4260) to the 4s state of charmonium and the possible existence of a 5s bottomonium resonance around 10748 MeV.
Production of heavy quark antiquark systems in high energy heavy ion collisions must involve relativistic momentum components in a quantum mechanical approach. If the color forces are screened in a deconfining medium, one can define the analog of a formation or separation time by an overlap integral in the nonrelativistic bound state rest frame. This time parameter has some interesting properties which depend on the momentum spectrum of the initial quarks. Consequences of these properties for the phenomenology of deconfinement signals are discussed.
We review non-perturbative static potentials commonly used in potential models for quarkonia at finite T. Potentials derived from Polyakov loop correlators are shown to be inappropriate for this purpose. The q\bar{q} free energy is physical but has the wrong spatial decay and perturbative limit. The so-called singlet free energy is gauge dependent and unphysical. An appropriate static real time potential can be defined through a generalisation of pNRQCD to finite T. In perturbation theory, its real part reproduces the Debye-screened potential, its imaginary part accounts for Landau damping. Po…
We examined the effects of the weak magnetic field on the dissociation of heavy quarkonia immersed in a thermal medium of quarks and gluons. For that purpose, we have revisited the general structure of gluon self-energy tensor in the presence of a weak magnetic field in thermal medium and obtained the relevant structure functions. The structure functions give the real and imaginary parts of the resummed gluon propagator, which further give the respective dielectric permittivities. The real and imaginary parts of the dielectric permittivity will be used to evaluate the real and imaginary parts …
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…
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, …
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…
Finite-temperature spectra of heavy quarkonia are calculated by combining potential model and thermofield dynamics formalisms. The mass spectra of the heavy quarkonia with various quark contents are calculated. It is found that binding mass of the quarkonium decreases as temperature increases.
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…
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…
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…
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.…
We present the quarkonia correlators for charmonium and bottomonium systems in the pseudoscalar, vector and scalar channels. For the description of quark-antiquark interaction we adopt the temperature dependant colour screening potential of the power law form. The spectroscopic parameters defined from the model are employed in the spectral functions to compute the quarkonia correlators. We find considerable medium modifications to the effective masses of the quarkonia as well as in the behaviour of the respective radial wave functions. These modifications are then reflected in the computed cor…
The temperature dependent energy, mass and some of thermodynamic quantities of charmonium and bottomonium have been calculated by solving the radial Schr{ö}dinger equation with the extended Cornell potential at finite temperature using the Nikiforov-Uvarov method. Obtained results accord with experimental data and theoretical results of the previous studies. We have found the spectrum of quarkonia mass strictly decreases at high values of temperature.
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…
We update our recent calculation of quarkonium Euclidean correlators at finite temperatures in a potential model by including the effect of zero modes in the lattice spectral functions. These contributions cure most of the previously observed discrepancies with lattice calculations, supporting the use of potential models at finite temperature as an important tool to complement lattice studies.
The N-dimensional radial Schrödinger equation has been solved using the analytical exact iteration method (AEIM), in which the Cornell potential is generalized to finite temperature and chemical potential. The energy eigenvalues have been calculated in the N-dimensional space for any state (n, l). The present results have been applied for studying quarkonium properties such as charmonium and bottomonium masses. The binding energies and the mass spectra of heavy quarkonia are studied in the N-dimensional space. The dissociation temperatures for different states of heavy quarkonia are calculated…
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…
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.
Masses and decay constants of the scalar quarkonia, $χ_{Q0} (Q=b,c)$ with quantum numbers $I^G(J^{PC})=0^{+}(0^{++})$ are calculated in the framework of the QCD sum rules approach both in vacuum and finite temperature. The masses and decay constants remain unchanged up to $T\simeq100~MeV$ but they start to diminish with increasing the temperature after this point. At near the critic or deconfinement temperature, the decay constants reach approximately to 25% of their values in vacuum, while the masses are decreased about 6% and 23% for bottom and charm cases, respectively. The results at zero …
S-wave states of charmonium and bottomonium are described using bottom-up AdS/QCD. We propose a holographic model that unifies the description of masses and decay constants, leading to a precise match with experimental data on heavy quarkonia. Finite temperature effects are considered by calculating the current-current spectral functions of heavy vector mesons. The identification of quasi-particle states as Breit-Wigner resonances in the holographic spectral function was made. We develop a prescription to subtract background contributions from the spectral function to isolate the Breit-Wigner …
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.
Rapid thermalization in ultra-relativistic heavy-ion collisions leads to fast changing potential between a heavy quark and antiquark from zero temperature potential to the finite temperature one. Time dependent perturbation theory can then be used to calculate the survival probability of the initial quarkonium state. In view of very short time scales of thermalization at RHIC and LHC energies, we calculate the survival probability of $J/ψ$ and $Υ$ using sudden approximation. Our results show that quarkonium decay may be significant even when temperature of QGP remains low enough so that the co…
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 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…
We extract the $Q$-$\bar Q$ potential by using the thermodynamic quantities obtained in lattice gauge calculations. The potential is tested and found to give dissociation temperatures that agree well with those from lattice gauge spectral function analysis. Using such a $Q$-$\bar Q$ potential, we examine the quarkonium states in a quark-gluon plasma and determine the `quark drip lines' which separate the region of bound color-singlet $Q\bar Q$ states from the unbound region. The characteristics of the quark drip lines severely limit the region of possible bound $Q\bar Q$ states with light quar…
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）
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…
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 …
Quenched lattice data for the quark-antiquark interaction (in terms of heavy quark free energies) in the color singlet channel at finite temperatures are fitted and used within the nonrelativistic Schroedinger equation formalism to obtain binding energies and scattering phase shifts for the lowest eigenstates in the charmonium and bottomonium systems in a hot gluon plasma. The partial dissociation rate due to the Bhanot-Peskin process is calculated using different assumptions for the gluon distribution function, including free massless gluons, massive gluons, and massive damped gluons. It is d…
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…
Recent lattice calculations showed that the quarkonia will survive beyond the phase transition temperature, and will dissolve at different temperatures depending on the type of the quarkonium. In this work, we calculate the thermal width of the quarkonium at finite temperature before it dissolves into open heavy quarks. The input of the calculation are the parton quarkonium dissociation cross section to NLO in QCD, the quarkonium wave function in a temperature-dependent potential from lattice QCD, and a thermal distribution of partons with thermal masses. We find that for the J/psi, the total …
By simulating the finite temperatures magnetized background in the RHIC and LHC energies, we systematically study the characteristics of thermal widths and potentials of heavy quarkonia. It is found that the magnetic field has less influence on the real potential, but has a significant influence on the imaginary potential, especially in the low deconfined temperature. Extracted from the effect of thermal worldsheet fluctuations about the classical configuration, the thermal width of $Υ(1s)$ in the finite temperature magnetized background is investigated. It is found that at the low deconfined …
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…
We discuss how the spectral changes of quarkonia at T_c can reflect the ``critical'' behaviour of QCD phase transition. Starting from the temperature dependencies of the energy density and pressure from lattice QCD calculation, we extract the temperature dependencies of the scalar and spin 2 gluon condensates near T_c. We also parameterize these changes into the electric and magnetic condensate near T_c. While the magnetic condensate hardly changes across T_c, we find that the electric condensate increases abruptly above T_c. Similar abrupt change is also seen in the scalar condensate. Using t…
We investigate the in-medium modifications of heavy quarkonia in the vector channel and the heavy quark diffusion coefficient by comparing Euclidean correlators from the lattice to a perturbative spectral function. On the lattice side, we work with continuum extrapolated data from four different large and fine lattices with Clover-improved Wilson fermions in the quenched approximation at five temperatures (0.75, 1.1, 1.3, 1.5 and 2.25$T_c$). On the perturbative side, we use a combination of pNRQCD and vacuum asymptotics to describe the spectral function. After accounting for systematic errors,…
I review recent progress in studying in-medium modification of inter-quark forces at finite temperature in lattice QCD. Some applications to the problem of quarkonium binding in potential models is also discussed.
We have investigated the effects of strong magnetic field on the properties of quarkonia immersed in a thermal medium of quarks and gluons and studied its quasi-free dissociation due to the Landau-damping. Thermalizing the Schwinger propagator in the lowest Landau levels for quarks and the Feynman propagator for gluons in real-time formalism, we have calculated the resummed retarded and symmetric propagators, which in turn give the real and imaginary components of dielectric permittivity, respectively. The magnetic field affects the large-distance interaction more than the short-distance inter…
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)…
The screened quasi-relativistic potential is used for describing spin-orbit splitting in $^{3}P_{J}$ waves of quark-antiquark system. Fermi-Breit equation is solved numerically in configuration interaction approximation. This approximation takes into account the mixing of wave functions up to fifth order and corrects substantially perturbation calculations. The nature of potentials Lorenz transformation property is elucidated. Very good quantitative results for $b\bar{b}$ and $c\bar{c}$ quarkonia and quite acceptable qualitative characteristics as well as for systems with unequal masses are ob…
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.
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…
Decoherence dynamics of quarkonia is studied in the high-temperature deconfined phase of SU($N_c$) gauge theories. In particular, we analyze the symmetry properties of SU($N_c$) stochastic potential model and find a novel "event-by-event" symmetry for $N_c=2$ case, similar to the $G$-parity of hadronic systems. This novel symmetry constrains the relation between diagonal and off-diagonal components of quarkonium density matrix, leaving the latter to be finite at late times. We also present one-dimensional numerical simulation of the model, which indicates the usefulness of the complex potentia…
We consider the quark antiquark potential of a quarkonium moving with velocity $v$ through a quark-gluon plasma at temperature T. An explicit, configuration-space expression is found for the screened interaction between the quarks constituting the meson. This potential is non-spherical, but axially symmetric about the direction of $v$.
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…
