Quarkonium Semiclassical Transport in Quark-Gluon Plasma: Factorization and Quantum Correction

Abstract

We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.

35 pages, 3 figures; v2: added an appendix to explain the Wilson lines at infinite time; v3: make the assumed hierarchy more general; v4: typos in (2.12) and (2.13) corrected

References in corpus (75)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Collective flow and viscosity in relativistic heavy-ion collisions
• Potential NRQCD: an effective theory for heavy quarkonium
• Hydrodynamic Modeling of Heavy-Ion Collisions
• Effective field theories for heavy quarkonium
• Hard Scattering Factorization from Effective Field Theory
• Enhanced J/Psi Production in Deconfined Quark Matter
• Final state interactions and gauge invariant parton distributions
• Real-time static potential in hot QCD
• Heavy Quark Diffusion in Strongly Coupled $\mathbb{N}=4$ Yang Mills
• Static quark-antiquark pairs at finite temperature
• Jet quenching in high-energy heavy-ion collisions
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Real and imaginary-time $Q\bar{Q}$ correlators in a thermal medium
• Complex Heavy-Quark Potential at Finite Temperature from Lattice QCD
• J/psi Transverse Momentum Distribution in High Energy Nuclear Collisions
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• In-Medium Effects on Charmonium Production in Heavy-Ion Collisions
• Quarkonium suppression in heavy-ion collisions: an open quantum system approach
• J/psi Production in Quark-Gluon Plasma
• Heavy quarkonium suppression in a fireball
• Factorization for groomed jet substructure beyond the next-to-leading logarithm
• Color Screening and Regeneration of Bottomonia in High-Energy Heavy-Ion Collisions
• An Effective Field Theory for Forward Scattering and Factorization Violation
• Heavy quark master equations in the Lindblad form at high temperatures
• The heavy-quark potential in an anisotropic plasma
• Heavy quark diffusion in QCD and N=4 SYM at next-to-leading order
• High transverse momentum quarkonium production and dissociation in heavy ion collisions
• Thermal width and gluo-dissociation of quarkonium in pNRQCD
• Stochastic potential and quantum decoherence of heavy quarkonium in the quark-gluon plasma
• Thermal width and quarkonium dissociation by inelastic parton scattering
• The imaginary part of the static gluon propagator in an anisotropic (viscous) QCD plasma
• Evidence for charmonium generation at the phase boundary in ultra-relativistic nuclear collisions
• Quantum and Classical Dynamics of Heavy Quarks in a Quark-Gluon Plasma
• Quarkonium In-Medium Transport Equation Derived from First Principles
• Lattice QCD constraints on the heavy quark diffusion coefficient
• Heavy quark bound states in a quark-gluon plasma: dissociation and recombination
• The Renormalization Group Improvement of the QCD Static Potentials
• Doubly Heavy Baryons, Heavy Quark-DiQuark Symmetry and NRQCD
• The Schrödinger-Langevin equation with and without thermal fluctuations
• The approach to equilibrium of a quarkonium in a quark-gluon plasma
• Bottomonia suppression in 2.76 TeV Pb-Pb collisions
• Charmonium and open charm production in nuclear collisions at SPS/FAIR energies and the possible influence of a hot hadronic medium
• Dynamical dissociation of quarkonia by wave function decoherence
• Bottomonium Production at RHIC and LHC
• Coupled Boltzmann Transport Equations of Heavy Quarks and Quarkonia in Quark-Gluon Plasma
• Quarkonium inside Quark-Gluon Plasma: Diffusion, Dissociation, Recombination and Energy Loss
• Transport coefficients from in medium quarkonium dynamics
• Is bottomonium suppression in proton-nucleus and nucleus-nucleus collisions at LHC energies due to the same effects?
• Excited bottomonia in quark-gluon plasma from lattice QCD
• Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma
• Heavy quarkonia in a medium as a quantum dissipative system: Master-equation approach
• A Soft-Collinear Mode for Jet Cross Sections in Soft Collinear Effective Theory
• Probing Transverse-Momentum Distributions With Groomed Jets
• Thermal Broadening of Bottomonia: Lattice Non-Relativistic QCD with Extended Operators
• Quarkonium above deconfinement as an open quantum system
• Collisional and thermal dissociation of $J/\psi$ and ${\rm Y}$ states at the LHC
• Doubly charmed baryon production in heavy ion collisions
• Bottomonia suppression in heavy-ion collisions
• Constraint equations for heavy-to-light currents in SCET
• Bottomonium Continuous Production from Unequilibrium Bottom Quarks in Ultrarelativistic Heavy Ion Collisions
• Quantum dissipation of a heavy quark from a nonlinear stochastic Schrödinger equation
• An effective field theory approach to quarkonium at small transverse momentum
• Probing Transverse-Momentum Dependent Evolution With Groomed Jets
• Bottomonium suppression and elliptic flow from real-time quantum evolution
• Bottomium suppression in PbPb collisions at LHC energies
• Strong Diffusion Effect of Charm Quarks on $J/\psi$ Production in Pb-Pb collisions at the LHC
• Fate of in-medium heavy quarks via a Lindblad equation
• Collinear Drop
• Quarkonium production in heavy ion collisions: coupled Boltzmann transport equations
• Quarkonium production in heavy ion collisions: coupled Boltzmann transport equations
• An Effective Theory of Quarkonia in QCD Matter
• Bethe-Salpeter amplitudes of Upsilons

Cited by in corpus (29)

• Quantum simulation of non-equilibrium dynamics and thermalization in the Schwinger model
• Bottomonium suppression in an open quantum system using the quantum trajectories method
• Quantum simulation of open quantum systems in heavy-ion collisions
• Bottomonium production in heavy-ion collisions using quantum trajectories: Differential observables and momentum anisotropy
• Non-Abelian Electric Field Correlator at NLO for Dark Matter Relic Abundance and Quarkonium Transport
• Heavy quarkonium dynamics at next-to-leading order in the binding energy over temperature
• X(3872) Production in Relativistic Heavy-Ion Collisions
• Regeneration of bottomonia in an open quantum systems approach
• Real Time Quarkonium Transport Coefficients in Open Quantum Systems from Euclidean QCD
• Phenomenological study of quarkonium suppression and the impact of the energy gap between singlets and octets
• Liouvillian Dynamics of the Open Schwinger Model: String Breaking and Kinetic Dissipation in a Thermal Medium
• Gauge Invariance of Non-Abelian Field Strength Correlators: the Axial Gauge Puzzle
• Dilaton-induced open quantum dynamics
• A new method for directly computing reduced density matrices
• Bottom energy loss and non-prompt $J/\psi$ production in relativistic heavy ion collisions
• Chromoelectric field correlator for quarkonium transport in the strongly coupled $\mathcal{N}=4$ Yang-Mills plasma from AdS/CFT
• Quarkonium dynamics in the quantum Brownian regime with non-abelian quantum master equations
• The impact of fluctuating initial conditions on bottomonium suppression in 5.02 TeV heavy-ion collisions
• Generalized Gluon Distribution for Quarkonium Dynamics in Strongly Coupled $\mathcal{N}=4$ Yang-Mills Theory
• Bottomonium suppression at RHIC and LHC in an open quantum system approach
• Quarkonium Polarization in Medium from Open Quantum Systems and Chromomagnetic Correlators
• Open quantum system approach for heavy quark thermalization
• Transverse momentum dependent feed-down fractions for bottomonium production
• Non-thermal distributions of charm and charmonium in relativistic heavy-ion collisions
• Energy loss of heavy quarkonia in hot QCD plasmas
• Charmonium dissociation at high baryon chemical potential
• Anisotropic flows of charmonium in the relativistic heavy-ion collisions
• A simple model to include initial-state and hot-medium effects in the computation of quarkonium nuclear modification factor
• Non-Markovian dynamics of bottomonia in the QGP