Confinement and Z_3 symmetry in three-flavor QCD

Abstract

We investigate the confinement mechanism in three-flavor QCD with imaginary isospin chemical potentials $({\mu }_u,{\mu }_d,{\mu }_s)=(i\theta T,-i\theta T,0)$, using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model, where $T$ is temperature. As for three degenerate flavors, the system has ${\mathbb{Z}}_3$ symmetry at $\theta =2\pi /3$ and hence the Polyakov loop $\Phi$ vanishes there for small $T$. As for 2+1 flavors, the symmetry is not preserved for any $\theta$, but $\Phi$ becomes zero at $\theta ={\theta }_{\mathrm{conf}}<2\pi /3$ for small $T$. The confinement phase defined by $\Phi =0$ is realized, even if the system does not have ${\mathbb{Z}}_3$ symmetry exactly. In the $\theta$-$T$ plane, there is a critical endpoint of deconfinement transition. The deconfinement crossover at zero chemical potential is a remnant of the first-order deconfinement transition at $\theta ={\theta }_{\mathrm{conf}}$. The relation between the non-diagonal element ${\chi }_{us}$ of quark number susceptibilities and the deconfinement transition is studied. The present results can be checked by lattice QCD simulations directly, since the simulations are free from the sign problem for any $\theta$.

21 pages, 22 figures. Typos have been revised. Six references are added

References in corpus (21)

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• Average phase factor in the PNJL model
• Violations of parity and charge conjugation in the theta vacuum with imaginary chemical potential
• Investigation of meson masses for real and imaginary chemical potential

Cited by in corpus (28)

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• Order parameters and color-flavor center symmetry in QCD
• Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
• QCD on a small circle
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• Anomaly matching in QCD thermal phase transition
• Lattice study on QCD-like theory with exact center symmetry
• Roberge-Weiss endpoint and chiral symmetry restoration in $N_f=2+1$ QCD
• Excited Scalar and Pseudoscalar Mesons in the Extended Linear Sigma Model
• Understanding of QCD at high density from Z3-symmetric QCD-like theory
• Polyakov-Nambu-Jona-Lasinio phase diagrams and quarkyonic phase from order parameters
• Quark-hadron phase transition in a three flavor PNJL model for interacting quarks
• Vacuum structure of Yang-Mills theory as a function of $\theta$
• The Instanton-Dyon Liquid Model V: Twisted Light Quarks
• High-temperature domain walls of QCD with imaginary chemical potentials
• Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model
• Instanton-dyon Ensembles III: Exotic Quark Flavors
• Sign problem in $Z_3$-symmetric effective Polyakov-line model
• Lectures on nonperturbative QCD ( Nonperturbative Topological Phenomena in QCD and Related Theories)
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly
• Color superconductivity in the Nambu Jona-Lasinio model complemented by a Polyakov loop
• Crossover-model approach to QCD phase diagram, equation of state and susceptibilities in the 2+1 and 2+1+1 flavor systems
• Winding theta and destructive interference of instantons
• Recent progress in understanding deconfinement and chiral restoration phase transitions
• Roberge-Weiss transitions at different center symmetry breaking patterns in a ${\mathbb{Z}}_3$-QCD model
• ${\mathbb{Z}}_N$ stability and continuity in twisted Eguchi-Kawai model with two-flavor adjoint fermions
• Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses