Collective Modes of an Anisotropic Quark-Gluon Plasma

Abstract

We analyze the collective modes of high-temperature QCD in the case when there is an anisotropy in the momentum-space distribution function for the gluons. We perform a tensor decomposition of the gluon self-energy and solve the dispersion relations for both stable and unstable modes. Results are presented for a class of anisotropic distribution functions which can be obtained by stretching or squeezing an isotropic distribution function along one direction in momentum space. We find that there are three stable modes and either one or two unstable modes depending on whether the distribution function is stretched or squeezed. The presence of unstable modes which have exponential growth can lead to a more rapid thermalization and isotropization of the soft modes in a quark gluon plasma and therefore may play an important role in the dynamical evolution.

13 pages, 4 figures. v2: Final published version; Typos corrected; Figure 3 updated

Cited by in corpus (318)

• Some Features of the Glasma
• New theories of relativistic hydrodynamics in the LHC era
• Dissipative Dynamics of Highly Anisotropic Systems
• Multi-system Bayesian constraints on the transport coefficients of QCD matter
• Isotropization and hydrodynamization in weakly coupled heavy-ion collisions
• Collective modes of an Anisotropic Quark-Gluon Plasma II
• Collective non-Abelian instabilities in a melting Color Glass Condensate
• Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies
• The Unstable Glasma
• Apparent Thermalization due to Plasma Instabilities in Quark-Gluon Plasma
• Hard-Loop Dynamics of Non-Abelian Plasma Instabilities
• Violation of the Holographic Viscosity Bound in a Strongly Coupled Anisotropic Plasma
• Chiral Plasma Instabilities
• Three-loop HTLpt thermodynamics at finite temperature and chemical potential
• The anisotropic N=4 super Yang-Mills plasma and its instabilities
• Thermal Bottomonium Suppression at RHIC and LHC
• Testing viscous and anisotropic hydrodynamics in an exactly solvable case
• Bose--Einstein Condensation and Thermalization of the Quark Gluon Plasma
• Advances in perturbative thermal field theory
• Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics
• From Color Glass Condensate to Quark Gluon Plasma through the event horizon
• Second order hydrodynamic coefficients from kinetic theory
• The anisotropic non-equilibrium hydrodynamic attractor
• Dynamics of Quark-Gluon-Plasma Instabilities in Discretized Hard-Loop Approximation
• The Fate of Non-Abelian Plasma Instabilities in 3+1 Dimensions
• Hard-Loop Effective Action for Anisotropic Plasmas
• Second-order (2+1)-dimensional anisotropic hydrodynamics
• Chromomagnetic instability in dense quark matter
• Anomalous Viscosity of an Expanding Quark-Gluon Plasma
• QCD Plasma Instabilities: The Nonabelian Cascade
• Perturbative Thermal QCD: Formalism and Applications
• Small Shear Viscosity of a Quark-Gluon Plasma Implies Strong Jet Quenching
• Color Glass Condensate and Glasma
• The heavy-quark potential in an anisotropic plasma
• Highly-anisotropic hydrodynamics in 3+1 space-time dimensions
• Quarkonia in the Quark Gluon Plasma
• Instabilities of an anisotropically expanding non-Abelian plasma: 1D+3V discretized hard-loop simulations
• Shear Viscosity in a Gluon Gas
• Hydrodynamic afterburner for the Color Glass Condensate and the parton energy loss
• Pre-equilibrium dilepton production from an anisotropic quark-gluon plasma
• Initial Singularity of the Little Bang
• Thermal Upsilon(1s) and chi_b1 suppression in sqrt(s_NN)=2.76 TeV Pb-Pb collisions at the LHC
• Transport coefficients for bulk viscous evolution in the relaxation time approximation
• Bottom-up isotropization in classical-statistical lattice gauge theory
• The imaginary part of the static gluon propagator in an anisotropic (viscous) QCD plasma
• Relativistic hydrodynamics in heavy-ion collisions: general aspects and recent developments
• The First fm/c of Heavy-Ion Collisions
• Turbulence in nonabelian gauge theory
• Measurements of long-range azimuthal anisotropies and associated Fourier coefficients for $pp$ collisions at $\sqrt{s}=5.02$ and $13$ TeV and $p$+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ATLAS detector
• The turbulent spectrum created by non-Abelian plasma instabilities
• Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow
• Screening masses in neutral two-flavor color superconductor
• Non-boost-invariant anisotropic dynamics
• Simulating plasma instabilities in SU(3) gauge theory
• Momentum Broadening in an Anisotropic Plasma
• Relativistic anisotropic hydrodynamics
• Quarkonium states in an anisotropic QCD plasma
• Plasma Instabilities in an Anisotropically Expanding Geometry
• Quarkonium states in a complex-valued potential
• Do nuclear collisions create a locally equilibrated quark-gluon plasma?
• QCD Plasma Instabilities and Isotropization
• Photon production from an anisotropic quark-gluon plasma
• The non-equilibrium attractor for kinetic theory in relaxation time approximation
• Quarkonium dissociation in the presence of a small momentum space anisotropy
• The Abelianization of QCD Plasma Instabilities
• Equilibration in phi^4 theory in 3+1 dimensions
• Non-resistive dissipative magnetohydrodynamics from the Boltzmann equation in the 14-moment approximation
• Dragging Heavy Quarks in Quark Gluon Plasma at the Large Hadron Collider
• Instabilities of an anisotropically expanding non-Abelian plasma: 3D+3V discretized hard-loop simulations
• Exact solution of the (0+1)-dimensional Boltzmann equation for a massive gas
• Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
• Ultraviolet avalanche in anisotropic non-Abelian plasmas
• A model of the effect of collisions on QCD plasma instabilities
• 3+1d quasiparticle anisotropic hydrodynamics for ultrarelativistic heavy-ion collisions
• Non-Abelian plasma instabilities: SU(3) vs. SU(2)
• Longitudinal Broadening of Quenched Jets in Turbulent Color Fields
• Bulk viscous evolution within anisotropic hydrodynamics
• Bottomonium suppression using a lattice QCD vetted potential
• Projection method and new formulation of leading-order anisotropic hydrodynamics
• Non-Abelian Plasma Instabilities for Extreme Anisotropy
• Collisional Energy Loss of a Heavy Quark in an Anisotropic Quark-Gluon Plasma
• The Glasma, Photons and the Implications of Anisotropy
• Predictions for bottomonia suppression in 5.023 TeV Pb-Pb collisions
• Jet broadening in unstable non-Abelian plasmas
• Non-equilibrium attractor in high-temperature QCD plasmas
• Thermalization and isotropization in heavy-ion collisions
• From Entropy and Jet Quenching to Deconfinement?
• Shear-bulk coupling in nonconformal hydrodynamics
• Prescaling and far-from-equilibrium hydrodynamics in the quark-gluon plasma
• Hydrodynamic attractors in heavy ion collisions: a review
• Constraining relativistic viscous hydrodynamical evolution
• Dissociation of Quarkonium in a Complex Potential
• Fluctuations of the initial color fields in high energy heavy ion collisions
• Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of moment of the Boltzmann equation
• Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions
• Jet quenching and broadening: the transport coefficient $\hat{q}$ in an anisotropic plasma
• Relativistic quantum transport coefficients for second-order viscous hydrodynamics
• Energy Loss of a Heavy Fermion in an Anisotropic QED Plasma
• Measuring Quark-Gluon-Plasma Thermalization Time with Dileptons
• Theories of Relativistic Dissipative Fluid Dynamics
• Probing quark gluon plasma properties by heavy flavours
• Instability-induced fermion production in quantum field theory
• On Kolmogorov Wave Turbulence in QCD
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Weak and strong coupling equilibration in nonabelian gauge theories
• Spin alignment of vector mesons by glasma fields
• The non-linear Glasma
• Instability induced pressure isotropization in a longitudinally expanding system
• What Do Electromagnetic Plasmas Tell Us about Quark-Gluon Plasma?
• Fermionic Collective Modes of an Anisotropic Quark-Gluon Plasma
• Coupled kinetic equations for quarks and gluons in the relaxation time approximation
• Nonequilibrium fixed points in longitudinally expanding scalar theories: infrared cascade, Bose condensation and a challenge for kinetic theory
• Leading-order anisotropic hydrodynamics for systems with massive particles
• Revisit to electrical and thermal conductivities, Lorenz number and Knudsen number in thermal QCD in a strong magnetic field
• Equilibration of weakly coupled QCD plasmas
• Dissociation of quarkonium in an anisotropic hot QCD medium
• Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma
• Anisotropic matching principle for the hydrodynamics expansion
• The dynamics of quark-gluon plasma and AdS/CFT
• A Possible Modified "bottom-up" Thermalization in Heavy Ion Collisions
• Gradient expansion for anisotropic hydrodynamics
• Can Thermalization in Heavy Ion Collisions be Described by QCD Diagrams?
• A Weibel Instability in the Melting Color Glass Condensate
• The impact of QCD plasma instabilities on bottom-up thermalization
• Hydrodynamics of anisotropic quark and gluon fluids
• Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics
• On non-conformal kinetic theory and hydrodynamics for Bjorken flow
• The momentum broadening of energetic partons in an anisotropic plasma
• Anisotropic fluid dynamics for Gubser flow
• Shear viscosity $\eta$ to electrical conductivity ${\sigma }_{el}$ ratio for an anisotropic QGP
• Electrical Conductivity of an Anisotropic Quark Gluon Plasma : A Quasiparticle Approach
• Quantum Kinetic Theory for Quantum Electrodynamics
• General structure of gauge boson propagator and its spectra in a hot magnetized medium
• Thermalization and the chromo-Weibel instability
• Photon production from a non-equilibrium quark-gluon plasma
• Dilepton rate and quark number susceptibility with the Gribov action
• Development of transverse flow at small and large opacities in conformal kinetic theory
• On higher order and anisotropic hydrodynamics for Bjorken and Gubser flows
• Dilepton production from the quark-gluon plasma using (3+1)-dimensional anisotropic dissipative hydrodynamics
• Photon polarization as a probe for quark-gluon plasma dynamics
• Suppression of forward dilepton production from an anisotropic quark-gluon plasma
• Out of equilibrium dynamics of coherent non-abelian gauge fields
• Anisotropic hydrodynamic modeling of 200 GeV Au-Au collisions
• The emission of electromagnetic radiation from the early stages of relativistic heavy-ion collisions
• Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
• Isotropization far from equilibrium
• Collective excitations of hot QCD medium in a quasi-particle description
• Collective excitations of a hot anisotropic QCD medium with Bhatnagar-Gross-Krook collisional kernel within an effective description
• Collective modes and instabilities in anisotropically expanding ultarelativistic plasmas
• Transport properties of anisotropically expanding quark-gluon plasma within a quasi-particle model
• On the bulk viscosity of anisotropically expanding hot QCD plasma
• Screening of a Moving Parton in the Quark-Gluon Plasma
• A flow paradigm in heavy-ion collisions
• Anisotropic hydrodynamics with a scalar collisional kernel
• Plasmons in Anisotropic Quark-Gluon Plasma
• High-order quadrature-based lattice Boltzmann models for the flow of ultrarelativistic rarefied gases
• Dynamical Origin of Power Spectra
• Photon emission from quark-gluon plasma out of equilibrium
• Photon production and elliptic flow from momentum-anisotropic quark-gluon plasma
• Anisotropic Hydrodynamics: Motivation and Methodology
• Energy gain of heavy quarks by fluctuations in the QGP
• Heavy quark transport in an anisotropic hot QCD medium: Collisional and Radiative processes
• (3+1)-dimensional anisotropic fluid dynamics with a lattice QCD equation of state
• Glasma Evolution and Bose-Einstein Condensation with Elastic and Inelastic Collisions
• Chromohydrodynamical instabilities induced by relativistic jets
• Quarkonia in anisotropic hot QCD medium in a quasi-particle model
• Matching pre-equilibrium dynamics and viscous hydrodynamics
• Energy Loss in Unstable Quark-Gluon Plasma
• Searching Evidence for the Color Glass Condensate at RHIC
• A hydrodynamic approach to boost invariant free streaming
• Spin polarization and correlation of quarks from glasma
• Transverse momentum diffusion and jet energy loss in non-Abelian plasmas
• Anisotropic hydrodynamics for mixture of quark and gluon fluids
• Heavy quark radiation in an anisotropic hot QCD medium
• The static hard-loop gluon propagator to all orders in anisotropy
• Whitening of the Quark-Gluon Plasma
• Momentum broadening in unstable quark-gluon plasma
• Testing different formulations of leading-order anisotropic hydrodynamics
• Bjorken flow attractors with transverse dynamics
• Exact solution of the (0+1)-dimensional Boltzmann equation for massive Bose-Einstein and Fermi-Dirac gases
• Initialization of hydrodynamics in relativistic heavy ion collisions with an energy-momentum transport model
• Initial state and thermalization in the Color Glass Condensate framework
• Modified equilibrium distributions for Cooper--Frye particlization
• QTRAJ 1.0: A Lindblad equation solver for heavy-quarkonium dynamics
• Time evolution of linearized gauge field fluctuations on a real-time lattice
• Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma
• Quantum kinetic theory for spin transport of quarks with background chromo-electromagnetic fields
• Femtoscopy with identified charged pions in proton-lead collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with ATLAS
• Exponential Approach to the Hydrodynamic Attractor in Yang-Mills Kinetic Theory
• Momentum and its affiliated transport coefficients for a hot QCD matter in a strong magnetic field
• Thermoelectric properties of (an-)isotropic QGP in magnetic fields
• Effective dynamics of a nonabelian plasma out of equilibrium
• Kinetic evolution of the glasma and thermalization in heavy ion collisions
• Transient oscillations in a macroscopic effective theory of the Boltzmann equation
• Chromoelectric oscillations in a dynamically evolving anisotropic background
• Charge-dependent directed flows in heavy-ion collisions by Boltzmann-Maxwell equations
• Refractive Index of Light in the Quark-Gluon Plasma with the Hard-Thermal-Loop Perturbation Theory
• Virtual photon polarization in ultrarelativistic heavy-ion collisions
• Shear Viscosity at Infinite Coupling: A Field Theory Calculation
• Dragging heavy quark in an anisotropic QCD medium beyond the static limit
• Anisotropic-hydrodynamics approach to a quark-gluon fluid mixture
• (3+1)-dimensional framework for leading-order non conformal anisotropic hydrodynamics
• Jets in a strongly coupled anisotropic plasma
• Hard Thermal Loop -- theory and applications
• Jet quenching parameter in QCD kinetic theory
• Electromagnetic response of hot QCD medium in the presence of background time-varying fields
• Light Probes in a Strongly Coupled Anisotropic Plasma
• Response of a weakly magnetized hot QCD medium to inhomogeneous electric field
• Study of the gluon propagator in the large-N_f limit at finite temperature and chemical potential for weak and strong couplings
• Thoughts on Non-Perturbative Thermalization and Jet Quenching in Heavy Ion Collisions
• Impact of momentum-space anisotropy on heavy quark dynamics in a QGP medium
• The Color Glass Condensate: an overview
• Broad excitations in a 2+1D overoccupied gluon plasma
• The complex heavy-quark potential in an anisotropic quark-gluon plasma -- Statics and dynamics
• Modified Kolmogorov Wave Turbulence in QCD matched onto "Bottom-up" Thermalization
• Isotropization by QCD Plasma Instabilities
• Radiative energy loss in an anisotropic Quark-Gluon-Plasma
• Energy loss of a fast moving parton in Gribov-Zwanziger plasma
• Dilepton polarization as a signature of plasma anisotropy
• Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation
• Hydrodynamic attractors for the speed of sound in holographic Bjorken flow
• Quasinormal modes of a semi-holographic black brane and thermalization
• Quark self-energy in an ellipsoidally anisotropic quark-gluon plasma
• QGP collective effects and jet transport
• Drag and Diffusion of Heavy Quarks in a hot and anisotropic QCD medium
• Wake potential in collisional anisotropic quark-gluon plasma
• Parton self-energies for general momentum-space anisotropy
• Impact of chiral asymmetry and magnetic field on passage of an energetic test parton in a QCD medium
• Collective modes in anisotropic plasmas
• Probes of the quark-gluon plasma and plasma instabilities
• Fast kinetic simulator for relativistic matter
• Plasmon mass scale in classical nonequilibrium gauge theory
• Numerical Simulation of Non-Abelian Particle-Field Dynamics
• Causal Relativistic Hydrodynamics of Conformal Fermi-Dirac Gases
• Next-to-leading order static gluon self-energy for anisotropic plasmas
• An improved anisotropic hydrodynamics ansatz
• Impact of momentum anisotropy and turbulent chromo-fields on thermal particle production in quark-gluon plasma medium
• Energy loss of heavy quarks in the presence of magnetic field
• Anisotropic hydrodynamics with number-conserving kernels
• Plasmon mass scale in two dimensional classical nonequilibrium gauge theory
• Strongly Interacting Matter at High Energy Density
• Far-from-equilibrium attractors with Full Relativistic Boltzmann approach in 3+1 D: moments of distribution function and anisotropic flows $v_n$
• Strongly and Weakly Unstable Anisotropic Quark-Gluon Plasma
• Anomalous viscosity of an expanding quark-gluon plasma
• Nuclear modification factor in an anisotropic {\em Quark-Gluon-Plasma}
• Wake in anisotropic Quark-Gluon Plasma
• Thermodynamics and phase diagram of anisotropic Chern-Simons deformed gauge theories
• The imaginary part of the heavy-quark potential from real-time Yang-Mills dynamics
• Shock Waves in Relativistic Anisotropic Hydrodynamics
• Far-off-equilibrium expansion trajectories in the QCD phase diagram
• Understanding thermalization in a non-Abelian gauge theory in terms of its soft modes
• Relativistic second-order dissipative and anisotropic fluid dynamics in the relaxation-time approximation for an ideal gas of massive particles
• Deconfinement transition dynamics and early thermalization in QGP
• Momentum anisotropy effects for quarkonium in a weakly-coupled quark-gluon plasma below the melting temperature
• Polarization of Direct Photons from Gluon Anisotropy in Ultrarelativistic Heavy Ion Collisions
• Quarkonia dissociation at finite magnetic field in the presence of momentum anisotropy
• Impact of Medium Anisotropy on Quarkonium Dissociation and Regeneration
• Soft-gluon exchange matters: isotropic screening in QCD kinetic theory
• Covariant formulation of gluon self-energy in presence of ellipsoidal anisotropy
• Thermalization and plasma instabilities
• Sound propagation and Mach cone in anisotropic hydrodynamics
• Lessons from Non-Abelian Plasma Instabilities in Two Spatial Dimensions
• Effective Debye Screening Mass in an Anisotropic Quark Gluon Plasma
• Shear viscosity of classical Yang-Mills field
• The right choice of moment for anisotropic fluid dynamics
• Yoctosecond metrology through HBT correlations from a quark-gluon plasma
• Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma
• Collective modes of a collisional anisotropic quark-gluon plasma
• Quarkonium Polarization in Medium from Open Quantum Systems and Chromomagnetic Correlators
• Thermalization of the world's smallest fluids: recent developments
• Hard-loop dynamics of non-abelian plasma instabilities
• Collective modes of gluons in an anisotropic thermo-magnetic medium
• Gluon Propagator and Heavy Quark Potential in an Anisotropic QCD Plasma
• A hydrodynamic approach to QGP instabilities
• Metric anisotropies and emergent anisotropic hydrodynamics
• Dynamical Friction in Interacting Relativistic Systems
• On the Chiral imbalance and Weibel Instabilities
• Hard probes of non-equilibrium quark-gluon plasma
• Visualizing Color Plasma Instabilities
• On the imaginary part of the next-to-leading-order static gluon self-energy in an anisotropic plasma
• Locally anisotropic momentum distributions of hadrons at freeze-out in relativistic heavy-ion collisions
• Thermalization & hydrodynamics in Bjorken & Gubser flows
• Theoretical aspects of photon production in high energy nuclear collisions
• Impact of strong magnetic field, baryon chemical potential, and medium anisotropy on polarization and spin alignment of hadrons
• Jet-dilepton conversion from an anisotropic quark-gluon plasma
• On nonadditive anisotropic relativistic hydrodynamics
• Penetrating probes: Jets and photons in a non-equilibrium quark-gluon plasma
• Electromagnetic radiation from the pre-equilibrium/pre-hydro stage of the quark-gluon plasma
• What the inflaton might tell us about RHIC/LHC
• Collective modes in the anisotropic collisional hot QCD medium at finite chemical potential
• Jet evolution in Yang-Mills-Wong simulations
• From the colour glass condensate to filamentation: Systematics of classical Yang-Mills theory
• Thermoelectric response of a hot and weakly magnetized anisotropic QCD medium
• Bottomonia in the Quark Gluon Plasma
• Lattice Boltzmann study of the one-dimensional boost-invariant expansion with anisotropic initial conditions
• Thermalization vs. Isotropization & Azimuthal Fluctuations
• Jet quenching in out-of-equilibrium QCD matter
• Numerical Studies of QGP Instabilities and Implications
• SQM 2006: Theory Summary and Perspectives
• Anomalous Viscosity of the Quark-Gluon Plasma
• Energy loss in unstable QGP - problem of the upper cut-off
• Quark matter with an anisotropic momentum distribution
• Chaotic thermalization in Yang-Mills-Higgs theory on a spacial lattice
• Linear Stability of Shock Waves in Ultrarelativistic Anisotropic Hydrodynamics
• Transport properties of the QCD medium
• Viscous anisotropic hydrodynamics for the Gubser flow
• Thermalization of parton spectra in the color-flux-tube model
• Bottomonia suppression in an anisotropic quark-gluon plasma
• The chromo-Weibel instability in an expanding background
• Anomalous spin polarization from turbulent color fields
• Kinetic equations and anisotropic hydrodynamics for quark and gluon fluids
• Collective excitations in the hot QCD medium and the propagation of Heavy Quarks
• Anisotropy effects on heavy quark dynamics in Gribov modified gluon plasma
• Spin alignment of Quarkonia: A Possible Probe of Deconfined QCD matter in Pb+Pb Collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
• Energy loss of heavy-flavor quarks in color string medium
• Unstable dynamics of Yang-Mills fields at early times of heavy ion collisions
• New formulation of leading order anisotropic hydrodynamics
• Nonabelian plasma instabilities in Bjorken expansion