Momentum Diffusion Coefficient Research Articles

Dynamics of heavy flavor in a weakly magnetized hot QCD medium

We obtain the spatial and momentum-diffusion coefficients (Ds and κ) and the collisional energy loss (dE/dx) of a heavy quark (HQ) traversing through a thermal medium of quarks and gluons in a weak magnetic field (B), for the two cases of the HQ moving either parallel or perpendicular to B. For that purpose, we consider Coulomb scatterings (t-channel) of the HQ with the light quarks, obtained from the imaginary part of the HQ self-energy via the cutting rules. Both the normalized (by T3) κ, and dE/dx, for charm quarks are larger than that for bottom quarks due to the larger mass of the latter. Also, the effect of B is more feeble on the bottom quark, compared to the charm quark. Comparatively, the magnitudes of both κ and dE/dx are significantly smaller for the case of v⊥B. For both the cases, our results show that the momentum transfer between the HQ and the medium takes place preferentially along the direction of HQ velocity, thus leading to a significant increase in the momentum-diffusion anisotropy, compared to B=0. We also calculate the (scaled) spatial diffusion coefficient, which we find to be independent of the heavy flavor mass and is almost unaffected by changes in B. Published by the American Physical Society 2024

Lattice B -field correlators for heavy quarks

We analyze the color-magnetic (or “B”) field two-point function that encodes the finite-mass correction to the heavy-quark momentum-diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at 1.5Tc, using a range of gradient flow times for noise suppression and operator renormalization. The continuum extrapolation is performed at fixed flow time followed by a second extrapolation to zero flow time. Perturbative calculations to next-to-leading order of this correlation function, matching gradient-flowed correlators to MS¯, are used to resolve nontrivial renormalization issues. We perform a spectral reconstruction based on perturbative model fits to estimate the coefficient κB of the finite-mass correction to the heavy-quark momentum-diffusion coefficient. The approach we present here yields high-precision data for the correlator with all renormalization issues incorporated at next-to-leading order and is also applicable for actions with dynamical fermions. Published by the American Physical Society 2024

Heavy-Quark Momentum Broadening in a Non-Abelian Plasma away from Thermal Equilibrium.

We perform classical-statistical real-time lattice simulations to compute real-time spectral functions and momentum broadening of quarks in the presence of strongly populated non-Abelian gauge fields. Based on a novel methodology to extract the momentum broadening for relativistic quarks, we find that the momentum distribution of quarks exhibit interesting nonperturbative features as a function of time due to correlated momentum kicks it receives from the medium, eventually going over to a diffusive regime. We extract the momentum diffusion coefficient for a mass range describing charm and bottom quarks and find sizable discrepancies from the heavy-quark limit.

Statistical Properties of Exohiss Waves and Associated Scattering Losses of Radiation Belt Electrons

AbstractExohiss waves are a type of structureless whistler‐mode waves that exist in the low density plasmatrough outside the plasmapause and may potentially perturb the motions of electrons in the radiation belt and ring current. Using data from Van Allen Probe A, we analyze the distribution of magnetic power spectral density (PSD) of exohiss waves in different magnetic local time (MLT) and L‐shell regions near the geomagnetic equator. The results reveal that the peak magnetic PSD of exohiss waves is the weakest at MLT = 0–6 and the strongest at MLT = 12–18. The magnetic PSDs of exohiss waves are much lower than those of chorus and hiss waves except for the MLT = 12–18 sector. In addition, we calculated the quasi‐linear bounce‐averaged pitch angle and momentum diffusion coefficients (〈Dαα〉 and 〈Dpp〉) of electrons caused by exohiss waves. The diffusion coefficients are then compared with those caused by chorus and hiss waves. The peak 〈Dαα〉 of electrons driven by exohiss waves becomes stronger as L‐shell increases at all MLTs and is the greatest on the dayside, especially in the sector of MLT = 12–18. Exohiss waves have more significant effect on the loss of radiation belt electrons with specific energy levels related to MLT and L‐shell region compared to chorus and hiss waves. On the other hand, 〈Dpp〉 of electrons caused by exohiss waves is very small, which illustrates that exohiss waves have almost no acceleration effect on electrons.

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

A one-dimensional urban flow model with an eddy-diffusivity mass-flux (EDMF) scheme and refined turbulent transport (MLUCM v3.0)

Abstract. In recent years, urban canopy models (UCMs) have been used as fully coupled components of mesoscale atmospheric models as well as offline tools to estimate temperature and surface fluxes using atmospheric forcings. Examples include multi-layer urban canopy models (MLUCMs), where the vertical variability of turbulent fluxes is calculated by solving prognostic momentum and turbulent kinetic energy (TKE, k) using mixing length scale (l) and drag parameterizations. These parameterizations are based on the well-established 1.5-order k−l turbulence closure theory and are often informed by microscale fluid dynamics simulations. However, this approach can include simplifications such as assuming the same diffusion coefficient for momentum, TKE, and scalars. In addition, the dispersive stresses arising from spatially averaged flow properties have been parameterized together with the turbulent fluxes despite being controlled by different mechanisms. Both of these assumptions impact the quantification of the turbulent exchange of flow properties and subsequent air temperature predictions in urban canopies. To assess these assumptions and improve corresponding parameterization, we analyzed 49 large-eddy simulations (LES) for idealized urban arrays, encompassing variable building height distributions and a comprehensive range of urban densities (λp∈[0.0625,0.64]) seen in global cities. We find that the efficiency of turbulent transport (numerically described via diffusion coefficients) is similar for scalars and momentum but is 3.5 times higher for TKE. Additionally, parameterizing the dispersive momentum flux using the k−l closure was a source of error, while scaling with the pressure gradient and urban morphological parameters appears more appropriate. In response to these findings, we propose two changes to the previous version of MLUCM: (a) separate characterization for turbulent diffusion coefficient for momentum and TKE and (b) introduction of an explicit physics-based “mass-flux” term to represent the fraction of the dispersive momentum transport directly induced from buildings as an amendment to the existing “eddy-diffusivity” framework. The updated one-dimensional model, after being tuned for building height variability, is further compared against the original LES results and demonstrates improved performance in predicting vertical turbulent exchange in urban canopies.

Heavy quark diffusion and radiation at intermediate momentum

Heavy quark diffusion and radiation are discussed in an intermediate-momentum regime where finite mass effects can be significant. Diffusion processes are described in the Fokker-Planck approximation for soft momentum transfer, while radiative ones are taken into account by nearly collinear gluon emission from a single scattering in the Boltzmann equation. There are also radiative corrections to the transverse momentum diffusion coefficient, which are O(g2) suppressed more than the leading-order diffusion coefficient but logarithmically enhanced. Numerical results show that the heavy quark distribution function depends on the energy loss mechanism so that the medium modifications by diffusion and radiation are distinguishable. The nuclear modification factor is estimated by employing the heavy quark diffusion coefficient which is constrained by lattice quantum chromodynamics data. The suppression factor exhibits a transition from diffusion at low momentum to radiation at high momentum. The significance of the radiative effects at intermediate momentum depends on the diffusion coefficient and the running coupling constant. Published by the American Physical Society 2024

Heavy quark diffusion coefficients in magnetized quark-gluon plasma

We evaluate the heavy quark momentum diffusion coefficients in a hot magnetized medium for the most general scenario of any arbitrary values of the external magnetic field. We choose to work with the systematic way of incorporating the effect of the magnetic field, by using the effective gluon and quark propagators, generalized for a hot and magnetized medium. To get gauge independent analytic form factors valid through all Landau levels, we apply the hard thermal loop technique for the resummed effective gluon propagator. The derived effective hard thermal loop gluon propagator and the generalized version of Schwinger quark propagator subsequently allow us to analytically evaluate the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Within the static limit we also explore another way of incorporating the effect of the magnetic field, i.e. through the magnetized medium modified Debye mass and compare the results to justify the need for structural changes. Published by the American Physical Society 2024

Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD.

We present the first study of the quark mass dependence of the heavy quark momentum and spatial diffusion coefficients using lattice QCD with light dynamical quarks corresponding to a pion mass of 320MeV. We find that, for the temperature range 195 MeV<T<293 MeV, the spatial diffusion coefficients of the charm and bottom quarks are smaller than those obtained in phenomenological models that describe the p_{T} spectra and elliptic flow of open heavy flavor hadrons.

Heavy quark diffusion coefficient in heavy-ion collisions via kinetic theory

We compute the heavy quark momentum diffusion coefficient κ using QCD kinetic theory for a system going through bottom-up isotropization in the initial stages of a heavy ion collision. We find that the values of κ are within 30% from a thermal system at the same energy density. When matching for other quantities we observe considerably larger deviations. We also observe that the diffusion coefficient in the transverse direction is larger at high occupation numbers, whereas for an underoccupied system the longitudinal diffusion coefficient dominates. The behavior of the diffusion coefficient can be understood on a qualitative level based on the Debye mass mD and the effective temperature of soft modes T*. Our findings for the kinetic evolution of κ in different directions can be used in phenomenological descriptions of heavy quark diffusion and quarkonium dynamics to include the impact of preequilibrium stages. Published by the American Physical Society 2024

Heavy quark momentum diffusion coefficient during hydrodynamization via effective kinetic theory

In these proceedings, we compute the heavy quark momentum diffusion coefficient using QCD effective kinetic theory for a plasma going through the bottom-up thermalization scenario until approximate hydrodynamization. This transport coefficient describes heavy quark momentum diffusion in the quark-gluon plasma and is used in many phenomenological frameworks, e.g. in the open quantum systems approach. Our extracted nonthermal diffusion coefficient matches the thermal one for the same energy density within 30%. At large occupation numbers in the earliest stage, the transverse diffusion coefficient dominates, while the longitudinal diffusion coefficient is larger for the underoccupied system in the later stage of hydrodynamization.

Temperature dependence of the static quark diffusion coefficient

The propagation of a low momentum heavy quark in a deconfined quark-gluon plasma can be understood in terms of a Langevin description. The momentum exchange with the plasma in thermal equilibrium can then be parametrized in terms of a single heavy quark momentum diffusion coefficient κ, which needs to be determined nonperturbatively. In this work, we study the temperature dependence of κ for a static quark in a gluonic plasma, with a particular emphasis on the temperature range of interest for heavy ion collision experiments.

Acceleration of cosmic rays in presence of magnetohydrodynamic fluctuations at small scales

ABSTRACT This work investigates the evolution of the distribution of charged particles (cosmic rays) due to the mechanism of stochastic turbulent acceleration (STA) in presence of small-scale turbulence with a mean magnetic field. STA is usually modelled as a biased random walk process in the momentum space of the non-thermal particles. This results in an advection-diffusion type transport equation for the non-thermal particle distribution function. Under quasi-linear approximation, and by assuming turbulent spectra with power being available only in the sub-gyroscale range, we find that the Fokker–Planck diffusion coefficients Dγγ and Dμμ scale with the Lorentz factor γ as Dγγ ∝ γ−2/3 and Dμμ ∝ γ−8/3. We consider Alfvèn and fast waves in our calculations, and find a universal trend for the momentum diffusion coefficient irrespective of the properties of the small-scale turbulence. Such universality has already been reported regarding the spatial diffusion of the cosmic rays, and, here too, we observe a universality in the momentum diffusion coefficient. Furthermore, with the calculated transport coefficients, we numerically solve the advection-diffusion-type transport equation for the non-thermal particles. We demonstrate the interplay of various mircophysical processes such as STA, synchrotron loss, and particle escape on the particle distribution by systematically varying the parameters of the problem. We observe that the effect of the small-scale turbulence is more impactful for the high-energy protons as compared to the electrons and such turbulence is capable of sustaining the energy of the protons from catastrophic radiative loss processes. Such a finding is novel and helps us to enhance our understanding about the hadronic emission processes that are typically considered as a competitor for the leptonic emission for certain astrophysical systems.

Efficient Scattering Loss of Energetic Electrons by Enhanced Higher‐Band ECH Waves Observed by Van Allen Probes

AbstractElectron cyclotron harmonic (ECH) waves, which are responsible for the diffuse aurora, are usually observed with the strongest intensity in the first band. Here, we present observations of enhanced higher‐band ECH with wave intensities above 10−3 mV2m−2 Hz−1 by Van Allen Probes. Fully thermal simulation results indicate that these waves can be locally excited by the observed electron distributions, and higher plasma density and lower magnetic strength are favorable for generating the enhanced higher‐band ECH. The pitch angle diffusion coefficient of the higher‐band ECH can exceed 10−5 s−1 inside the loss cone for energetic electrons (300 eV–∼15 keV), greater than the momentum diffusion coefficient by ∼100 times. It is suggested that the enhanced higher‐band ECH can also efficiently scatter these electrons into the loss cone and contribute to the diffuse aurora.

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.

Understanding the QCD medium by the diffusion of charm quarks using a color string percolation model

We study the drag and diffusion coefficients of the charm quark in the deconfined matter produced in the ultra-relativistic collisions by taking the Color String Percolation Model (CSPM) approach. CSPM, being a QCD-inspired model, can give us essential information about the hot and dense system produced in ultra-relativistic collisions. With the information on initial percolation temperature and percolation density, we estimate the relaxation time ($\tau_{c}$), drag coefficient ($\gamma$), transverse momentum diffusion coefficient ($B_{0}$), and spatial diffusion coefficient ($D_{s}$) of charm quark inside a deconfined medium. Finally, we compare the obtained results with lattice QCD and with various other theoretical models. A good agreement can be observed between the results obtained from CSPM and lattice QCD.

FARWEST: Efficient Computation of Wave‐Particle Interactions for a Dynamic Description of the Electron Radiation Belt Diffusion

AbstractIn this paper, we present a new method to compute rapidly, wave particle interaction induced pitch angle and momentum diffusion coefficients. Those terms are normally obtained by the numerical solving of equations based on the quasi‐linear theory. However, this bulk resolution leads to a high computational cost, preventing the integration of plasma density and VLF waves nowcasts and forecasts. Therefore, and in the context of the SAFESPACE project (H2020), we implemented a new wave particle interaction code called FARWEST (FAst Radiation diffusion with Waves ESTimator), with an efficient interpolation based method. The proposed implementation was validated against reference results obtained by WAPI, ONERA's wave particle interaction legacy code, with a substantial reduction of the computing time while conserving the physical accuracy of the generated coefficients. The FARWEST code is later used to measure the impact of a time‐dependent plasma density distribution (numerically computed by BIRA's plasmaspheric model SPM) on the coefficients and on the representation of the electron flux map by Salammbô, ONERA's radiation belt code.

Lattice study of a magnetic contribution to heavy quark momentum diffusion

Heavy quarks placed within a hot QCD medium undergo Brownian motion, characterized by specific transport coefficients. Their determination can be simplified by expanding them in T/M, where T is the temperature and M is a heavy quark mass. The leading term in the expansion originates from the colour-electric part of a Lorentz force, whereas the next-to-leading order involves the colour-magnetic part. We measure a colour-magnetic 2-point correlator in quenched QCD at T ∼ (1.2 − 2.0)Tc. Employing multilevel techniques and non-perturbative renormalization, a good signal is obtained, and its continuum extrapolation can be estimated. Modelling the shape of the corresponding spectral function, we subsequently extract the momentum diffusion coefficient, κ. For charm (bottom) quarks, the magnetic contribution adds ∼ 30% (10%) to the electric one. The same increases apply also to the drag coefficient, η. As an aside, the colour-magnetic spectral function is computed at NLO.

Transport coefficients of heavy quarkonia comparing with heavy quark coefficients

We revisit the transport coefficients of heavy quarkonia moving in high-temperature QCD plasmas. The thermal width and mass shift for heavy quarkonia are closely related to the momentum diffusion coefficient and its dispersive counterpart for heavy quarks, respectively. For quarkonium at rest in plasmas the longitudinal gluon part of the color-singlet self-energy diagram is sufficient to determine the leading-order thermal width, whereas the momentum dependence is obtained from the transverse gluon channel. Using the quarkonium-gluon effective vertex based on the dipole interaction of color charges, we discuss the damping rate, the effective rest and kinetic mass shifts of slowly moving quarkonia and compare with the corresponding coefficients of heavy quarks.

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.