Nonequilibrium pion dynamics near the critical point in a constituent quark model

Abstract

We study static and dynamical critical phenomena of chiral symmetry breaking in a two-flavor Nambu--Jona-Lasinio constituent quark model. We obtain the low-energy effective action for scalar and pseudoscalar degrees of freedom to lowest order in quark loops and to quadratic order in the meson fluctuations around the mean field. The \emph{static} limit of critical phenomena is shown to be described by a Ginzburg-Landau effective action including \emph{spatial} gradients. Hence \emph{static} critical phenomena is described by the universality class of the O(4) Heisenberg ferromagnet. \emph{Dynamical} critical phenomena is studied by obtaining the equations of motion for pion fluctuations. We find that for $T<T_c$ the are stable long-wavelength pion excitations with dispersion relation ${\omega }_{\pi }(k)=k$ described by isolated pion poles. The residue of the pion pole vanishes near $T_c$ as $Z\propto 1/|\ln (1-T/T_c)|$ and long-wavelength fluctuations are damped out by Landau damping on a time scale $t_{\mathrm{rel}}(k)\propto 1/k$, reflecting \emph{critical slowing down} of pion fluctuations near the critical point. At the critical point, the pion propagator features mass shell logarithmic divergences which we conjecture to be the harbinger of a (large) dynamical anomalous dimension. We find that while the \emph{classical spinodal} line coincides with that of the Ginzburg-Landau theory, the growth rate of long-wavelength spinodal fluctuations has a richer wavelength dependence as a consequence of Landau damping. We argue that Landau damping prevents a \emph{local} low energy effective action in terms of a derivative expansion in real time.

arXiv comment22 pages 5 figures. to appear in Nucl. Phys. A

References in corpus (47)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• Lattice determination of the critical point of QCD at finite T and μ
• The QCD thermal phase transition in the presence of a small chemical potential
• Static and Dynamic Critical Phenomena at a Second Order QCD Phase Transition
• Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory
• Lattice Results on QCD Thermodynamics
• From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory
• Slowing Out of Equilibrium Near the QCD Critical Point
• Chiral Phase Transition within Effective Models with Constituent Quarks
• The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density
• Emergence of Coherent Long Wavelength Oscillations After a Quench: Application to QCD
• Reheating and Thermalization, Linear Vs. Non-Linear Relaxation
• Phase transitions in quantum chromodynamics
• The phase diagram and bulk thermodynamical quantities in the NJL model at finite temperature and density
• A Precursor of Chiral Symmetry Restoration in the Nuclear Medium
• Nonequilibrium Quantum Dynamics Of Disoriented Chiral Condensates
• How to Make Large Domains of Disoriented Chiral Condensate
• Phase Transitions out of Equilibrium: domain formation and growth
• Can Disordered Chiral Condensates Form? A Dynamical Perspective
• Pion Propagation near the QCD Chiral Phase Transition
• Dynamical renormalization group approach to relaxation in quantum field theory
• Real-time pion propagation in finite-temperature QCD
• Dynamical renormalization group resummation of finite temperature infrared divergences
• Lattice QCD Results at Finite Temperature and Density
• Mean-field treatment of the linear sigma model in dynamical calculations of DCC observables
• A Two-dimensional Model with Chiral Condensates and Cooper Pairs having QCD-like Phase Structure
• Evolution of Inhomogeneous Condensates after Phase Transitions
• Non-Equilibrium Production of Photons via π^0\to 2γin DCC's
• Real-time nonequilibrium dynamics in hot QED plasmas: dynamical renormalization group approach
• Anomalous Transverse Distribution of Pions as a signal for the production of DCC's
• The Chiral Fermion Meson Model at Finite Temperature
• Quantum evolution of the disoriented chiral condensates
• Photoproduction Enhancement from Non Equilibrium Disoriented Chiral Condensates
• Quantum Spinodal Decomposition
• Fermion Damping in a Fermion-Scalar Plasma
• Dynamical renormalization group approach to transport in ultrarelativistic plasmas: the electrical conductivity in high temperature QED
• Damping Rates and Mean Free Paths of Soft Fermion Collective Excitations in a Hot Fermion-Gauge-Scalar Theory
• Equilibrium and nonequilibrium properties associated with the chiral phase transition at finite density in the Gross-Neveu Model
• Relaxing Near the Critical Point
• Quantum Field Treatment of DCC Dynamics
• Traversing the QCD Phase Transition: Quenching Out of Equilibrium vs. Slowing Out of Equilibrium vs. Bubbling Out of Equilibrium
• Dynamics near the critical point: the hot renormalization group in quantum field theory
• Dynamics of the chiral phase transition in the 2+1 dimensional Gross-Neveu model
• Anomalous Pseudoscalar-Photon Vertex In and Out of Equilibrium
• The Fermion Boson Interaction Within the Linear Sigma Model at Finite Temperature
• Analytic Properties of Thermal Corrected Boson Propagators

Cited by in corpus (4)

• Quantum Opacity, the RHIC HBT Puzzle, and the Chiral Phase Transition
• Cosmological Implications of Light Sterile Neutrinos produced after the QCD Phase Transition
• Polishing the Lens: I Pionic Final State Interactions and HBT Correlations- Distorted Wave Emission Function (DWEF) Formalism and Examples
• The case for mixed dark matter from sterile neutrinos