Binding Energies and Melting Temperatures of Heavy Hadrons in Quark-Gluon Plasma
I. M. Narodetskiy, Yu. A. Simonov, A. I. Veselov
备注：
a slightly extended version of the talk delivered at "Quark Confinement and the Hadron Spectrum IX - QCHS IX" International Conference (30 August - 3 September 2010, Madrid, Spain), a reference added, minor comments added
We analyze the static potential of a quark-antiquark pair at $T\,\geq\,T_c$, where $T_c$ is a temperature of a deconfinement phase transition in QCD. We discuss the possibility that the non-perturbative part of this potential can be studied through the modification of the correlation functions, which define the quadratic field correlators of the nonperturbative vaccuum fields. We use the non-perturbative quark-antiquark potential derived in this way and the screened one-gluon-exchange potential with $T$-dependent Debye screening mass to calculate $J/ψ$, $Υ$ and $Ω_{bbb}$ binding energies and melting temperatures in the deconfined phase of the full 2-flavors QCD.
We consider a black hole solution with a non-trivial dilaton from IIB super gravity which is expected to describe a strongly coupled hot gauge plasma with non-vanishing gluon condensation present. We construct a rotating and moving baryon to probe the screening and phases of the plasma. Melting of the baryons in hot plasma in this background had been studied previously, however, we show that baryons melt much lower temperature than has been suggested previously.
We study the fate of P wave bottomonium states in the quark-gluon plasma, using a spectral function analysis of euclidean lattice correlators. The correlators are obtained from lattice QCD simulations with two light quark flavours on highly anisotropic lattices, treating the bottom quark nonrelativistically. We find clear indications of melting immediately after the deconfinement transition.
A strong $J/ψ$ suppression in central Au+Au collisions has been observed by the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC). We develop a hydro+$J/ψ$ model in which hot quark-gluon matter is described by the full (3+1)-dimensional relativistic hydrodynamics and $J/ψ$ is treated as an impurity traversing through the matter. The experimental $J/ψ$ suppression pattern in mid-rapidity is reproduced well by the sequential melting of $χ_{\rm c}$, $ψ'$, and $J/ψ$ in dynamically expanding fluid. The melting temperature of directly produced $J/ψ$ is well constrained by the participa…
In this work, we calculate the binding energies of the $J/ψ$, the $Υ$, and the Toponium in quark-gluon plasma. We also calculate the temperature of the quark-gluon plasma at which these quarkonia dissociate. We approach the problem from a quantum mechanical point of view. We use the variational method and the screening Debye potential in order to obtain these binding energies.
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 …
The quarkonium states in a quark-gluon plasma is examined with the potential implied by AdS/CFT duality. Both the vanila AdS-Schwarzschild metric and the one with an infrared cutoff are considered. The calculated dissociation temperatures for $J/ψ$ and $Υ$ are found to agree with the lattice results within a factor of two.
We analyse mesons at finite temperature in a chiral, confining string dual. The temperature dependence of low-spin as well as high-spin meson masses is shown to exhibit a pattern familiar from the lattice. Furthermore, we find the dissociation temperature of mesons as a function of their spin, showing that at a fixed quark mass, mesons with larger spins dissociate at lower temperatures. The Goldstone bosons associated with chiral symmetry breaking are shown to disappear above the chiral symmetry restoration temperature. Finally, we show that holographic consideration imply that large-spin meso…
In the early stages of heavy-ion collisions, the hot QCD matter expands more longitudinally than transversely. This imbalance causes the system to become rapidly colder in the longitudinal direction and a local momentum anisotropy appears. In this paper, we study the heavy-quarkonium spectrum in the presence of a small plasma anisotropy. We work in the framework of pNRQCD at finite temperature. We inspect arrangements of non-relativistic and thermal scales complementary to those considered in the literature. In particular, we consider temperatures larger and Debye masses smaller than the bindi…
We fit the lattice QCD data of Kaczmarek et al for the free energy F1 and internal energy U1 with a class of Coulomb, constant and linear potentials, both pure and screened, matching the large distance to the short distance parts of the lattice QCD finite temperature energies. We also include the hyperfine potential in F1 and U1. We detail the bottomonium (and charmonium) binding and the melting temperatures, both for the groundstate and for the excited states, relevant for Hard Probes in Heavy Ion Collisions at LHC, where temperatures well above Tc will be reached, much higher than the temper…
We study the melting temperature of heavy mesons in the hot medium of light quarks. By solving the covariant Schrödinger equations at finite temperature for mesons $D$, $ϕ$ and $J/ψ$, we obtained the temperature dependence of their masses, binding energies and averaged sizes and found the flavor dependence of the melting temperature: $T_D \simeq T_ϕ< T_{J/ψ}$. The sequential melting temperature can explain the difference in meson elliptic flow observed in heavy ion collisions.
We have developed a hydrodynamic model to study sequential melting of charmonium states in an expanding QGP medium. According to the initial fluid temperature profile, $J/ψ$'s are randomly distributed in the transverse plane. As the fluid evolve in time, the free streaming $J/ψ$'s are suppressed if the local fluid temperature exceed a critical temperature. PHENIX data on the centrality dependence of $J/ψ$ suppression in Au+Au collisions at mid-rapidity are explained by sequential melting of the charmonium states, $χ_c$, $ψ\prime$ and $J/ψ$, in the expanding medium. The critical temperatures $T…
We extend our analysis of holographic meson dissociation in the presence of an intense magnetic field. In addition to the previously known critical temperature above which the mesons melt, we found that for certain magnetic field intensities there exists a second lower critical temperature, below which stable mesons cease to exist. While we showed before that there is a range of high temperatures for which mesons can be melted by changing the magnetic field intensity, here we show that, as a consequence of the second critical point, there is also a range of low temperatures for which this phen…
At high temperatures, strongly interacting matter becomes a plasma of deconfined quarks and gluons. In statistical QCD, deconfinement and the properties of the resulting quark-gluon plasma can be investigated by studying the in-medium behaviour of heavy quark bound states. In high energy nuclear interactions, quarkonia probe different aspects of the medium formed in the collision. We survey the results of recent charmonium production studies in SPS and RHIC experiments.
We study in this paper mechanisms of hadron melting based on the spectral representation of hadronic quantum channels, and examine the hadron width dependence of the pressure. The findings are applied to a statistical hadron model of QCD thermodynamics, where hadron masses are distributed by the Hagedorn model and a uniform mechanism for producing hadron widths is assumed. According to this model the hadron - quark gluon plasma transition occurs at $T\approx 200$-250 MeV, the numerically observable $T_c=156$ MeV crossover temperature is relevant for the onset of the hadron melting process.
A charmonium produced in heavy ion collisions at RHIC and LHC propagates through a dense co-moving matter with a rather high relative momentum, <p_T^2>=4-10GeV^2. In spite of Debye screening of the binding potential, the charmonium survives with a substantial probability, even if the c-cbar potential is completely screened in the hot environment. In addition, the color-exchange interaction with the medium is another important source of charmonium suppression. Attenuation in a hot medium caused by both effects is evaluated by means of the path integral technique, which requires ability of boost…
Hypothesis of quark binding through condensation of gluons inside hadrons is formulated in the context of a renormalization group procedure for effective particles (RGPEP) in the light-front (LF) Hamiltonian approach to QCD. At the momentum scales of relative motion of hadronic constituents that are comparable with Lambda_QCD, the hypothetical boost-invariant constituent dynamics is identified using gauge symmetry. The resulting picture of mesons and baryons closely resembles constituent quark models with harmonic oscillator potentials, shares some features of AdS/QCD, and can be systematicall…
Thermal color superconducting phase transitions in high density three-flavor quark matter are investigated in the Ginzburg-Landau approach. Effects of nonzero strange quark mass, electric and color charge neutrality, and direct instantons are considered. Weak coupling calculations show that an interplay between the mass and electric neutrality effects near the critical temperature gives rise to three successive second-order phase transitions as the temperature increases: a modified color-flavor locked (mCFL) phase (ud, ds, and us pairings) -> a ``dSC'' phase (ud and ds pairings) -> an isoscala…
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 study the binding energy of a heavy quark-antiquark ($q\bar{q}$) pair using the first-order path integral formalism. This makes the Yang-Mills constraint equation explicit, and highlights that it is valid without relying on a semiclassical approximation. A generalized gauge-covariant Coulomb gauge is chosen to allow for a decomposition of the chromoelectric field into a gauge-covariant generalization of transverse and longitudinal parts. This decomposition makes it clear that the $q\bar{q}$ binding energy is determined solely by the solution to the constraint equation. Assuming that the low…
The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons and the colored valence gluons shows that QCD can be viewed as the restricted QCD (RCD) made of the binding gluons which has the valence gluons as colored source, and simplifies the QCD dynamics greatly. In particular, it tells that the gauge covariant valence gluons can be treated as the constituents of hadrons, and generalizes the quark model to the quark and valence gluon model. So it provides a comprehensive picture of glueballs and their mixing with quarkoniums, and predicts new hybrid hadrons…
The decay of 2-gluon colour singlets in quarks: 2g --> q-qbar +2q-2qbar has been simulated with the Monte-Carlo method, taking into account an effective 1-gluon exchange interaction between the emitted quarks, which was folded with a 2-gluon density determined self-consistently. 2-gluon densities were found with different radii, which correspond to 0^{++} glueballs of the size of light q-qbar, s-sbar, c-cbar, b-bbar, and heavier q-qbar systems. Binding potentials between the two gluons have been deduced, which are consistent with the confinement potential from lattice results. However, self-co…
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…
A comprehensive study of the color singlet heavy quark states above T_c is given, using the Field Correlator Method (FCM) for nonperturbative Q{\bar Q} potentials and the screened Coulomb potential with the T-dependent Debye radius. Using these potentials we calculate binding energies and melting temperatures of heavy mesons and baryons in the deconfined phase of quark-gluon plasma and the J/ψand Upsilon disintegration cross sections via the gluon absorption.
Although at temperatures $T\gg Λ_{QCD}$ the quark-gluon plasma (QGP) is a gas of weakly interacting quasiparticles (modulo long-range magnetism), it is strongly interacting in the regime $T=(1-3) T_c$. As both heavy ion experiments and lattice simulations are now showing, in this region the QGP displays rather strong interactions between the constituents. In this paper we investigate the relationship between four (previously disconnected) lattice results: {\bf i.} spectral densities from MEM analysis of correlators; {\bf ii.} static quark free energies $F(R)$; {\bf iii.} quasiparticle masses; …
We compute the Noncommutative QCD (NCQCD) contributions to the three gluon decay modes of heavy quarkonia. For triplet quarkonia (ortho-quarkonia), the NCQCD correction to the QCD three gluon decay mode, like the standard model contribution, is infrared finite. In the case of singlet quarkonia (para-quarkonia), whose QCD three gluon decay mode has infrared singularities which are removed using one-loop corrections to the two gluon mode, we find that NCQCD contribution is also infrared finite. The calculations are performed in the weak binding limit and do not require the introduction of additi…
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.
We consider heavy quark interactions in quenched and unquenched lattice QCD. In a region just above the deconfinement point, non-Abelian gluon polarization leads to a strong increase in the binding. Comparing quark-antiquark and quark-quark interaction, the dependence of the binding on the separation distance $r$ is found to be the same for the colorless singlet $Q\bar Q$ and the colored anti-triplet $QQ$ state. In a potential model description of in-medium $J/Ψ$ behavior, this enhancement of the binding leads to a survival up to temperatures of 1.5 $T_c$ or higher; it could also result in $J/…
We investigate some consequences of the possibility that heavy quarkonia in a quark-gluon plasma possess different (quasi-) bound states, between which transitions are possible. In particular, we show that the time-evolution eigenstates in the medium are mixtures of the vacuum eigenstates. This leads to abundance ratios of quarkonia that differ from those predicted in statistical models or in the sequential-melting picture.
The decay of colour neutral 2-gluon systems in qqbar and 2q2qbar has been simulated with the Monte-Carlo method, taking into account an effective 1-gluon exchange interaction between the emitted quarks, which was folded with a 2-gluon density determined self-consistently. Finite 2-gluon densities were obtained with a mean square radius <r^2> of about 0.5 fm^2. These give a significant contribution to the 2-gluon field correlators and the gluon propagator from lattice QCD. By solving a relativistic Schroedinger equation the binding potential of the 2-gluon density is computed. By the relation 2…
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.
The effect of quark-antiquark potential on the dissociation energy and critical screening length of heavy meson like $b\overline{b}$ and $c\overline{c}$ have been investigated when the respective meson is in quark Gluon Plasma(QGP). The different types of interquark potential have been used which get screened in the QGP medium. The dissociation energy and critical screening length have been studied for both ground and excited states. It has been observed that the form of interquark potential has substantial effect on the critical screening length when the meson is in QGP. A comparison with oth…
We present first results for 3+1-D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a Weibel instability leading soft modes to grow with proper time $τ$ as $\exp(Γ\sqrt{g^2μτ})$, where $g^2μ$ is a scale arising from the saturation of gluons in the nuclear wavefunction. The scale for the growth rate $Γ$ is set by a plasmon mass, defined as $ω_{\rm pl}= κ_0 \sqrt{\frac{g^2μ}τ}$, generated dynamically in the collision. We compare the numerical ratio $Γ/κ_0$ to the corresponding value predicted by the H…
We investigate the phenomenon of Bottomonium melting in a thermal quark-gluon plasma using three-dimensional stochastic simulations based on the concept of open-quantum systems. In this non-relativistic framework, introduced in [Phys.Rev. D85 (2012) 105011], which makes close contact to the potentials derived in effective field theory, the $b\bar{b}$ system evolves unitarily under the incessant kicks by the constituents of the surrounding heat bath. In particular thermal fluctuations and the presence of a complex potential in the EFT are naturally related. An intricate interplay between state …
We introduce a method for reducing anisotropic heavy-quark potentials to isotropic potentials by using an effective screening mass that depends on the quantum numbers $l$ and $m$ of a given state. We demonstrate that, using the resulting 1D effective potential model, one can solve a 1D Schrödinger equation and reproduce the full 3D results for the energies and binding energies of low-lying heavy-quarkonium bound states to relatively high accuracy. This includes the splitting of different p-wave polarizations. The resulting 1D effective model provides a way to include momentum anisotropy effect…
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…
We discuss the shortfalls of existing resolutions of the long-standing gauge invariance problem of the canonical decomposition of the nucleon spin to the spin and angular momentum of quarks and gluons. We provide two logically flawless expressions of nucleon spin which have different physical meanings, using the gauge independent Abelian decomposition. The first one is based on the assumption that all gluons (binding and valence gluons) contribute to the nucleon spin, but the second one is based on the assumption that only the binding gluons (and the quarks) contribute to it. We propose the se…
We estimate the effective heavy quark and antiquark potential in the quark gluon plasma using the gravity dual theory. Two models are considered: $AdS_{5}$ and Sakai-Sugimoto model. The effective potential, obtained by using the rotating fundamental open-string configurations, has the angular momentum dependence which generalizes the static central potential. Motivated by the asymptotic form for zero angular momentum state, we fit the effective potential for $J=1,2$ states in the binding region. The fitting parameters are found to be functions of temperature. Finally, we discuss the difference…
Recently there was a significant change of views on physical properties and underlying dynamics of Quark-Gluon Plasma at $T=170-350 MeV$, produced in heavy ion collisions at RHIC. Instead of weakly coupled gas of quasiparticles, it is rather a liquid-like matter with multiple bound states. In this paper we discuss how one can test these ideas experimentally, using the ``penetrating probes'' and looking for certain peaks at some invariant masses. In dileptons the most promising are modified $ρ,ω$, with $M(T\approx T_c)\sim .5 GeV$ and also near zero binding at $M(T\approx (1.5-2)T_c)=1.5-2 GeV$…
We consider a non-uniqueness problem of gauge invariant nucleon spin decomposition. A gauge invariant decomposition with a generalized Coulomb constraint for the physical gluon has been constructed. The decomposition scheme is consistent with the concept of helicity in non-Abelian gauge theory. We provide an explicit representation for the gauge invariant Abelian projection which implies further separation of gluon into binding and valence parts.
In this work, we investigate the spectroscopy and decay rates of charmonia within the framework of non-relativistic Schrödinger equation by employing an approximate inter quark-antiquark potential. The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are employed to compute the spectroscopy of the excited S states and few low-lying P and D waves. The resultant wave functions at zero inter quark separation as well as some finite separation are employed to predict the di-gamma, di-leptonic and di-gluon decay rates of charmonia states by using the conventiona…
We use the screened Coulomb potential with $r$-dependent coupling constant and the non--perturbative quark--antiquark potential derived within Field Correlator Method (FCM) to calculate $J/ψ$ and $Υ$ binding energies and melting temperatures in the deconfined phase of quark-gluon plasma.
We study the production of bottomonium states in heavy-ion reactions at collider energies available at RHIC and LHC. We employ an earlier constructed rate equation approach which accounts for both suppression and regeneration mechanisms in the quark-gluon plasma (QGP) and hadronization phases of the evolving thermal medium. Our previous predictions utilizing two limiting cases of strong and weak bottomonium binding in the QGP are updated by (i) checking the compatibility of the pertinent spectral functions with lattice-QCD results for euclidean correlators, (ii) adapting the initial conditions…
The fraction of heavy vector mesons produced in a heavy ion collision, as compared to a proton proton collision, serves as an important indication of the formation of a thermal medium, the quark gluon plasma. This sort of analysis strongly depends on understanding the thermal effects of a medium like the plasma on the states of heavy mesons. In particular, it is crucial to know the temperature ranges where they undergo a thermal dissociation, or melting. AdS/QCD models are know to provide an important tool for the calculation of hadronic masses, but in general are not consistent with the obser…
The medium-modifications of processes characterized by the presence of a hard scale provide the most diverse tools to characterize the properties of the matter created in high-energy nuclear collisions. Indeed, jet quenching, the suppression of particles produced at high transverse momentum, has been established at RHIC almost a decade ago as one of the main tools in heavy-ion collisions. The melting of quarkonia is expected to provide also information about the temperature and the properties of the produced medium. The beginning of the LHC era for hot QCD studies starts with the first nuclear…
We propose a simple explanation for the connection between chiral symmetry restoration and deconfinement in QCD at high temperature. In the Higgs description of the QCD vacuum both spontaneous chiral symmetry breaking and effective gluon masses are generated by the condensate of a color octet quark-antiquark pair. The transition to the high temperature state proceeds by the melting of this condensate. Quarks and gluons become (approximately) massless at the same critical temperature. For instanton-dominated effective multiquark interactions and three light quarks with equal mass we find a firs…
A Q-Qbar bound state represents a balance between repulsive kinetic and attractive potential energy. In a hot quark-gluon plasma, the interaction potential experiences medium effects. Color screening modifies the attractive binding force between the quarks, while the increase of entropy with Q-Qbar separation gives rise to a growing repulsion. We study the role of these phenomena for in-medium Q-Qbar binding and dissociation. It is found that the relevant potential for Q-Qbar binding is the free energy F; with increasing Q-Qbar separation, further binding through the internal energy U is compe…
We show that the boundary between quark-dominated and hadron-dominated regions of nuclear structure may be blurred by multi-nucleon quark clusters arising from color percolation. Recent experiments supporting partial percolation in cold nuclei and full percolation in hot/dense nuclear matter include: deep inelastic lepton-nucleus scattering, relativistic heavy-ion collisions and the binding energy in $^5 He_Λ$.
Recently there was a significant change of views on physical properties and underlying dynamics of Quark-Gluon Plasma at $T=170-350 MeV$, produced in heavy ion collisions at RHIC. Instead of being a gas of $q,g$ quasiparticles, a near-perfect liquid is observed. Also, precisely in this temperature interval, the interaction deduced from lattice studies is strong enough to support multiple binary bound states. This work is the first variational study of {\em multibody} bound states. We will consider: (i) ``polymer chains'' of the type $\bar q g g ..g q$; (ii) baryons $(qqq)$; (iii) closed (3-)ch…
