Heavy Quark Drag Research Articles

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

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.

Equation of State and Energy Loss of Hot and Dense Quark-Gluon matter from Holographic Black Holes

By using gravity/gauge correspondence, we construct a holographic model, constrained to mimic the lattice QCD equation of state at zero density, to investigate the temperature and baryon chemical potential dependence of the equation of state. We also obtained the energy loss of light and heavy partons within the hot and dense plasma represented by the heavy quark drag force, Langevin diffusion coefficients and jet quenching parameter at the critical point and across the first-order transition line predicted by the model.

Drag of heavy quarks in an anisotropic QCD medium beyond the static limit

Heavy quark dynamics in an anisotropic QCD medium have been analyzed within the Fokker-Planck approach. Heavy quark drag force and the momentum diffusion tensor have been decomposed by employing a general tensor basis for an anisotropic medium. Depending upon the relative orientation of the direction of the momentum anisotropy of the medium and heavy quark motion, two drag and four diffusion coefficients have been estimated in the anisotropic QCD medium. The relative significance of different components of drag and momentum diffusion coefficients has been explored. The dependence of the angle between the anisotropic vector and heavy quark motion to the drag and diffusion coefficients has also been studied. Furthermore, the energy loss of heavy quarks due to the elastic collisional process in an anisotropic medium has been studied. It is seen that the anisotropic contributions to heavy quark transport coefficients and its collisional energy loss have a strong dependence on the direction and strength of momentum anisotropy in the QCD medium.

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.

Heavy quark transport coefficients in a viscous QCD medium with collisional and radiative processes

The heavy quark drag and momentum diffusion coefficients in the presence of both the collisional and radiative processes have been studied in a hot viscous QCD medium. The thermal medium effects are incorporated by employing the effective fugacity quasiparticle model based on the lattice QCD equation of state. Viscous effects are embedded into the heavy quark transport through the near-equilibrium distribution functions of the constituent medium particles of the quark-gluon plasma. The viscous corrections to the momentum distributions have been estimated from the effective Boltzmann equation. The effect of shear viscous correction to drag and diffusion is investigated by considering the soft gluon radiation by heavy quarks along with the elastic collisional processes of the heavy quark with the light quarks and gluons within the QGP medium. The momentum and temperature dependence of the heavy quark transport coefficients are seen to be sensitive to the viscous coefficient of the QGP for the collisional and radiative processes. The collisional and radiative energy loss of the heavy quark in the viscous quark-gluon plasma has also been explored.

New developments in lattice QCD on equilibrium physics and phase diagram

I review recent new lattice QCD results on a few selected topics which are relevant to the heavy ion physics community. Special emphasis is put on the QCD phase diagram towards the chiral limit and at nonzero baryon density as well as the fate of quarkonia and heavy quark drag coefficients.

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.

Heavy quark dynamics in a hot magnetized QCD medium

The heavy quark drag and momentum diffusion have been investigated in a hot magnetized quark-gluon plasma, along the directions parallel and perpendicular to the magnetic field. The analysis is done within the framework of Fokker-Planck dynamics by considering the heavy quark scattering with thermal quarks and gluons at the leading order in the coupling constant. An extended quasiparticle model is adopted to encode the thermal QCD medium interactions in the presence of a magnetic field. Further, the higher Landau level effects on the temperature behaviour of the parallel and perpendicular components of the drag force and diffusion coefficients have studied. It has been observed that both the equation of state and the magnetic field play key roles in the temperature dependence of the heavy quark dynamics.

Large Directed Flow of Open Charm Mesons Probes the Three-Dimensional Distribution of Matter in Heavy-Ion Collisions.

Thermalized matter created in noncentral relativistic heavy-ion collisions is expected to be tilted in the reaction plane with respect to the beam axis. The most notable consequence of this forward-backward symmetry breaking is the observation of rapidity-odd directed flow for charged particles. On the other hand, the production points for heavy quarks are forward-backward symmetric and shifted in the transverse plane with respect to the fireball. The drag on heavy quarks from the asymmetrically distributed thermalized matter generates substantial directed flow for heavy flavor mesons. We predict a very large rapidity-odd directed flow of D mesons in noncentral Au-Au collisions at sqrt[s_{NN}]=200 GeV, several times larger than for charged particles. A possible experimental observation of a large directed flow for heavy flavor mesons would represent an almost direct probe of the three-dimensional distribution of matter in heavy-ion collisions.

Momentum transport in strongly coupled anisotropic plasmas in the presence of strong magnetic fields

We present a holographic perspective on momentum transport in strongly coupled, anisotropic non-Abelian plasmas in the presence of strong magnetic fields. We compute the anisotropic heavy quark drag forces and Langevin diffusion coefficients and also the anisotropic shear viscosities for two different holographic models, namely, a top-down deformation of strongly coupled $\mathcal{N} = 4$ Super-Yang-Mills (SYM) theory triggered by an external Abelian magnetic field, and a bottom-up Einstein-Maxwell-dilaton (EMD) model which is able to provide a quantitative description of lattice QCD thermodynamics with $(2+1)$-flavors at both zero and nonzero magnetic fields. We find that, in general, energy loss and momentum diffusion through strongly coupled anisotropic plasmas are enhanced by a magnetic field being larger in transverse directions than in the direction parallel to the magnetic field. Moreover, the anisotropic shear viscosity coefficient is smaller in the direction of the magnetic field than in the plane perpendicular to the field, which indicates that strongly coupled anisotropic plasmas become closer to the perfect fluid limit along the magnetic field. We also present, in the context of the EMD model, holographic predictions for the entropy density and the crossover critical temperature in a wider region of the $(T,B)$ phase diagram that has not yet been covered by lattice simulations. Our results for the transport coefficients in the phenomenologically realistic magnetic EMD model could be readily used as inputs in numerical codes for magnetohydrodynamics.

Toward an understanding of the RAA and v2 puzzle for heavy quarks

One of the primary aims of the ongoing nuclear collisions at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies is to create a Quark Gluon Plasma (QGP). The Heavy Quarks (HQ) constitutes a unique probe of the QGP properties. Both at RHIC and LHC energies a puzzling relation between the nuclear modification factor RAA(pT) and the elliptic flow v2(pT) related to heavy quark has been observed which challenged all the existing models.We discuss how the temperature dependence of the heavy quark drag coefficient can address for a large part of such a puzzle. We have considered four different models to evaluate the temperature dependence of drag and diffusion coefficients propagating through a quark gluon plasma (QGP). All the four different models are set to reproduce the same RAA(pT) experimentally observed at RHIC energy. We have found that for the same RAA(pT) one can generate 2–3 times more v2 depending on the temperature dependence of the heavy quark drag coefficient.

Impact of momentum space anisotropy on heavy quark dynamics in a QGP medium

Momentum space anisotropy present in the quark and gluon distribution functions in relativistic heavy ion collisions induces Chromo-Weibel instability in the hot QCD medium created therein. The impact of the Chromo-Weibel instability on the dynamics of a heavy-quark (HQ) traversing in the QGP medium is investigated within the framework of kinetic theory by studying the momentum and temperature behavior of HQ drag and diffusion coefficients. The physics of anisotropy is captured in an effective Vlasov term in the transport equation. The effects of the instability are handled by making a relation with the phenomenologically known jet quenching parameter in RHIC and LHC. Interestingly, the presence of instability significantly affect the temperature and momentum dependences of the HQ drag and diffusion coefficients. These results may have appreciable impact on the experimental observables such as, the nuclear suppression factor, $R_{AA}(p_T)$, and the elliptic flow, $v_2(p_T)$, of heavy mesons in heavy ion collisions at RHIC and LHC energies which is a matter of future investigation.

The charmonium dissociation in an “anomalous wind”

We study the charmonium dissociation in a strongly coupled chiral plasma in the presence of magnetic field and axial charge imbalance. This type of plasma carries "anomalous flow" induced by the chiral anomaly and exhibits novel transport phenomena such as chiral magnetic effect. We found that the "anomalous flow" would modify the charmonium color screening length by using the gauge/gravity correspondence. We derive an analytical expression quantifying the "anomalous flow" experienced by a charmonium for a large class of chiral plasma with a gravity dual. We elaborate on the similarity and {\it qualitative} difference between anomalous effects on the charmonium color screening length which are {\it model-dependent} and those on the heavy quark drag force which are fixed by the second law of thermodynamics. We speculate on the possible charmonium dissociation induced by the chiral anomaly in heavy ion collisions.

Toward a solution to the RAA and v2 puzzle for heavy quarks

The heavy quarks constitute a unique probe of the quark–gluon plasma properties. A puzzling relation between the nuclear modification factor RAA(pT) and the elliptic flow v2(pT) has been observed both at RHIC and LHC energies. Predicting correctly both observables has been a challenge to all existing models, especially for D mesons. We discuss how the temperature dependence of the heavy quark drag coefficient is responsible for a large part of such a puzzle. In particular, we have considered four different models to evaluate the temperature dependence of drag and diffusion coefficients propagating through a quark gluon plasma (QGP). All the four different models are set to reproduce the same RAA(pT) observed in experiments at RHIC and LHC energy. We point out that for the same RAA(pT) one can generate 2–3 times more v2 depending on the temperature dependence of the heavy quark drag coefficient. A non-decreasing drag coefficient as T→Tc is a major ingredient for a simultaneous description of RAA(pT) and v2(pT).

Drag of heavy quarks in quark gluon plasma at energies available at the CERN Large Hadron Collider (LHC)

The drag and diffusion coefficients of charm and bottom quarks propagating through quark gluon plasma (QGP) have been evaluated for conditions relevant to nuclear collisions at Large Hadron Collider (LHC). The dead cone and Landau-Pomeronchuk-Migdal (LPM) effects on radiative energy loss of heavy quarks have been considered. Both radiative and collisional processes of energy loss are included in the {\it effective} drag and diffusion coefficients. With these effective transport coefficients we solve the Fokker Plank (FP) equation for the heavy quarks executing Brownian motion in the QGP. The solution of the FP equation has been used to evaluate the nuclear suppression factor, $R_{\mathrm AA}$ for the non-photonic single electron spectra resulting from the semi-leptonic decays of hadrons containing charm and bottom quarks. The effects of mass on $R_{\mathrm AA}$ has also been highlighted.

Heavy quark jet tomography of the ultradense sQGP phase of nuclear matter

Heavy quark jet quenching in high energy nuclear collisions became a decisive tool to distinguish between theories based on Standard Model perturbative QCD and AdS/CFT gravity dual models. The momentum independence and inverse quark mass dependence of the drag coefficient in AdS/CFT differs substantially from the characteristic log ( p T / M ) / p T variation of the heavy quark drag in QCD, which was obtained from early calculations. The latest pQCD efforts on heavy quark energy loss include color magnetic dynamical effects and final size non-static coherence effects in perturbative quark gluon plasmas and the obtained results are much closer to the experimental data for heavy quarks. We discuss our recent understanding of heavy quark quenching and summarize the measurable quantities to distinguish between the pQCD and AdS/CFT scenarios.

Shock treatment: Heavy quark drag in a novel AdS geometry

We calculate the drag force on a heavy quark hit by a shock wave, thus generalizing the strongly coupled AdS/CFT heavy quark drag calculations to both hot and cold nuclear matter. The derivation employs the trailing string configuration, similar to that used in the literature for a quark moving through a thermal medium, though in the shock metric the string profile is described by a much simpler analytic function. Our expression for the drag depends on the typical transverse momentum scale of the matter in the shock. For a thermal medium this scale becomes proportional to the temperature, making our drag coefficient and momentum limit of applicability identical to those found previously. As the shock wave can be composed of either thermalized or non-thermalized media, our derivation extends the existing drag calculations to the case of arbitrarily distributed matter.

Heavy Quark Diffusion in AdS/CFT

The purpose of this short note is to clarify how thermal noise arises within the context of AdS/CFT.∗) Recently the AdS/CFT correspondence has been used to calculate several items of great interest to the heavy ion physics community. This list includes: the drag of heavy quarks,1)–3) higher order hydrodynamics,4),5) and radiative processes.6) All of these processes are intrinsically related to noise in thermal field theory. However, noise does not appear naturally within the AdS/CFT context. This is essentially manifest since it is difficult to acquire stochastic terms by solving linearized classical equations of motion. However it turns out that the quantum mechanics of AdS5 produces the required thermal noise. To address the question of noise we will consider the simplest stochastic process — Brownian motion. General considerations of heavy quarks would indicate that the heavy quark should obey a Langevin equation of motion

Heavy quark three-body collisional energy loss in QGP

Heavy quark drag coefficients due to three-body elastic scattering in a quark–gluon plasma have been evaluated in the lowest order in QCD. They are found to have similar values as those due to two-body elastic scattering, and both are larger than those due to two-body radiative scattering if the momenta of charm and bottom quarks are below about 4 and 9 GeV/c, respectively. Including three-body elastic scattering increases the momentum degradation of heavy quarks in QGP, bringing the nuclear modification factor for electrons from the decays of produced heavy mesons in Au+Au collisions at closer to the measured one.