Heavy Quark Diffusion Research Articles

Hadronization of heavy quarks

Heavy-flavor hadrons produced in ultrarelativistic heavy-ion collisions are a sensitive probe for studying hadronization mechanisms of the quark-gluon-plasma. In this paper, we survey how different transport models for the simulation of heavy-quark diffusion through a quark-gluon plasma in heavy-ion collisions implement hadronization and how this affects final state observables. Utilizing the same input charm-quark distribution in all models at the hadronization transition, we find that the transverse-momentum dependence of the nuclear modification factor of various charm hadron species has significant sensitivity to the hadronization scheme. In addition, the charm-hadron elliptic flow exhibits a nontrivial dependence on the elliptic flow of the hadronizing partonic medium. Published by the American Physical Society 2024

Heavy quark drag and diffusion coefficients in the prehydrodynamic QCD plasma

Kinetic and chemical equilibrations play important roles in the formation of the quark-gluon plasma (QGP) in relativistic heavy-ion collisions (HICs). These processes further influence the production of hard and electromagnetic probes in HICs, in particular, the thermalization of heavy quarks, which are produced at an extremely early time before the formation of the QGP. I calculate the drag and diffusion coefficients of heavy quarks in the prehydrodynamic quantum chromodynamic (QCD) plasma with the state-of-the-art QCD effective kinetic theory (EKT) solver. The time, momentum, and angular dependencies of these coefficients for gluon and quark contributions are presented separately, showing the effects of isotropization and chemical equilibration from the QCD plasma. I also provide a simple formula to estimate the heavy quark drag and diffusion coefficients, as well as its energy loss, within the prehydrodynamic plasma at different coupling strengths based on the attractor theory. Finally, I discuss the validity of these estimations with leading-order calculations and leading-logarithmic rescaling factors. Published by the American Physical Society 2024

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.

Memory effects on energy loss and diffusion of heavy quarks in the quark-gluon plasma

We study the dynamics of heavy quarks in a thermalized quark-gluon plasma with a time-correlated thermal noise, $\ensuremath{\eta}$. In this case, it is said that $\ensuremath{\eta}$ has memory. We use an integro-differential Langevin equation in which the memory enters via the thermal noise and the dissipative force. We assume that the time correlations of the noise decay exponentially on a timescale, $\ensuremath{\tau}$, which we treat as a free parameter. We compute the effects of $\ensuremath{\tau}\ensuremath{\ne}0$ on the thermalization time of the heavy quarks, on their momentum broadening, and on the nuclear modification factor. We find that overall memory slows down the momentum evolution of heavy quarks: In fact, transverse momentum broadening and the formation of ${R}_{AA}$ are slowed down by memory and the thermalization time of the heavy quarks become larger. The potential impact on other observables is discussed briefly.

Fluid-dynamic approach to heavy-quark diffusion in the quark-gluon plasma

A fluid-dynamic approach to the diffusion of heavy quarks in the quark-gluon plasma (QGP) is presented. Specifically, we analyze the Fokker-Planck equation for the momentum transport of heavy quarks from a fluid perspective and use a mapping to second-order fluid dynamics to determine conductivities and relaxation times governing their spatial diffusion. By investigating the relation between the two approaches, we provide new insights concerning the level of local thermalization of charm and bottom quarks inside the expanding QGP. Our results indicate that a fluid-dynamic description of diffusion is feasible for charm quarks at least for the latest stages of the fireball evolution.

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.

Effect of magnetic screening mass on the diffusion of heavy quarks

The drag and diffusion coefficients of heavy quarks propagating through quark–gluon plasma (QGP) have been estimated by shielding the infra-red divergences using electric and magnetic screening masses. The electric-type screening in perturbative quantum chromodynamics (pQCD) has been widely studied and used in evaluating the diffusion coefficient of heavy quarks (HQs). The impact of magnetic screening on diffusion coefficients of HQs is not studied before to the best of our knowledge. We explore the effect of magnetic screening mass on the drag and diffusion coefficients of HQs and found it to be non-negligible. Therefore, the effect of magnetic screening should be taken into consideration to characterize hot and dense matter formed in the collisions of nuclei at ultra-relativistic energies. We estimate the suppression of heavy flavored mesons in heavy ion collisions compared to proton+proton collisions at high transverse momenta and found that the suppression is less with the inclusion of magnetic screening. The value of the magnetic screening mass is not known exactly because of its nonperturbative nature. Moreover, it may not be possible to single out the effect of magnetic mass because of the uncertainties in other parameters involved in the diffusion process of HQs. Still it is important to include the effects of magnetic screening because of its physical origin in QCD.

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.

1-loop matching of a thermal Lorentz force

Studying the diffusion and kinetic equilibration of heavy quarks within a hot QCD medium profits from the knowledge of a coloured Lorentz force that acts on them. Starting from the spatial components of the vector current, and carrying out two matching computations, one for the heavy quark mass scale (M) and another for thermal scales left(sqrt{MT},Tright) , we determine 1-loop matching coefficients for the electric and magnetic parts of a Lorentz force. The magnetic part has a non-zero anomalous dimension, which agrees with that extracted from two other considerations, one thermal and the other in vacuum. The matching coefficient could enable a lattice study of a colour-magnetic 2-point correlator.

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.

Ballistic diffusion of heavy quarks in the early stage of relativistic heavy ion collisions at RHIC and the LHC

We study the diffusion of charm quarks in the early stage of high energy nuclear collisions at the RHIC and the LHC. The main novelty of the present study is the introduction of the color current carried by the heavy quarks that propagate in the evolving glasma (EG), which is responsible of the energy loss via polarization of the medium. We compute the transverse momentum broadening, ${\ensuremath{\sigma}}_{p}$, of charm in the prethermalization stage, and the impact of the diffusion on the nuclear modification factor in nucleus-nucleus collisions. The net effect of energy loss is marginal in the prethermalization stage. The study is completed by the calculation of coordinate spreading, ${\ensuremath{\sigma}}_{x}$, and by a comparison with Langevin dynamics. ${\ensuremath{\sigma}}_{p}$ in EG overshoots the result of standard Langevin dynamics at the end of the prehydro regime. We interpret this as a result of memory of the color force acting on the charm quarks that implies ${\ensuremath{\sigma}}_{p}\ensuremath{\propto}{t}^{2}$. Moreover, ${\ensuremath{\sigma}}_{x}\ensuremath{\propto}{t}^{2}$ in the prehydro stage shows that the charm quark in the EG is in the regime of ballistic diffusion.

Mass-suppressed effects in heavy quark diffusion

Many lattice studies of heavy quark diffusion originate from a colour-electric correlator, obtained as a leading term after an expansion in the inverse of the heavy-quark mass. In view of the fact that the charm quark is not particularly heavy, we consider subleading terms in the expansion. Working out correlators up to mathcal{O} (1/M2), we argue that the leading corrections are suppressed by mathcal{O} (T/M), and one of them can be extracted from a colour-magnetic correlator. The corresponding transport coefficient is non-perturbative already at leading order in the weak-coupling expansion, and therefore requires a non­perturbative determination.

Diffusion of heavy quarks in the early stage of high-energy nuclear collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider

We study the diffusion of charm and beauty in the early stage of high energy nuclear collisions at RHIC and LHC energies, considering the interaction of these heavy quarks with the evolving Glasma by means of the Wong equations. In comparison with previous works, we add the longitudinal expansion as well as we estimate the effect of energy loss due to gluon radiation. We find that heavy quarks diffuse in the strong transverse color fields in the very early stage (0.2-0.3 fm/c) and this leads to a suppression at low $p_T$ and enhancement at intermediate low $p_T$. The shape of the observed nuclear suppression factor obtained within our calculations is in qualitative agreement with the experimental results of the same quantity for $D-$mesons in proton-nucleus collisions. We compute the nuclear suppression factor in nucleus-nucleus collisions as well, for both charm and beauty, finding a substantial impact of the evolving Glasma phase on these, suggesting that initialization of heavy quarks spectra in the quark-gluon plasma phase should not neglect the early evolution in the strong gluon fields.

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.