We consider quarkonium in a hot QCD plasma which, due to expansion and non-zero viscosity, exhibits a local anisotropy in momentum space. At short distances the heavy-quark potential is known at tree level from the hard-thermal loop resummed gluon propagator in anisotropic perturbative QCD. The potential at long distances is modeled as a QCD string which is screened at the same scale as the Coulomb field. At asymptotic separation the potential energy is non-zero and inversely proportional to the temperature. We obtain numerical solutions of the three-dimensional Schroedinger equation for this potential. We find that quarkonium binding is stronger at non-vanishing viscosity and expansion rate, and that the anisotropy leads to polarization of the P-wave states.
We report a recent calculation of the heavy quarkonium energy levels and decay widths in a quark- gluon plasma whose temperature is much smaller than the inverse radius of the bound state, based on a Non-Relativistic Effective Field theory framework for heavy quarkonium at finite temperature. Relevance for the phenomenology of the Y(1S) in heavy ion collisions is also discussed.
We have investigated the properties of quarkonium states in an anisotropic hot QCD medium by correcting the full Cornell potential, not the Coulomb term alone as usually done in the literature, with a dielectric function from the hard-loop resummed gluon propagator. We have found that in-medium modification in anisotropic medium causes less screening than in isotropic medium. In the short distance limit, potential does not show any medium dependence whereas in the long-distance limit, it reduces to the Coulomb potential with a dynamically screened color charge. In addition, anisotropy in momen…
We derive equations of motion for the reduced density matrix of a heavy quarkonium in contact with a quark-gluon plasma in thermal equilibrium. These equations allow in particular a proper treatment of the regime when the temperature of the plasma is comparable to the binding energy of the quarkonium. These equations are used to study how the quarkonium approaches equilibrium with the plasma, and we discuss the corresponding entropy increase, or free energy decrease, depending on the temperature regime. The effect of collisions can be accounted for by the generalization of the imaginary potent…
We report about a recent calculation of the heavy quarkonium mass and decay width in a quark-gluon plasma, whose temperature T and screening mass m_D satisfy the hierarchy m alpha_s >> pi T >> m alpha_s^2 >> m_D, m being the heavy-quark mass, up to order m alpha_s^5. The calculation may be relevant to understand the behavior of the Y(1S) in a quark-gluon plasma at present-day colliders.
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…
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 …
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.
In relativistic heavy ion collisions at RHIC and the LHC, a quark gluon plasma (QGP) is created for a short duration of about 10fm/c. Quarkonia (bound states of $c\bar{c}$ and $b\bar{b}$) are sensitive probes of this phase on length scales comparable to the size of the bound states which are less than 1fm. Observations of quarkonia in these collisions provide us with a lot of information about how the presence of a QGP affects various quarkonium states. This has motivated the development of the theory of heavy quarks and their bound states in a thermal medium, and its application to the phenom…
We consider the quarkonium diffusion, dissociation and recombination inside quark-gluon plasma. We compute scattering amplitudes in potential nonrelativistic QCD for relevant processes. These processes include the gluon absorption/emission at the order $gr$, inelastic scattering at the order $g^2r$ and elastic scattering with medium constituents at the order $g^2r^2$. We show these amplitudes satisfy the Ward identity. We also consider one-loop corrections. The dipole interaction between the color singlet and octet is not running at the one-loop level. Interference between the tree-level gluon…
I consider the dissociation of a boosted quarkonium in a quark-gluon plasma. This dissociation is due to absorption of a thermal gluon. I discuss the dissociation in terms of the velocity of the quarkonium and the temperature of the quark-gluon plasma. I compare this dissociation rate to the one calculated without including the velocity of the quarkonium.
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 determine the hard-loop resummed propagator in an anisotropic QCD plasma in general covariant gauges and define a potential between heavy quarks from the Fourier transform of its static limit. We find that the potential exhibits angular dependence and that binding of very small quarkonium states is stronger than in an isotropic plasma.
In this paper, quarkonium dissociation is investigated in an anisotropic plasma in the hot and dense media. For that purpose, the multidimensional Schrodinger equation is solved analytically by Nikiforov-Uvarov (NU) method for the real part of the potential in an anisotropic medium. The binding energy and dissociation temperature are calculated. In comparison with an isotropic medium, the binding energy of quarkonium is enhanced in the presence of an anisotropic medium. The present results show that the dissociation temperature increases with increasing anisotropic parameter for 1S state of th…
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)…
We study the impact of magnetic fields generated in relativistic heavy ion collisions on the decay probability of quarkonium produced in the central rapidity region. The quark and anti-quark components are subject to mutually orthogonal electric and magnetic fields in the quarkonium comoving frame. In the presence of an electric field, quarkonium has finite dissociation probability. We use the WKB approximation to derive the dissociation probability. We found that quarkonium dissociation energy, i.e. the binding energy at which dissociation probability is of order unity, increases with the mag…
We discuss the behavior of charmonia and bottomonia correlators and spectral functions above the deconfinement temperature and determine melting temperatures for different mesonic states.
Using an effective Hamiltonian derived from the QCD multipole expansion, we calculate the cross sections of gluo-dissociation of heavy quarkonia in the quark-gluon plasma, by including both the chromo-electric dipole ($E_1$) as well as the chromo-magnetic dipole ($M_1$) transition mechanisms. While the former allows to reproduce the results from operator-product-expansion calculations in the Coulomb approximation, the latter as a novel contribution is shown to be significant at low energies close to the threshold. Using thus obtained cross sections, we further carry out a full calculation of t…
The real-time dissociation of the heavy quarkonium in a strongly coupled boost-invariant non-Abelian plasma relaxing towards equilibrium is analyzed in a holographic framework. The effects driving the plasma out of equilibrium are described by boundary quenching, impulsive variations of the boundary metric. Quarkonium is represented by a classical string with endpoints kept close to the boundary. The evolution of the string profile is computed in the time-dependent geometry, and the dissociation time is evaluated for different configurations with respect to the direction of the plasma expansio…
The polarization of quarkonium states produced in hadron collisions exhibits strong non-perturbative effects - for example, at small transverse momentum $p_t$ charmonia appear unpolarized, in sharp contradiction to the predictions of perturbation theory. The quark--gluon plasma is expected to screen away the non-perturbative physics; therefore those quarkonia which escape from the plasma should possess polarization as predicted by perturbative QCD. We estimate the expected $J/ψ$ polarization at small $p_t$, and find that it translates into the asymmetry of the $e^+e^- (μ^+μ^-)$ angular distrib…
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…
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…
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 study the properties of the Lindbladian quantum mechanical evolution of quarkonia with non-Abelian charges (color-singlet and octet) in the quark-gluon plasma. We confirm that heavy quark recoils in the Lindblad equation correctly thermalize quarkonium colorful states within statistical errors from the simulation method. We also demonstrate that the Lindblad equation in the dipole limit can provide an efficient alternative method, which is applicable to a finite time evolution before thermalization and dramatically reduces the numerical cost. Our findings will serve as a foundation for larg…
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.
Using the chromo-electric dipole coupling Hamiltonian from QCD multipole expansion, we derive the dissociation cross sections of heavy quarkonia by thermal gluons at next-to-leading order (NLO, also known as inelastic parton scattering dissociation) in the Quark-Gluon Plasma (QGP) in the framework of second order quantum mechanical perturbation theory. While suffering divergence (infrared and soft-collinear divergences) in vacuum, the cross sections thus derived become finite in the QGP as rendered by the finite thermal gluon masses. In contrast to the leading order (LO, also known as gluo-dis…
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…
Due to the rapid longitudinal expansion of the quark-gluon plasma created in heavy-ion collisions, large local-rest-frame momentum-space anisotropies are generated during the system's evolution. These momentum-space anisotropies complicate the modeling of heavy-quarkonium dynamics in the quark-gluon plasma due to the fact that the resulting inter-quark potentials are spatially anisotropic, requiring real-time solution of the 3D Schrödinger equation. Herein, we introduce a method for reducing anisotropic heavy-quark potentials to isotropic ones by introducing an effective screening mass that de…
Quarkonium spectra with magnetically induced anisotropic confinement
Advanced Science Research Center, Japan Atomic Energy Agency（日本原子力机构先进科学研究中心）；Research Center for Nuclear Physics, The University of Osaka（大阪大学核物理研究中心）
Recently we have proved the NRQCD factorization in heavy quarkonium production at high energy colliders at all orders in coupling constant. In this paper we extend this to non-equilibrium QCD and prove the NRQCD factorization in heavy quarkonium production at all orders in coupling constant in non-equilibrium QCD. This proof is necessary to study heavy quarkonium production from quark gluon plasma at RHIC and LHC.
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…
The possibility of describing the behavior of a $Q\overline{Q}$ pair in a hot plasma in terms of an effective potential is investigated. It is shown that as long as medium effects can be embodied in a gaussian action, like in the QED case, the $Q\overline{Q}$ propagator obeys a closed temporal evolution equation whose large-time behavior is governed by an effective potential. The latter, beside screening, displays also an imaginary part related to collisions.
The non-equilibrium properties of quark-gluon plasma (QGP) have been a topic of intensive research. In this contribution, we explore the nature of heavy quarkonia immersed in a QGP with bulk viscosity. We incorporate the bulk viscous effect through the deformation of the distribution functions of thermal quarks and gluons, with which the color dielectric permittivity can be computed. We use the color dielectric permittivity to compute the heavy quark potential inside a bulk viscous plasma and solve the Schrödinger equation using the potential to obtain the physical properties such as binding e…
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.
The peak of the heavy quark pair entropy at the deconfinement transition, observed in lattice QCD, suggests that the transition is effectively driven by the increase of the entropy of bound states. The growth of the entropy with the inter-quark distance leads to the emergent entropic force that induces dissociation of quarkonium states. Since the quark-gluon plasma around the transition point is a strongly coupled system, we use the gauge-gravity duality to study the entropy of heavy quarkonium and the real-time dynamics of its dissociation. In particular, we employ the Improved Holographic QC…
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…
By means of effective field theory techniques, we study the modifications of some properties of weakly coupled heavy quarkonium states propagating through a quark-gluon plasma at temperatures much smaller than the heavy quark mass, m_Q. Two different cases are considered, corresponding to two different hierarchies between the typical size of the bound state, r, the binding energy, E, the temperature, T, and the screening mass, m_D. The first case corresponds to the hierarchy m_Q >> 1/r >> T >> E >> m_D, relevant for moderate temperatures, and the second one to the hierarchy m_Q >> T >> 1/r, m_…
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.
We calculate the dissociation and recombination rates of $Υ(1S)$ in quark-gluon plasma by using potential non-relativistic QCD. We then study the dynamical in-medium evolution of the $b\bar{b}-Υ$ system in a periodic box via the Boltzmann equation and explore how the system reaches equilibrium. We find that interactions between the free heavy quarks and the medium are necessary for the system to reach equilibrium. We find that the angular distribution of $Υ(1S)$ probes the stages at which recombination occurs. Finally, we study the system under a longitudinal expansion and show that different …
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…
Transport equations have been applied successfully to describe the quarkonium evolution inside the quark-gluon plasma, which include both plasma screening effects and recombination. We demonstrate how the quarkonium transport equation is derived from QCD by using the open quantum system framework and effective field theory. Weak coupling and Markovian approximations used in the derivation are justified from a separation of scales. By solving the equations numerically, we study the Upsilon production in heavy ion collisions.
We propose an open quantum systems approach to the physics of heavy quarkonia in a thermal medium, based on stochastic quantum evolution. This description emphasizes the importance of collisions with the environment and focuses on the concept of spatial decoherence of the heavy quarkonium wave function. It is shown how to determine the parameters of the dynamical evolution, i.e. the real potential and the noise strength, from a comparison with quantities to be obtained from lattice QCD. Furthermore the imaginary part of the lattice QCD heavy quark potential is found to be naturally related to …
In this work we calculate the lifetime of quarkonium moving with velocity $v$ through a quark gluon plasma at temperature $T$. We also investigate the stability of heavy mesons with respect to the effects of color charge screening. An explicit, configuration-space potential is found for the screened interaction between the quarks constituting the meson. We solve the Schrödinger equation for the relative motion of the quarks in this non-spherical potential. In this way, we determine the range of $v,T$ values for which the meson is bound. When a bound state exists, we use the bound-state wavefun…
We study the dispersion relations of mesons in a particular hot strongly coupled supersymmetric gauge theory plasma. We find that at large momentum k the dispersion relations become omega = v_0 k + a + b/k + ..., where the limiting velocity v_0 is the same for mesons with any quantum numbers and depends only on the ratio of the temperature to the quark mass T/m_q. We compute a and b in terms of the meson quantum numbers and T/m_q. The limiting meson velocity v_0 becomes much smaller than the speed of light at temperatures below but close to T_diss, the temperature above which no meson bound st…
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.
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）
Recently we have proved NRQCD color octet factorization of S-wave and P-wave heavy quarkonia production at all orders in coupling constant in QCD in vacuum at high energy colliders in Eur. Phys. J. C76 (2016) 448 and in arXiv:1807.04722 [hep-ph] respectively. In this paper we extend this to prove NRQCD color octet factorization of P-wave heavy quarkonium production in non-equilibrium QCD at RHIC and LHC at all orders in coupling constant. This proof is necessary to study the quark-gluon plasma at RHIC and LHC.
Previous research has shown that the peak of the quarkonium entropy at the deconfinement transition would be related to the entropic force which induces the melting of quarkonium. In this article, we study the effect of backreaction on the entropic force in a strongly coupled plasma of adjoint matter. The backreaction covered here comes from the presence of static heavy quarks evenly distributed over such a plasma. It is found that the inclusion of backreaction increases the entropic force thus enhancing the quarkonium dissociation, in accord with the findings of the imaginary potential.
We use the open quantum system formalism to study the dynamical in-medium evolution of quarkonium. The system of quarkonium is described by potential non-relativistic QCD while the environment is a weakly coupled quark-gluon plasma in local thermal equilibrium below the melting temperature of the quarkonium. Under the Markovian approximation, it is shown that the Lindblad equation leads to a Boltzmann transport equation if a Wigner transform is applied to the system density matrix. Our derivation illuminates how the microscopic time-reversibility of QCD is consistent with the time-irreversible…
We compute the screening length for quarkonium mesons moving through an anisotropic, strongly coupled N=4 super Yang-Mills plasma by means of its gravity dual. We present the results for arbitrary velocities and orientations of the mesons, as well as for arbitrary values of the anisotropy. The anisotropic screening length can be larger or smaller than the isotropic one, and this depends on whether the comparison is made at equal temperatures or at equal entropy densities. For generic motion we find that: (i) mesons dissociate above a certain critical value of the anisotropy, even at zero tempe…
