Heavy Quark Dynamics Research Articles

Subdiffusion of heavy quarks in hot QCD matter by the fractional Langevin equation

The subdiffusion phenomena are studied for heavy quarks dynamics in the hot QCD matter. Our approach aims to provide a more realistic description of heavy quark dynamics through detailed theoretical analyses and numerical simulations, utilizing the fractional Langevin equation framework with the Caputo fractional derivative. I present numerical schemes for the fractional Langevin equation for subdiffusion and calculate the time evolution mean squared displacement and mean squared momentum of the heavy quarks. My results indicate that the mean squared displacements of the heavy quarks for the subdiffusion process deviate from a linear relationship with time. Further, I calculate the normalized momentum correlation function, kinetic energy, and momentum spread. Finally, I show the effect of subdiffusion on experimental observables, the nuclear modification factor. Published by the American Physical Society 2024

Anomalous diffusion of the heavy quarks through the fractional Langevin equation

The dynamics of heavy quarks within the hot QCD medium have been revisited, considering the influence of anomalous diffusion. This study has been conducted using the framework of the fractional Langevin equation involving the Caputo fractional derivative. We introduce a numerical scheme for the fractional Langevin equation and demonstrate that the mean-squared displacement of the particle exhibits anomalous diffusion, deviating from a linear relationship with time. Our analysis calculates various entities, such as mean-squared momentum, momentum spread, and the nuclear suppression factor RAA. Notably, our findings indicate that superdiffusion strongly suppresses the RAA compared to normal diffusion in the hot QCD medium. The possible impacts on other parameters are also discussed. Published by the American Physical Society 2024

Responses of quark-antiquark interactions and heavy quark dynamics to magnetic fields

We investigate the impact of the magnetic field generated by colliding nuclei on heavy quark-antiquark interactions and heavy quark dynamics in the quark-gluon plasma (QGP). By means of the hard-thermal-loop resummation technique combined with dimension-two gluon condensates, the static heavy quark potential and heavy quark momentum diffusion coefficient, which incorporate both perturbative and nonperturbative interactions between heavy quarks and the QGP medium, are computed beyond the lowest Landau level approximation. We find that the imaginary part of the heavy quark potential in the magnetic field exhibits significant anisotropy. Specifically, the absolute value of the imaginary part is larger when the quark-antiquark separation is aligned perpendicular to the magnetic field direction, compared to when it is aligned parallel to the magnetic field direction. The heavy quark momentum diffusion coefficient in the magnetized QGP medium also becomes anisotropic. As the temperature rises, the influence of higher Landau levels becomes increasingly significant, resulting in a decrease in the anisotropy ratio of the heavy quark momentum diffusion coefficient to values even below 1. At sufficiently high temperatures, this ratio ultimately approaches 1. The nonperturbative interactions are indispensable for understanding heavy quark dynamics in the low-temperature region. We also study the response of viscous quark matter to the magnetic field and explore its implications for heavy quark potential, thermal decay widths of quarkonium states, as well as heavy quark momentum diffusion coefficient. Published by the American Physical Society 2024

Dynamics of heavy quarks in the Fock space

Dynamics of heavy quarks in the Fock space

Comparative study of the heavy-quark dynamics with the Fokker-Planck equation and the Plastino-Plastino equation

The Fokker-Planck Equation (FPE) is a fundamental tool for the investigation of kinematic aspects of a wide range of systems. The Plastino-Plastino Equation (PPE) is the correct generalization describing the kinematic evolution of complex systems consistent with q-statistics. In the present work, we use this particular problem to compare the results obtained with the FPE and the PPE, and discuss the different aspects of the dynamical evolution of the system according to the solutions for each equation. We observe clear differences in the solutions for all the cases studied here and discuss possible experimental investigations that can indicate which of those equations better describes the heavy-quark kinematics in the medium. The results obtained here have implications in the study of anomalous diffusion in porous and granular media, in Cosmology and Astrophysics. The obtained results reinforce the validity of the relation (q−1)−1=(11/3)Nc−(4/3)(Nf/2), where Nc and Nf are, respectively, the number of colours and the effective number of flavours. This equation was recently established in the context of a fractal approach to QCD in the non-perturbative regime.

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.

Heavy quark dynamics in a strongly magnetized quark-gluon plasma

We present a calculation of the heavy quark momentum diffusion coefficients in a quark-gluon plasma under the presence of a strong external magnetic field, within the Lowest Landau Level (LLL) approximation. In particular, we apply the Hard Thermal Loop (HTL) technique for the resummed effective gluon propagator, generalized for a hot and magnetized medium. Using the derived effective HTL gluon propagator and the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients as well as the energy losses for charm and bottom quarks beyond the static limit. We also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.

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.

Heavy quark dynamics in a strongly magnetized medium

We present a calculation of the heavy quark momentum diffusion coefficients in a strongly magnetized medium, within the Lowest Landau Level (LLL) approximation. In particular, we use the Hard Thermal Loop (HTL) resummed effective gluon propagator, generalized for a hot and magnetized medium. Using this effective HTL gluon propagator along with the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Going beyond the static limit of the heavy quark, we also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.

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 transport in an anisotropic hot QCD medium: Collisional and radiative processes

The impact of momentum anisotropy on the heavy quark transport coefficients due to collisional and radiative processes in the QCD medium has been studied within the ambit of kinetic theory. Anisotropic aspects (momentum) are incorporated into the heavy quark dynamics through the non-equilibrium momentum distribution function of quarks, antiquarks, and gluons. These non-equilibrium distribution functions that encode the physics of momentum anisotropy and turbulent chromo-fields have been obtained by solving the ensemble-averaged diffusive Vlasov-Boltzmann equation. The momentum dependence of heavy quark transport coefficients in the medium is seen to be sensitive to the strength of the anisotropy for both collisional and radiative processes. In addition, the collisional and radiative energy loss of the heavy quark in the anisotropic hot QCD medium have been analyzed. The effects of anisotropy on the drag and diffusion coefficients are observed to have a visible impact on the nuclear suppression factor both at the RHIC and LHC.

Probing the Effects of Strong Electromagnetic Fields with Charge-Dependent Directed Flow in Pb-Pb Collisions at the LHC

The first measurement at the LHC of charge-dependent directed flow (v_{1}) relative to the spectator plane is presented for Pb-Pb collisions at sqrt[s_{NN}]=5.02 TeV. Results are reported for charged hadrons and D^{0} mesons for the transverse momentum intervals p_{T}>0.2 GeV/c and 3<p_{T}<6 GeV/c in the 5%-40% and 10%-40% centrality classes, respectively. The difference between the positively and negatively charged hadron v_{1} has a positive slope as a function of pseudorapidity η, dΔv_{1}/dη=[1.68±0.49(stat)±0.41(syst)]×10^{-4}. The same measurement for D^{0} and D[over ¯]^{0} mesons yields a positive value dΔv_{1}/dη=[4.9±1.7(stat)±0.6(syst)]×10^{-1}, which is about 3 orders of magnitude larger than the one of the charged hadrons. These measurements can provide new insights into the effects of the strong electromagnetic field and the initial tilt of matter created in noncentral heavy ion collisions on the dynamics of light (u, d, and s) and heavy (c)quarks. The large difference between the observed Δv_{1} of charged hadrons and D^{0} mesons may reflect different sensitivity of the charm and light quarks to the early time dynamics of a heavy ion collision. These observations challenge some recent theoretical calculations, which predicted a negative and an order of magnitude smaller value of dΔv_{1}/dη for both light flavor and charmed hadrons.

Impact of longitudinal bulk viscous effects to heavy quark transport in a strongly magnetized hot QCD medium

The effects of longitudinal bulk viscous pressure on the heavy quark dynamics have been estimated in a strongly magnetized quark-gluon plasma within the Fokker-Planck approach. The bulk viscous modification to the momentum distribution of bulk degrees of freedom has been obtained in the presence of a magnetic field while incorporating the realistic equation of state of the hot magnetized QCD medium. As the magnetic field breaks the isotropy of the medium, the analysis is done along the directions longitudinal and transverse to the field. The longitudinal bulk viscous contribution is seen to have sizable effects in the heavy quark momentum diffusion in the magnetized medium. The dependence of higher Landau levels and the equation of state on the viscous correction to the heavy quark transport has been explored in the analysis.

Traces of nonequilibrium effects, initial condition, bulk dynamics, and elementary collisions in the charm observables

We study how heavy quark dynamics is affected by the nature of the bulk evolution of the QCD matter, the initial condition of the system, and the treatment of elementary interactions between heavy quarks and the surrounding medium. For the same initial condition and the same QGP expansion scenario we discuss the consequences of the assumption of a local equilibrium by comparing the consequences for the nuclear modification factor and the elliptic flows of charm quarks. For this purpose we employ the parton-hadron-string dynamics (PHSD), which is an off-shell microscopic transport approach, as well as the linearized-Boltzmann (LB) scheme obtained by coarse graining the PHSD bulk and assuming local equilibrium for the interactions of the charm quarks with the bulk. The $R_{\rm AA}$ of charm quarks stemming from the later LB approach is also compared to a genuine fluid dynamics evolution initiated by the coarse grained PHSD, which allows to further assess the consequences of reducing the full n-body dynamics. We then proceed to a systematic comparison of PHSD with MC@HQ, another transport model for heavy flavors which also relies on LB approach. In particular, we investigate the consequences for the nuclear modification factor of charm quarks if we vary separately the initial heavy quark distribution function in matter, the expansion dynamics of the QGP and the elementary interactions of heavy quarks of these models. We find that the results for both models vary significantly depending on the details of the calculation. However, both models achieve very similar predictions for key heavy quark observables for certain combinations of initial condition, bulk evolution and interactions. We conclude that this ambiguity limits our ability to determine the different properties of the system based on the current set of observables.

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.

Quantum and Classical Dynamics of Heavy Quarks in a Quark-Gluon Plasma

Heavy quarkonium related observables are very useful to obtain information about the medium created in relativistic heavy ion collisions. In recent years the theoretical description of quarkonium in a medium has moved towards a more dynamical picture in which decay and recombination processes are very important. In this talk we will discuss the equations that describe the evolution of the heavy quark reduced density matrix in different approximations, highlighting the color dynamics that is absent in the Abelian case, and we will study their semi-classical limit. This will allow us to obtain stochastic equations (similar to Langevin or Boltzmann equations) that can be useful to obtain phenomenological predictions. We will observe that the region of validity of the Langevin-like or Boltzmann-like equations in QCD is much smaller than the corresponding QED case. The reason for this can be understood by studying how differently the free energy evolves in these two theories, and this observation will allow us to propose an equation with a small computational cost that captures many of the essential features of quarkonium evolution in a QCD plasma. These results are based on [J.-P. Blaizot, M. A. Escobedo, Quantum and classical dynamics of heavy quarks in a quark-gluon plasma, JHEP 06 (2018) 034. arXiv:1711.10812, doi:10.1007/JHEP06(2018)034; J.-P. Blaizot, M. A. Escobedo, The approach to equilibrium of a quarkonium in a quark-gluon plasma. arXiv:1803.07996].

Quantum and classical dynamics of heavy quarks in a quark-gluon plasma

We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling between the heavy quarks and the plasma, the fast response of the plasma to the perturbation caused by the heavy quarks. An additional semi-classical approximation is performed. This allows us to recover results previously obtained for the abelian plasma using the influence functional formalism. In the case of QCD, specific features of the color dynamics make the implementation of the semi-classical approximation more involved. We explore two approximate strategies to solve numerically the resulting equations in the case of a quark-antiquark pair. One involves Langevin equations with additional random color forces, the other treats the transition between the singlet and octet color configurations as collisions in a Boltzmann equation which can be solved with Monte Carlo techniques.

Heavy-quark dynamics in a hydrodynamically evolving medium

In this talk we will discuss the recent advances in describing heavy-quark dynamics in the quark-gluon plasma (QGP), which evolves hydrodynamically. Special emphasis is put on the collective flow of the heavy-quarks with the medium constituents, for which we present our latest results obtained within the MC@sHQ+EPOS2 model at √s = 5 TeV.

Production of charm quarks in a parton cascade model for relativistic heavy ion collisions at sNN=200 GeV

We study the production and dynamics of heavy quarks in the parton cascade model for relativistic heavy ion collisions. The model is motivated by the QCD parton picture and describes the dynamics of an ultra-relativistic heavy-ion collision in terms of cascading partons which undergo scattering and multiplication while propagating. We focus on the dynamics of charm quark production and evolution in p+p and Au+Au collisions for several different interaction scenarios, i.e. collisions only between primary partons without radiation of gluons, multiple collisions without radiation of gluons and multiple collisions with radiation of gluons, allowing us to isolate the contributions of parton rescattering and radiation to charm production. We also discuss results of an eikonal approximation of the collision which provides a valuable comparison with mini-jet calculations and clearly brings out the importance of multiple collisions.