Dynamics of Heavy Quarks in Strongly Coupled $\mathcal{N}=4$ SYM Plasma

Abstract

We calculate the probability distribution $P(\mathbf{k})$ for a heavy quark with velocity $v$ propagating through strongly coupled $\mathcal{N}=4$ SYM plasma in the 't Hooft limit at a temperature $T$ to acquire a momentum $\mathbf{k}$ due to interactions with the plasma. This distribution encodes the well-known drag coefficient ${\eta }_D$ and the transverse and longitudinal momentum diffusion coefficients ${\kappa }_T$ and ${\kappa }_L$. Furthermore, our calculation determines all of the higher order and mixed moments to leading order in $1/\sqrt{\lambda }$ for the first time. These non-Gaussian features of $P(\mathbf{k})$ include qualitatively novel correlations between longitudinal energy loss and transverse momentum broadening at nonzero $v$. We demonstrate that these non-Gaussian characteristics can be sizable in magnitude and even dominant in physically relevant situations. We use these results to derive a Kolmogorov equation for the evolution of the probability distribution for the total momentum of a heavy quark that propagates through strongly coupled plasma. This evolution equation accounts for all higher order correlations between transverse momentum broadening and longitudinal energy loss, which we have calculated from first principles. It reduces to a Fokker-Planck (FP) equation when truncated to only include the effects of ${\eta }_D$, ${\kappa }_T$ and ${\kappa }_L$. Remarkably, while heavy quarks do not reach kinetic equilibrium with the plasma if evolved with this FP equation, we demonstrate that heavy quarks do reach kinetic equilibrium if evolved with the all-order Kolmogorov equation we have derived. Our results thus provide a dynamically complete framework for understanding the thermalization of a heavy quark that may be initially far from equilibrium in the strongly coupled $\mathcal{N}=4$ SYM plasma -- as well as new insight into heavy quark transport and equilibration in quark-gluon plasma.

43 pages, 4 figures

References in corpus (49)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Wilson loops in large N field theories
• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Heavy Ion Collisions: The Big Picture, and the Big Questions
• Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma
• How Much do Heavy Quarks Thermalize in a Heavy Ion Collision?
• Drag force in AdS/CFT
• Wilson Loops and Minimal Surfaces
• Calculating the Jet Quenching Parameter from AdS/CFT
• Heavy Quark Diffusion in Strongly Coupled $\mathbb{N}=4$ Yang Mills
• Heavy-Quark Probes of the Quark-Gluon Plasma at RHIC
• Comments on gluon scattering amplitudes via AdS/CFT
• Real-time gauge/gravity duality: Prescription, Renormalization and Examples
• Basics of thermal field theory -- a tutorial on perturbative computations
• Wilson loops in heavy ion collisions and their calculation in AdS/CFT
• Real-time gauge/gravity duality
• Thermalization of Heavy Quarks in the Quark-Gluon Plasma
• An AdS/CFT Calculation of Screening in a Hot Wind
• Extraction of Heavy-Flavor Transport Coefficients in QCD Matter
• Heavy quark dynamics and hadronization in ultra-relativistic heavy-ion collisions: collisional versus radiative energy loss
• Momentum fluctuations of heavy quarks in the gauge-string duality
• Transverse Momentum Broadening of a Fast Quark in a $\mathbb{N}=4$ Yang Mills Plasma
• Heavy-flavour spectra in high energy nucleus-nucleus collisions
• Heavy ions and string theory
• Open Heavy Flavor in QCD Matter and in Nuclear Collisions
• The Energy of a Moving Quark-Antiquark Pair in an N=4 SYM Plasma
• Towards the determination of heavy-quark transport coefficients in quark-gluon plasma
• Transverse Momentum Broadening and the Jet Quenching Parameter, Redux
• Open Heavy-Flavor Production in Heavy-Ion Collisions
• Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann
• Thermal Noise and Stochastic Strings in AdS/CFT
• Heavy flavours in AA collisions: production, transport and final spectra
• Brownian motion in AdS/CFT
• Heavy-Quark Diffusion in the Quark-Gluon Plasma
• Real-time gauge/gravity duality and ingoing boundary conditions
• Stirring Strongly Coupled Plasma
• Fluctuation, dissipation, and thermalization in non-equilibrium AdS_5 black hole geometries
• Cracking the difference of estimating heavy quark transport coefficients in a Quark-Gluon Plasma
• Jet quenching in strongly coupled plasma
• Wilson Loop Renormalization Group Flows
• Stochastic trailing string and Langevin dynamics from AdS/CFT
• Transport properties and Langevin dynamics of heavy quarks and quarkonia in the Quark Gluon Plasma
• Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD
• Relativistic Langevin Dynamics in Expanding Media
• A limiting velocity for quarkonium propagation in a strongly coupled plasma via AdS/CFT
• Stochastic String Motion Above and Below the World Sheet Horizon
• Chromoelectric field correlator for quarkonium transport in the strongly coupled $\mathcal{N}=4$ Yang-Mills plasma from AdS/CFT
• Generalized Gluon Distribution for Quarkonium Dynamics in Strongly Coupled $\mathcal{N}=4$ Yang-Mills Theory

Cited by in corpus (1)

• Universal Equilibration Condition for Heavy Quarks