Confinement and Z_3 symmetry in three-flavor QCD

Abstract

We investigate the confinement mechanism in three-flavor QCD with imaginary isospin chemical potentials $(μ_u,μ_d,μ_s)=(iθT,-iθT,0)$, 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 $θ=2π/3$ and hence the Polyakov loop $Φ$ vanishes there for small $T$. As for 2+1 flavors, the symmetry is not preserved for any $θ$, but $Φ$ becomes zero at $θ=θ_{\rm conf} < 2π/3$ for small $T$. The confinement phase defined by $Φ=0$ is realized, even if the system does not have $\mathbb{Z}_{3}$ symmetry exactly. In the $θ$-$T$ 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 $θ=θ_{\rm conf}$. The relation between the non-diagonal element $χ_{us}$ 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 $θ$.

Figures (12)

• Figure 1: The $\theta$-variant TBC: Location of $e^{i\theta_f}$ ($f=u,d,s$) on a unit circle in the complex plane.
• Figure 2: $T$ dependence of (a) the chiral condensate $\sigma$ and the Polyakov loop $\Phi$ and (b) their susceptibilities $\chi_{\sigma\sigma}$ , $\chi_{\Phi_{\rm R}\Phi_{\rm R}}$ and $\chi_{\Phi_{\rm I}\Phi_{\rm I}}$ at $\mu_f =0$. Set R is taken in the PNJL calculation. The chiral condensate $\sigma$ is normalized by the value $\sigma_0$ at $T=0$. $\chi_{\Phi_{\rm R}\Phi_{\rm R}}$ and $\chi_{\Phi_{\rm I}\Phi_{\rm I}}$ are multiplied by 10 and 100, respectively.
• Figure 3: $T$ dependence of the chiral condensate $\sigma$ and the absolute value $|\Phi|$ at $\theta =2\pi /3$. The PNJL calculation is done with set R in panel (a) and set S in panel (b). The chiral condensate $\sigma$ is normalized by the value $\sigma_0$ at $T=0$.
• Figure 4: $T$ dependence of the chiral condensates $\sigma_f$ at $\theta =2\pi /3$. The PNJL calculation is done with set R in panel (a) and set S in panel (b). In panel (a), the solid line represents s-quark, while the dashed and dotted lines correspond to light quarks. In panel (b), the solid and dashed lines agree with each other.
• Figure 5: $T$ dependence of $\chi_{\sigma\sigma}$, $\chi_{\Phi_{\rm R}\Phi_{\rm R}}$ and $\chi_{\Phi_{\rm I}\Phi_{\rm I}}$ at $\theta =\theta_{\rm CEP}$. The PNJL calculation is done with set R. $\chi_{\sigma\sigma}$ is multiplied by -1. $\chi_{\Phi_{\rm R}\Phi_{\rm R}}$ is divided by 10, while $\chi_{\Phi_{\rm I}\Phi_{\rm I}}$ is multiplied by 100.