Toward a first-principle derivation of confinement and chiral-symmetry-breaking crossover transitions in QCD

Abstract

We give a theoretical framework to obtain a low-energy effective theory of quantum chromodynamics (QCD) towards a first-principle derivation of confinement/deconfinement and chiral-symmetry breaking/restoration crossover transitions. In fact, we demonstrate that an effective theory obtained using simple but non-trivial approximations within this framework enables us to treat both transitions simultaneously on equal footing. A resulting effective theory is regarded as a modified and improved version of nonlocal Polyakov-loop extended Nambu-Jona-Lasinio (nonlocal PNJL) models proposed recently by Hell, Rössner, Cristoforetti and Weise, and Sasaki, Friman and Redlich, extending the original (local) PNJL model by Fukushima and others. A novel feature is that the nonlocal NJL coupling depends explicitly on the temperature and Polyakov loop, which affects the entanglement between confinement and chiral symmetry breaking, together with the cross term introduced through the covariant derivative in the quark sector considered in the conventional PNJL model. The chiral symmetry breaking/restoration transition is controlled by the nonlocal NJL interaction, while the confinement/deconfinement transition in the pure gluon sector is specified by the nonperturbative effective potential for the Polyakov loop obtained recently by Braun, Gies, Marhauser and Pawlowski. The basic ingredients are a reformulation of QCD based on new variables and the flow equation of the Wetterich type in the Wilsonian renormalization group. This framework can be applied to investigate the QCD phase diagram at finite temperature and density.

23 pages, 8 figures (12 eps files); version accepted for publication in Physical Review D; Added are 3 footnotes, 1 paragraph from page 16 to 17, and 3 references [20],[24],[70]([63]updated). Some errors are corrected

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• Improved Polyakov-loop potential for effective models from functional calculations
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• Nonlocal PNJL model beyond mean field and the QCD phase transition
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• Quark-mass dependence of the three-flavor QCD phase diagram at zero and imaginary chemical potential: Model prediction
• Evidence of ghost suppression in gluon mass dynamics
• Polyakov loop and QCD thermodynamics from the gluon and ghost propagators
• Extensions and further applications of the nonlocal Polyakov--Nambu--Jona-Lasinio model
• Coupled dynamics in gluon mass generation and the impact of the three-gluon vertex
• Quark Matter in a Strong Magnetic Background
• Critical Temperature of Chiral Symmetry Restoration for Quark Matter with a Chiral Chemical Potential
• A low-energy effective Yang-Mills theory for quark and gluon confinement
• Width of the QCD transition in a Polyakov-loop DSE model
• Deconfinement and chiral restoration in nonlocal SU(3) chiral quark models
• Finite-volume effects on phase transition in the Polyakov-loop extended Nambu-Jona-Lasinio model with a chiral chemical potential
• Deconfinement and chiral restoration in nonlocal PNJL models at zero and imaginary chemical potential
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• Medium induced Lorentz symmetry breaking effects in nonlocal PNJL models
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• Theta vacuum and entanglement interaction in the three-flavor Polyakov-loop extended Nambu-Jona-Lasinio model
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• Dynamical Locking of the Chiral and the Deconfinement Phase Transition in QCD
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• Chiral symmetry in the low-energy limit of QCD at finite temperature
• Vacuum polarization corrections to low energy quark effective couplings
• Strong-interaction matter under extreme conditions from chiral quark models with nonlocal separable interactions
• Dressed Polyakov loop and flavor dependent phase transitions
• Violations of parity and charge conjugation in the theta vacuum with imaginary chemical potential
• Two-color QCD at imaginary chemical potential and its impact on real chemical potential
• Chiral symmetry in strongly interacting matter
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• Flavor-dependent U(3) Nambu Jona Lasinio coupling constant
• Spontaneous parity and charge-conjugation violations at real isospin and imaginary baryon chemical potentials
• SU(2) higher-order effective quark interactions from polarization
• QCD Flux Tubes and Anomaly Inflow
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• Deconfinement vs. chiral symmetry and higher representation matter
• Stability of chromomagnetic condensation and mass generation for confinement in SU(2) Yang-Mills theory
• Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model
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• The magnetized (2+1)-dimensional Gross-Neveu model at finite density
• Low energy limit of QCD and the emerging of confinement
• Vector meson spectral function and dilepton rate in the presence of strong entanglement effect between the chiral and the Polyakov loop dynamics
• $U_A(1)$ symmetry breaking quark interactions from vacuum polarization
• Confinement/deconfinement transition temperature from the Polyakov loop potential and gauge-invariant gluon mass
• Multivacuum States in a Fermionic Gap Equation with massive gluons and confinement