Heavy Quark Diffusion Research Articles

Heavy-Quark Diffusion Dynamics in Quark–Gluon Plasma under Strong Magnetic Fields

We discuss heavy-quark dynamics in the quark-gluon plasma under a strong magnetic field induced by colliding nuclei. By the use of the diagrammatic resummation techniques for Hard Thermal Loop and the external magnetic field, we show analytic results of heavy-quark diffusion coefficient and drag force which become anisotropic due to the preferred spatial orientation in the magnetic field. We argue that the anisotropic diffusion coefficient gives rise to an enhancement/suppression of the heavy-quark elliptic flow depending on the transverse momentum.

Drag and diffusion of heavy quarks in a hot and anisotropic QCD medium

The propagation of heavy quarks (HQs) in a medium was quite often modeled by the Fokker-Plank (FP) equation. Since the transport coefficients, related to drag and diffusion processes are the main ingredients in the FP equation, the evolution of HQs is thus effectively controlled by them. At the initial stage of the relativistic heavy ion collisions, asymptotic weak-coupling causes the free-streaming motions of partons in the beam direction and the expansion in transverse directions are almost frozen, hence an anisotropy in the momentum space sets in. Since HQs are too produced in the same time therefore the study of the effect of momentum anisotropy on the drag and diffusion coefficients becomes advertently desirable. In this article we have thus studied the drag and diffusion of HQs in the anisotropic medium and found that the presence of the anisotropy reduces both drag and diffusion coefficients. In addition, the anisotropy introduces an angular dependence to both the drag and diffusion coefficients, as a result both coefficients get inflated when the partons are moving transverse to the direction of anisotropy than parallel to the direction of anisotropy.

Quarkonium Suppression in a Strongly-Coupled Quark–Gluon Plasma

We compute the quarkonium nuclear modification factor in a strongly coupled quark–gluon plasma for quarkonia that are S-wave Coulombic bound states. We perform the analysis in a non-relativistic effective field theory framework that is accurate at leading-order in the heavy-quark density expansion and at next-to-leading order in the multipole expansion. We write and solve the Lindblad equation for the heavy quark–antiquark density. Thermal mass shift, width and the Lindblad equation depend on only two non-perturbative parameters: the heavy-quark momentum diffusion coefficient and its dispersive counterpart. Finally, we provide preliminary numerical results for the nuclear modification factors of the 1S and 2S bottomonium states.

Overview of recent results from the STAR experiment

The Solenoidal Tracker at RHIC (STAR) experiment utilizes its excellent mid-rapidity tracking and particle identification capabilities to study the emergent properties of Quantum Chromodynamics (QCD). The STAR heavy-ion program at vanishingly small baryon density is aimed to address questions about the quantitative properties of the strongly-interacting Quark Gluon Plasma (QGP) matter created in high energy collisions (η/s, qˆ, chirality, transport parameters, heavy quark diffusion coefficients…). At finite baryon density, the questions concern the phases of nuclear matter (the QCD phase diagram) and the nature of the phase transition, namely: what is the onset collision energy for the formation of QGP? What is the nature of phase transition in heavy-ion collisions? Are there two phase transition regions? If yes, where is the critical point situated? At Quark Matter 2015, the STAR collaboration has presented a wealth of new experimental results which address these questions. In these proceedings I highlight a few of those results.

Recent developments in heavy flavor probes in lattice QCD

The analysis of heavy flavor lattice correlation functions to obtain insights into transport phenomena and bound state dissociation patterns is a difficult and interesting challenge from the point of view of lattice QCD spectroscopy. In this contribution to “Hard Probes 2015”, the recent developments and advances from different lattice efforts to determine the relevant spectral properties will be reviewed and discussed. The difficulties underlying this line of research will be highlighted and the obtained results assessed. Among others, results on the dissociation of charm systems and bottomonia, as well as the diffusion of heavy quarks will be addressed.

Heavy quark diffusion in strong magnetic fields at weak coupling and implications for elliptic flow

We compute the momentum diffusion coefficients of heavy quarks, $\kappa_\parallel$ and $\kappa_\perp$, in a strong magnetic field $B$ along the directions parallel and perpendicular to $B$, respectively, at the leading order in QCD coupling constant $\alpha_s$. We consider a regime relevant for the relativistic heavy ion collisions, $\alpha_s eB\ll T^2\ll eB$, so that thermal excitations of light quarks are restricted to the lowest Landau level (LLL) states. In the vanishing light-quark mass limit, we find $\kappa_\perp^{\rm LO}\propto \alpha_s^2 T eB$ in the leading order that arises from screened Coulomb scatterings with (1+1)-dimensional LLL quarks, while $\kappa_\parallel$ gets no contribution from the scatterings with LLL quarks due to kinematic restrictions. We show that the first non-zero leading order contributions to $\kappa_\parallel^{\rm LO}$ come from the two separate effects: 1) the screened Coulomb scatterings with thermal gluons, and 2) a finite light-quark mass $m_q$. The former leads to $\kappa_\parallel^{\rm LO,\,gluon} \propto \alpha_s^2 T^3$ and the latter to $\kappa_\parallel^{\rm LO,\,massive}\propto \alpha_s (\alpha_s eB)^{1/2} m_q^2$. Based on our results, we propose a new scenario for the large value of heavy-quark elliptic flow observed in RHIC and LHC. Namely, when $\kappa_\perp\gg\kappa_\parallel$, an anisotropy in drag forces gives rise to a sizable amount of the heavy-quark elliptic flow even if heavy quarks do not fully belong to an ellipsoidally expanding background fluid.

The iEBE-VISHNU code package for relativistic heavy-ion collisions

The iEBE-VISHNU code package performs event-by-event simulations for relativistic heavy-ion collisions using a hybrid approach based on (2+1)-dimensional viscous hydrodynamics coupled to a hadronic cascade model. We present the detailed model implementation, accompanied by some numerical code tests for the package. iEBE-VISHNU forms the core of a general theoretical framework for model-data comparisons through large scale Monte-Carlo simulations. A numerical interface between the hydrodynamically evolving medium and thermal photon radiation is also discussed. This interface is more generally designed for calculations of all kinds of rare probes that are coupled to the temperature and flow velocity evolution of the bulk medium, such as jet energy loss and heavy quark diffusion. Program summaryProgram title: iEBE-VISHNUCatalogue identifier: AEYA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5257939No. of bytes in distributed program, including test data, etc.: 262822421Distribution format: tar.gzProgramming language: Fortran, C++, python, bash, SQLite.Computer: Laptop, desktop, cluster.Operating system: Tested on GNU/Linux Ubuntu 12.04 x64, Red Hat Linux 6, Mac OS X 10.8+.RAM: 2G bytesClassification: 17.11, 17.16, 17.20.External routines: GNU Scientific Library (GSL), HDF5 (Fortran and C++ enabled), NumpyNature of problem: Relativistic heavy-ion collisions are tiny in size (V≈10−42m3) and live in a flash (∼5×10−23s). It is impossible to use external probes to study the properties of the quark-gluon plasma (QGP), a novel state of matter created during the collisions. Experiments can only measure the momentum information of stable hadrons, who are the remnants of the collisions. In order to extract the thermal and transport properties of the QGP one needs to rely on Monte-Carlo event-by-event model simulations, which reverse-engineer the experimental measurements to the early time dynamics of the relativistic heavy-ion collisions.Solution method: Relativistic heavy-ion collisions contain multiple stages of evolution. The physics that governs each stage is implemented into individual code components. A general driver script glues all the modular packages as a whole to perform large-scale Monte-Carlo simulations. The final results are stored into SQLite database, which supports standard querying for massive data analysis. By tuning transport coefficients of the QGP as free parameters, e.g. the specific shear viscosity η/s, we can constrain various transport properties of the QGP through model-data comparisons.Additional comments: !!!!! The distribution file for this program is over 260 Mbytes and therefore is not delivered directly when download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. !!!!!Running time: The following running time is tested on a laptop computer with a 2.4 GHz Intel Core i5 CPU, 4 GB memory. All the C++ and Fortran codes are compiled with the GNU Compiler Collection (GCC) 4.9.2 and -O3 optimization (Table 1).

Melting of charmonium in a magnetic field from an effective AdS/QCD model

We study the influence of a background magnetic field on the melting of the $J/\ensuremath{\psi}$ vector meson by introducing a Born-Infeld modification of the soft-wall model. Out of the three polarizations of the massive vector meson, we find that the longitudinal one (parallel to the applied magnetic field) melts only at an even higher temperature than the deconfinement temperature, whereas the two transverse polarizations melt at a lower temperature than in the absence of a magnetic field. We also conduct a preliminary investigation of the effect of the magnetic field on the heavy quark diffusion coefficient, showing an increased diffusion constant for the longitudinal polarization with respect to the transverse polarizations.

Prospects for dilepton rates from lattice QCD

We discuss the prospects of computing thermal dilepton rates from first principles lattice QCD. The focus lies in the determination of the meson vector-vector current spectral function to estimate the electrical conductivity, heavy quark diffusion and quarkonium dissociation. We review and compare recent results from continuum-extrapolated, quenched calculations, as well as dynamical two-flavor setups.

Modifications of heavy-flavor spectra insNN=62.4GeV Au-Au collisions

We calculate open heavy-flavor (HF) production in Au+Au collisions at $\sqrt{s_{\rm NN}}$=62.4 GeV utilizing a nonperturbative transport approach as previously applied in nuclear collisions at top RHIC and LHC energies. The effects of hot QCD matter are treated in a strong-coupling framework, by implementing heavy-quark diffusion, hadronization and heavy-flavor meson diffusion within a hydrodynamic background evolution. Since in our approach the heavy-flavor coupling to the medium is strongest in the pseudo-critical region, it is of interest to test its consequences at lower collision energies where the sensitivity to this region should be enhanced relative to the hotter (early) fireball temperatures reached at top RHIC and LHC energies. We find that the suppression and flow pattern of the non-photonic electrons from heavy-flavor decays at 62.4 GeV emerges from an intricate interplay of thermalization and initial-state effects, in particular a Cronin enhancement which is known to become more pronounced toward lower collision energies.

Continuum estimate of the heavy quark momentum diffusion coefficient κ

Among quantities playing a central role in the theoretical interpretation of heavy ion collision experiments at RHIC and LHC are so-called transport coefficients. Out of those heavy quark diffusion coefficients play an important role e.g. for the analysis of the quenching of jets containing c or b quarks (D or B mesons) as observed at RHIC and LHC [1]. We report on a lattice investigation of heavy quark momentum diffusion within pure SU(3) plasma above the deconfinement transition with the quarks treated to leading order in the heavy mass expansion. We measure the relevant “colour-electric” Euclidean correlator and based on several lattice spacings perform the continuum extrapolation. This extends our previous studies [2], [3] progressing towards a removal of lattice artifacts and a physical interpretation of the results. We find that the correlation function clearly exceeds its perturbative counterpart which suggests that at temperatures just above the critical one, non-perturbative interactions felt by the heavy quarks are stronger than within the weak-coupling expansion. Using an Ansatz for the spectral function which includes NNLO perturbative contributions we were able to determine, for the first time, a continuum estimate for the heavy quark momentum diffusion coefficient.

Hard and thermal probes of QGP from the perspective of lattice QCD

In this talk I review the current status of lattice QCD results on the hard and thermal probes of QGP, including jet quenching parameters, the melting of quarkonia and open heavy flavours, thermal photon/dilepton rates, electrical conductivity as well as heavy quark diffusion coefficients.

Heavy Flavor Suppression: Boltzmann vs Langevin

The propagation of heavy flavor through the quark gluon plasma has been treated commonly within the framework of Langevin dynamics, i.e. assuming the heavy flavor momentum transfer is much smaller than the light one. On the other hand a similar suppression factor RAA has been observed experimentally for light and heavy flavors. We present a thorough study of the approximations involved by Langevin equation by mean of a direct comparison with the full collisional integral within the framework of Boltzmann transport equation. We have compared the results obtained in both approaches which can differ substantially for charm quark leading to quite different values extracted for the heavy quark diffusion coefficient. In the case of bottom quark the approximation appears to be quite reasonable.

Recent Developments in Lattice Studies for Quarkonia

Abstract After discussing results of dilepton rates and electrical conductivity obtained from continuum extrapolated results of light quark correlation functions in quenched QCD I will give a review on recent developments in lattice QCD studies for quarkonia in the quark gluon plasma medium. Recent progress in the extraction of spectral properties from lattice QCD calculations of hadronic correlation functions will be discussed. Besides medium modifications of bound states and their dissociation in the plasma I will focus on transport coefficients, like heavy quark diffusion constants extracted from different correlation functions on the lattice. Present limitations and future perspectives for studies of quarkonia and related transport coefficients on the lattice will be discussed. See also [B. Muller, these proceedings, arXiv:1207.7302 ; C. Gale, these proceedings, arXiv:1208.2289 ; A. Rothkopf, these proceedings, arXiv:1207.5486 ; H.-T. Ding, arXiv:1207.5187 ] for recent overviews and related discussions of those topics.

Heavy quark energy loss and thermalization in hot and dense nuclear matter

We study heavy quark energy loss and thermalization in hot and dense nuclear medium. The diffusion of heavy quarks is calculated via a Langevin equation, both for a static medium as well as for a quark-gluon plasma (QGP) medium generated by a (3+1)-dimensional hydrodynamic model. We investigate how the initial configuration of the QGP and its properties affect the final state spectra and elliptic flow of heavy flavor mesons and non-photonic electrons. It is observed that both the geometric anisotropy of the initial profile and the flow profile of the hydrodynamic medium play important roles in the heavy quark energy loss process and the development of elliptic flow. Within our definition of the thermalization criterion and for reasonable values of the diffusion constant, we observe thermalization times that are longer than the lifetime of the QGP phase.

Color path-integral Monte-Carlo simulations of quark-gluon plasma: Thermodynamic and transport properties

Based on the quasiparticle model of the quark-gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for calculation of thermodynamic properties and -- closely related to the latter -- a Wigner dynamics method for calculation of transport properties of the QGP are formulated. The QGP partition function is presented in the form of a color path integral with a new relativistic measure instead of the Gaussian one traditionally used in the Feynman-Wiener path integral. It is shown that the PIMC method is able to reproduce the lattice QCD equation of state at zero baryon chemical potential at realistic model parameters (i.e. quasiparticle masses and coupling constant) and also yields valuable insight into the internal structure of the QGP. Our results indicate that the QGP reveals quantum liquid-like (rather than gas-like) properties up to the highest considered temperature of 525 MeV. The pair distribution functions clearly reflect the existence of gluon-gluon bound states, i.e. glueballs, at temperatures just above the phase transition, while meson-like $q\bar{q}$ bound states are not found. The calculated self-diffusion coefficient agrees well with some estimates of the heavy-quark diffusion constant available from recent lattice data and also with an analysis of heavy-quark quenching in experiments on ultrarelativistic heavy ion collisions, however, appreciably exceeds other estimates. The lattice and heavy-quark-quenching results on the heavy-quark diffusion are still rather diverse. The obtained results for the shear viscosity are in the range of those deduced from an analysis of the experimental elliptic flow in ultrarelativistic heavy ions collisions, i.e. in terms the viscosity-to-entropy ratio, $1/4\pi < \eta/S < 2.5/4\pi$, in the temperature range from 170 to 440 MeV.

D(s) meson as a quantitative probe of diffusion and hadronization in nuclear collisions.

The modifications of D(s)-meson spectra in ultrarelativistic heavy-ion collisions are identified as a quantitative probe of key properties of the hot nuclear medium. The unique valence-quark content of the D(s)=cs̄ couples the well-known strangeness enhancement with the collective-flow pattern of primordially produced charm quarks. This idea is illustrated utilizing a consistent strong-coupling treatment with hydrodynamic bulk evolution and nonperturbative T-matrix interactions for both heavy-quark diffusion and hadronization in the quark-gluon plasma (QGP). A large enhancement of the D(s) nuclear modification factor at Relativistic Heavy Ion Collider is predicted, with a maximum of ∼1.5-1.8 at transverse momenta around 2 GeV/c. This is a direct consequence of the strong coupling of the heavy quarks to the QGP and their hadronization via coalescence with strange quarks. We furthermore introduce the effects of diffusion in the hadronic phase and suggest that an increase of the D-meson elliptic flow compared to the D(s) can disentangle the transport properties of hadronic and QGP liquids.

A Random Walk with Heavy Flavours

We focus on evaluating transport coefficients like drag and diffusion of heavy quarks (HQ) passing through Quark Gluon Plasma using perturbative QCD (pQCD). Experimental observable like nuclear suppression factor (RAA) of HQ is evaluated for both zero and non-zero baryonic chemical potential ({\mu}_B) scenarios using Fokker- Planck equation. Theoretical estimates of RAA are contrasted with experiments.

Massive vector current correlator in thermal QCD

We present an NLO analysis of the massive vector current correlator at temperatures above a few hundred MeV. The physics of this correlator originates from a transport peak, related to heavy quark diffusion, and from the quark-antiquark threshold, related to quarkonium physics. In the bottom case both can be studied with separate effective theories, but for charm these may not be accurate, so a study within the full theory is needed. Working in imaginary time, the NLO correlator can be computed in unresummed perturbation theory; comparing with lattice data, we find good agreement. Subsequently we inspect how non-perturbative modifications of the transport peak would affect the imaginary-time correlator. The massive NLO quark-number susceptibility is also contrasted with numerical measurement.

Heavy-quark diffusion and hadronization in quark-gluon plasma

We calculate diffusion and hadronization of heavy quarks in high-energy heavy-ion collisions, implementing the notion of a strongly coupled quark-gluon plasma in both micro- and macroscopic components. The diffusion process is simulated using relativistic Fokker-Planck dynamics for elastic scattering in a hydrodynamic background. The heavy-quark transport coefficients in the medium are obtained from nonperturbative $T$-matrix interactions which build up resonant correlations close to the transition temperature. The latter also form the basis for hadronization of heavy quarks into heavy-flavor mesons via recombination with light quarks from the medium. The pertinent resonance recombination satisfies energy conservation and provides an equilibrium mapping between quark and meson distributions. The recombination probability is derived from the resonant heavy-quark scattering rate. Recombination is found to dominate at low transverse momentum (${p}_{T}$) and to yield to fragmentation at high ${p}_{T}$. Our approach emphasizes the role of resonance correlations in the diffusion and hadronization processes. Calculations of the nuclear modification factor and elliptic flow of $D$ and $B$ mesons and their decay electrons in Au-Au collisions at the Relativistic Heavy Ion Collider indicate the importance of a realistic medium flow in a quantitative interpretation of heavy-flavor data.