Heavy-quark Diffusion Coefficient Research Articles

Heavy quark drag and diffusion coefficients in the prehydrodynamic QCD plasma

Heavy quark drag and diffusion coefficients in the prehydrodynamic QCD plasma

Bottom-hadron production in high-energy pp and heavy-ion collisions

The hadro-chemistry of bottom quarks produced in hadronic collisions encodes valuable information on the mechanism of color-neutralization in these reactions. We first compute the chemistry of bottom-hadrons in high-energy pp collisions employing statistical hadronization with a largely augmented set of states beyond the currently measured spectrum. This enables a comprehensive prediction of fragmentation fractions of weakly decaying bottom hadrons for the first time and a satisfactory explanation of the existing measurements in pp collisions at the LHC. Utilizing the bottom hadro-chemistry thus obtained as the baseline, we then perform transport simulations of bottom quarks in the hot QCD matter created in PbPb collisions at the LHC energy and calculate the pertinent bottom-hadron observables. The transverse momentum (pT) dependent modifications of the bottom baryon-to-meson ratio (Λb0/B-) relative to their pp counterparts are highlighted as a result of bottom quark diffusion and hadronization in the Quark-Gluon Plasma (QGP). We finally summarize the heavy quark (charm vs bottom) diffusion coefficients as extracted from transport simulations and compare them to result from recent full lattice QCD computations.

Machine Learning Approach to Analyze the Heavy Quark Diffusion Coefficient in Relativistic Heavy Ion Collisions.

The diffusion coefficient of heavy quarks in a deconfined medium is examined in this research using a deep convolutional neural network (CNN) that is trained with data from relativistic heavy ion collisions involving heavy flavor hadrons. The CNN is trained using observables such as the nuclear modification factor RAA and the elliptic flow v2 of non-prompt J/ψ from the B-hadron decay in different centralities, where B meson evolutions are calculated using the Langevin equation and the instantaneous coalescence model. The CNN outputs the parameters, thereby characterizing the temperature and momentum dependence of the heavy quark diffusion coefficient. By inputting the experimental data of the non-prompt J/ψ(RAA,v2) from various collision centralities into multiple channels of a well-trained network, we derive the values of the diffusion coefficient parameters. Additionally, we evaluate the uncertainty in determining the diffusion coefficient by taking into account the uncertainties present in the experimental data (RAA,v2), which serve as inputs to the deep neural network.

Holographic energy loss near critical temperature in an anisotropic background

We study the energy loss of a quark moving in a strongly coupled quark gluon plasma under the influence of anisotropy. The heavy quark drag force, diffusion coefficient, and jet quenching parameter are calculated using the Einstein–Maxwell-dilaton model, where the anisotropic background is characterized by an arbitrary dynamical parameter A. Our findings indicate that as the anisotropic factor A increases, the drag force and jet quenching parameter both increase, while the diffusion coefficient decreases. Additionally, we observe that the energy loss becomes more significant when the quark moves perpendicular to the anisotropy direction in the transverse plane. The enhancement of the rescaled jet quenching parameters near critical temperature T c , as well as drag forces for a fast-moving heavy quark is observed, which presents one of the typical features of quantum chromodynamics phase transition.

Heavy Quark Diffusion from 2+1 Flavor Lattice QCD with 320MeV Pion Mass.

We present the first calculations of the heavy flavor diffusion coefficient using lattice QCD with light dynamical quarks corresponding to a pion mass of around 320MeV. For temperatures 195 MeV<T<352 MeV, the heavy quark spatial diffusion coefficient is found to be significantly smaller than previous quenched lattice QCD and recent phenomenological estimates. The result implies very fast hydrodynamization of heavy quarks in the quark-gluon plasma created during ultrarelativistic heavy-ion collision experiments.

Heavy quark diffusion coefficient with gradient flow

We calculate chromo-electric and chromo-magnetic correlators in quenched QCD at $1.5T_c$ and $10^4 T_c$ with the aim to estimate the heavy quark diffusion coefficient at leading order in the inverse heavy quark mass expansion, $\kappa_E$, as well as the coefficient of first mass suppressed correction, $\kappa_B$. We use gradient flow for noise reduction. At $1.5T_c$ we obtain: $1.70 \le \kappa_E/T^3 \le 3.12$ and $1.03< \kappa_B/T^3 < 2.61$. The latter implies that the mass suppressed effects in the heavy quark diffusion coefficient are 20% for bottom quarks and 34% for charm quark at this temperature.

Estimation of the diffusion coefficient of heavy quarks in light of Gribov-Zwanziger action

The heavy quark momentum diffusion coefficient (κ) is one of the most essential ingredients for the Langevin description of heavy quark dynamics. In the temperature regime relevant to the heavy ion collision phenomenology, a substantial difference exists between the lattice estimations of κ and the corresponding leading order (LO) result from the hard thermal loop (HTL) perturbation theory. Moreover, the indication of poor convergence in the next-to-leading order (NLO) perturbative analysis has motivated the development of several approaches to incorporate the non-perturbative effects in the heavy quark phenomenology. In this work, we estimate the heavy quark diffusion coefficient based on the Gribov-Zwanziger prescription. In this framework, the gluon propagator depends on the temperature-dependent Gribov mass parameter, which has been obtained self-consistently from the one-loop gap equation. Incorporating this modified gluon propagator in the analysis, we find a reasonable agreement with the existing lattice estimations of κ within the model uncertainties.

Non-Abelian electric field correlator at NLO for dark matter relic abundance and quarkonium transport

We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU(Nc) plasma, which encodes properties of the plasma relevant for heavy particle bound state formation and dissociation, and is different from the correlator for the heavy quark diffusion coefficient. The calculation is carried out in the real-time formalism of thermal field theory and includes both vacuum and finite temperature contributions. By working in the Rξ gauge, we explicitly show the results are gauge independent, infrared and collinear safe. The renormalization group equation of this electric field correlator is determined by that of the strong coupling constant. Our next-to-leading order calculation can be directly applied to any dipole singlet-adjoint transition of heavy particle pairs. For example, it can be used to describe dissociation and (re)generation of heavy quarkonia inside the quark-gluon plasma well below the melting temperature, as well as heavy dark matter pairs (or charged co-annihilating partners) in the early universe.

Charming charm, beautiful bottom and quark–gluon plasma in the Large Hadron Collider era

After a few microseconds of the creation of our Universe through the Big Bang, the primordial matter was believed to be a soup of the fundamental constituents of matter -- quarks and gluons. This is expected to be created in the laboratory by colliding heavy nuclei at ultra-relativistic speeds. A plasma of quarks and gluons, called Quark-Gluon Plasma (QGP) can be created at the energy and luminosity frontiers in the Relativistic Heavy Ion Collider (RHIC), at Brookhaven National Laboratory, New York, USA, and the Large Hadron Collider (LHC) at CERN, Geneva, Switzerland. Heavy quarks, namely the charm and bottom quarks, are considered as novel probes to characterize QGP, and hence the produced Quantum Chromodynamics (QCD) matter. Heavy quark transport coefficients play a significant role in understanding the properties of QGP. Experimental measurements of nuclear suppression factor and elliptic flow can constrain the heavy quark transport coefficients, which are key ingredients for phenomenological studies, and they help to disentangle different energy loss mechanisms. We give a general perspective of the heavy quark drag and diffusion coefficients in QGP and discuss their potentials as probes to disentangle different hadronization mechanisms, as well as to probe the initial electromagnetic fields produced in non-central heavy-ion collisions. Experimental perspectives on future measurements are discussed with special emphasis on heavy-flavors as next-generation probes in view of new technological developments.

Langevin dynamics of heavy quarks in a soft-hard factorized approach

By utilizing a soft-hard factorized model, which combines a thermal perturbative description of soft scatterings and a perturbative QCD-based calculation for hard collisions, we study the energy and temperature dependence of the heavy quark diffusion coefficients in Langevin dynamics. The adjustable parameters are fixed from the comprehensive model-data comparison. We find that a small value of the spatial diffusion coefficient at transition temperature is preferred by data 2pi TD_{s}(T_{c}) simeq 6. With the parameter-optimized model, we are able to describe simultaneously the prompt D^{0}R_{mathrm{AA}} and v_{mathrm{2}} data at p_{mathrm{T}}le 8 GeV in Pb–Pb collisions at sqrt{s_{mathrm{NN}}}=2.76 and sqrt{s_{mathrm{NN}}}=5.02 TeV. We also make predictions for non-prompt D^{0} meson for future experimental tests down to the low momentum region.

Heavy quark diffusion in an overoccupied gluon plasma

We extract the heavy-quark diffusion coefficient κ and the resulting momentum broadening 〈p2〉 in a far-from-equilibrium non-Abelian plasma. We find several features in the time dependence of the momentum broadening: a short initial rapid growth of 〈p2〉, followed by linear growth with time due to Langevin-type dynamics and damped oscillations around this growth at the plasmon frequency. We show that these novel oscillations are not easily explained using perturbative techniques but result from an excess of gluons at low momenta. These oscillation are therefore a gauge invariant confirmation of the infrared enhancement we had previously observed in gauge-fixed correlation functions. We argue that the kinetic theory description of such systems becomes less reliable in the presence of this IR enhancement.

Heavy flavor quenching and flow: the roles of initial condition, pre-equilibrium evolution, and in-medium interaction * * Supported by the Natural Science Foundation of China (NSFC) (11805082, 11775095, 11890711, 11935007), a Project of Shandong Province Higher Educational Science and Technology Program (J17KB128), the China Scholarship Council (CSC) (201906775042), the U.S. Department of Energy (DOE) (DE-SC0013460), and the National Science Foundation

Within an advanced Langevin-hydrodynamics framework coupled to a hybrid fragmentation-coalescence hadronization model, we study heavy flavor quenching and flow in relativistic heavy-ion collisions. We investigate how the initial heavy quark spectrum, the in-medium energy loss and hadronization mechanisms of heavy quarks, the evolution profile of the pre-equilibrium stage, the medium flow, and the temperature dependence of heavy quark diffusion coefficients influence the suppression and elliptic flow of heavy mesons at the RHIC and the LHC. Our results show that the different modeling of initial conditions, pre-equilibrium evolution, and in-medium interactions can individually yield uncertainties of approximately 10-40% in D meson suppression and flow at a low transverse momentum. We also find that proper combinations of collisional versus radiative energy loss, coalescence versus fragmentation in hadronization, and the inclusion of medium flow are the most important factors for describing the suppression and elliptic flow of heavy mesons.

Data-driven extraction of heavy quark diffusion in quark-gluon plasma

Heavy quark production provides a unique probe of the quark-gluon plasma transport properties in heavy ion collisions. Experimental observables like the nuclear modification factor R_mathrm{AA} and elliptic anisotropy v_mathrm{2} of heavy flavor mesons are sensitive to the heavy quark diffusion coefficient. There now exist an extensive set of such measurements, which allow a data-driven extraction of this coefficient. In this work, we make such an attempt within our recently developed heavy quark transport modeling framework (Langevin-transport with Gluon Radiation, LGR). A question of particular interest is the temperature dependence of the diffusion coefficient, for which we test a wide range of possibility and draw constraints by comparing relevant charm meson data with model results. We find that a relatively strong increase of diffusion coefficient from crossover temperature T_c toward high temperature is preferred by data. We also make predictions for Bottom meson observables for further experimental tests.

Spectral and transport properties of quark–gluon plasma in a nonperturbative approach

Nonperturbative methods play an important role in quantum many-body systems, especially in situations with an interplay of continuum and bound states and/or large coupling strengths between the constituents. Employing the Luttinger-Ward functional (LWF) we have computed the equation of state (EoS) of the quark-gluon plasma (QGP) using fully dressed selfconsistent 1- and 2-body propagators. We first give an alternative derivation of our previously reported results for resumming the ladder diagram series of the LWF using a "matrix log" technique which accounts for dynamically formed bound and resonant states. Two types of solutions were found in selfconsistent fits to lattice-QCD data for the EoS, heavy-quark free energy and quarkonium correlators: a strongly coupled scenario (SCS) with broad parton spectral functions and strong meson resonances near the transition temperature vs. a weakly coupled scenario (WCS) with well-defined parton quasiparticles and weak meson resonances. Here, we discuss how these solutions can be distinguished by analyzing the pertinent transport properties. We focus on the specific shear viscosity, $(4\pi )\eta/s$, and the heavy-quark diffusion coefficient, $(2\pi T) {\cal D}_s$, including its mass dependence. At low temperatures, in the SCS, they turn out to be a factor of 2 within their conjectured quantum lower bound, while they are a factor of 2-5 larger in the WCS. At higher temperatures, the transport parameters of the two scenarios approach each other. We propose the ratio $ (4\pi\eta/s)/(2\pi T {\cal D}_s )$ as a measure to distinguish the perturbative and strong-coupling limits of 5/2 and 1, respectively.

Heavy quark diffusion in a Polyakov loop plasma

We calculate the transport coefficients, drag and momentum diffusion, of a heavy quark in a thermalized plasma of light quarks in the background of Polyakov loop. Quark thermal mass and the gluon Debye mass are calculated in a non-trivial Polyakov loop background. The constituent quark masses and the Polyakov loop is estimated within a Polyakov loop quark meson (PQM) model. The relevant scattering amplitudes for heavy quark and light partons in the background of Polyakov loop has been estimated within the matrix model. We have also compared the results with the Polyakov loop parameter estimated from lattice QCD simulations. We have studied the temperature and momentum dependence of heavy quark drag and diffusion coefficients. It is observed that the temperature dependence of the drag coefficient is quite weak which may play a key role to understand heavy quark observables at RHIC and LHC energies.

Transport phenomena with chiral fermions in strong magnetic fields

I discuss the electrical conductivity, bulk viscosity, and heavy-quark diffusion coefficient in strong magnetic fields putting emphasis on consequences of the chirality conservation on the perturbative relaxation dynamics.

From in-Medium Color Forces to Transport Properties of QGP

A thermodynamic quantum many-body T-matrix approach is employed to study the spectral and transport properties of the quark-gluon plasma at moderate temperatures where nonperturbative effects are essential. For the partonic two-body interaction we utilize a QCD-inspired Hamiltonian whose color forces are motivated by the heavy-quark (HQ) limit including remnants of the confining force, and augmented by relativistic corrections. We solve the in-medium parton propagators and T-matrices selfconsistently and resum the skeleton diagrams for the equation of state (EoS) to all orders thereby accounting for the dynamical formation of two-body bound states. Two types solutions for the in-medium potential are found in when fitting to lattice-QCD data for the EoS, HQ free energy and quarkonium correlators: a weakly-coupled scenario (WCS) with a (real part of the) potential close to the free energy, resulting in moderately broadened spectral functions and weak bound states near Tc, and a strongly-coupled scenario (SCS), with a much stronger potential which produces large imaginary parts (“melting” the parton spectral functions) and generates strong bound states near Tc. We calculate pertinent transport coefficients (specific shear viscosity and HQ diffusion coefficient) and argue that their constraints from heavy-ion phenomenology unambiguously favor the strongly-coupled scenario.

Charmonium and bottomonium spectral functions in the vector channel

In this paper we report our results on quarkonium spectral functions in the vector channel obtained from quenched lattice QCD simulations at T ∈ [0.75,2.25] Tc. The calculations have been performed on very large and fine isotropic lattices where both charm and bottom quarks can be treated relativistically. The spectral functions are reconstructed using the Maximum Entropy Method. We study the dissociation of quarkonium states from the temperature dependence of the spectral functions and estimate heavy quark diffusion coefficients using the low-frequency behavior of the vector spectral functions.

Drag force on heavy quarks and spatial string tension

Heavy quark transport coefficients in a strongly coupled Quark–Gluon Plasma can be evaluated using a gauge/string duality and lattice QCD. Via this duality, one can argue that for low momenta the drag coefficient for heavy quarks is proportional to the spatial string tension. Such a tension is well-studied on the lattice that allows one to straightforwardly make non-perturbative estimates of the heavy quark diffusion coefficients near the critical point. The obtained results are consistent with those in the literature.

Data-driven analysis for the temperature and momentum dependence of the heavy-quark diffusion coefficient in relativistic heavy-ion collisions

By applying a Bayesian model-to-data analysis, we estimate the temperature and momentum dependence of the heavy quark diffusion coefficient in an improved Langevin framework. The posterior range of the diffusion coefficient is obtained by performing a Markov chain Monte Carlo random walk and calibrating on the experimental data of $D$-meson $R_{\mathrm{AA}}$ and $v_2$ in three different collision systems at RHIC and the LHC: AuAu collisions at 200 GeV, PbPb collisions at 2.76 and 5.02 TeV. The spatial diffusion coefficient is found to be consistent with lattice QCD calculations and comparable with other models' estimation. We demonstrate the capability of our improved Langevin model to simultaneously describe the $R_{\mathrm{AA}}$ and $v_2$ at both RHIC and the LHC energies, as well as the higher order flow coefficient such as $D$-meson $v_3$. We show that by applying a Bayesian analysis, we are able to quantitatively and systematically study the heavy flavor dynamics in heavy-ion collisions.