The \bar q q Bound States and Instanton Molecule at T >~ T_c

Abstract

The main objective of this work is to explore the evolution in the structure of the quark-anti-quark bound states in going down in the chirally restored phase from the so-called "zero binding points" $T_{zb}$ to the full (unquenched) QCD critical temperature $T_c$ at which the Nambu-Goldstone and Wigner-Weyl modes meet. In doing this, we adopt the idea recently introduced by Shuryak and Zahed for charmed $\bar{c}c$, light-quark $\bar{q}q$ mesons $\pi ,\sigma ,\rho ,A_1$ and gluons that at $T_{zb}$, the quark-anti-quark scattering length goes through $\infty$ at which conformal invariance is restored, thereby transforming the matter into a near perfect fluid behaving hydrodynamically, as found at RHIC. We show that the binding of these states is accomplished by the combination of (i) the color Coulomb interaction, (ii) the relativistic effects, and (iii) the interaction induced by the instanton-anti-instanton molecules. The spin-spin forces turned out to be small. While near $T_{zb}$ all mesons are large-size nonrelativistic objects bound by Coulomb attraction, near $T_c$ they get much more tightly bound, with many-body collective interactions becoming important and making the $\sigma$ and $\pi$ masses approach zero (in the chiral limit). The wave function at the origin grows strongly with binding, and the near-local four-Fermi interactions induced by the instanton molecules play an increasingly more important role as the temperature moves downward toward $T_c$.

arXiv comment31 pages, 7 figures, final refereed version

References in corpus (21)

• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Instantons in QCD
• QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity
• Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
• Diquark Bose Condensates in High Density Matter and Instantons
• Flow at the SPS and RHIC as a Quark Gluon Plasma Signature
• Hidden Local Symmetry at Loop -- A New Perspective of Composite Gauge Boson and Chiral Phase Transition
• Elliptic flow at SPS and RHIC: from kinetic transport to hydrodynamics
• Measurement of interaction energy near a Feshbach resonance in a 6Li Fermi gas
• Baryonic Correlation Functions in the Random Instanton Vacuum
• Quark-Induced Correlations between Instantons Drive the Chiral Phase Transition
• Temporal quark and gluon propagators: measuring the quasiparticle masses
• The Chiral Phase Transition and Instanton Anti-instanton Molecules
• The Propagation of Quarks in the Spatial Direction in Hot QCD
• A Study of Charmonium Systems across the Deconfinement Transition
• Sliding Vacua in Dense Skyrmion Matter
• The Instanton Density at Finite Temperatures
• Chemical Equilibration in Relativistic Heavy Ion Collisions
• A New State Of Hadronic Matter At High Density
• Can hadrons survive the chiral phase transition ?
• $\mathcal{C}\mathcal{P}\mathcal{T}$-invariant two-fermion Dirac equation with extended hyperfine operator

Cited by in corpus (48)

• What RHIC Experiments and Theory tell us about Properties of Quark-Gluon Plasma ?
• Thermalization of Heavy Quarks in the Quark-Gluon Plasma
• The hot non-perturbative gluon plasma is an almost ideal colored liquid
• From Kadanoff-Baym dynamics to off-shell parton transport
• Quarkonia and Heavy-Quark Relaxation Times in the Quark-Gluon Plasma
• Dynamical quasiparticles properties and effective interactions in the sQGP
• QCD thermodynamics and confinement from a dynamical quasiparticle point of view
• Influence of hadronic bound states above $T_c$ on heavy-quark observables in Pb+Pb collisions at at the CERN Large Hadron Collider
• The Chiral Restoration Transition of QCD and Low Mass Dileptons
• Shear Viscosity to Entropy Density Ratio of QCD below the Deconfinement Temperature
• Lattice QCD Calculation for the Physical Equation of State
• Heavy-Quark Diffusion in the Quark-Gluon Plasma
• QCD Viscosity to Entropy Density Ratio in the Hadronic Phase
• Hadronic Modes and Quark Properties in the Quark-Gluon Plasma
• $T$-matrix Approach to Quark-Gluon Plasma
• Deconfinement in Matrix Models about the Gross--Witten Point
• Selfconsistent Evaluation of Charm and Charmonium in the Quark-Gluon Plasma
• Electrical neutrality and pion modes in the two flavor PNJL model
• Hydrodynamics and beyond in the strongly coupled N=4 plasma
• Effective degrees of freedom and gluon condensation in the high temperature deconfined phase
• Quark Spectrum above but near Critical Temperature of Chiral Transition
• Extraction of the Heavy-Quark Potential from Bottomonium Observables in Heavy-Ion Collisions
• Late Hadronization and Matter Formed at RHIC: Vector Manifestation, Brown-Rho Scaling and Hadronic Freedom
• Deconfinement and Quarkonium Suppression
• Chemical Equilibration in Relativistic Heavy Ion Collisions
• Quarkonia and Quark Drip Lines in Quark-Gluon Plasma
• Matter formed at the BNL relativistic heavy ion collider
• Beta-functions for a SU(2) Matrix Model in 2 + epsilon Dimensions
• Non-Fermi Liquid Behavior Induced by Resonant Diquark-pair Scattering in Heated Quark Matter
• Role of Glueballs in Non-Perturbative Quark-Gluon Plasma
• STAR ${\rho }^0/{\pi }^{-}$ Ratio in Au-Au Peripheral Collisions at RHIC and the Vector Manifestation of Hidden Local Symmetry
• Ultra-light Glueballs in Quark-Gluon Plasma
• To understand sQGP through non-topological FL model
• Chiral transition and mesonic excitations for quarks with thermal masses
• Nonlinear dynamics of soft boson collective excitations in hot QCD plasma III: bremsstrahlung and energy losses
• The Instanton Molecule Liquid and "Sticky Molasses" Above T_c
• Heavy Quarkonia and Quark Drip Lines in Quark-Gluon Plasma
• Correction to the Chiral Magnetic Effect from axial-vector interaction
• Sudden freeze-out vs continuous emission: duality in hydro-kinetic approach to A+A collisions
• Pion entropy and phase-space densities in A+A collisions
• Nonperturbative Heavy-Quark Interactions in the QGP
• The Problem of Mass: Mesonic Bound States Above T_c
• Jet quenching parameter \hat q in the stochastic QCD vacuum with Landau damping
• Hotter, Denser, Faster, Smaller...and Nearly-Perfect: What's the matter at RHIC?
• Quark Spectrum near Chiral Transition Points
• The Problem of Mass: Mesonic Bound States Above Tc
• Comparison of Models of Critical Opacity in the Quark-Gluon Plasma
• Further Analysis of Excitations of Quarks at Finite Temperature -- Mass Effect and Pole Structure --