The quarkynic phase and the Z_{Nc} symmetry

Abstract

We investigate the interplay between the Z_{Nc} symmetry and the emergence of the quarkyonic phase, adding the flavor-dependent complex chemical potentials μ_f=μ+iTθ_f with (θ_f)=(0, θ, -θ) to the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model. When θ=0, the PNJL model with the μ_f agrees with the standard PNJL model with the real chemical potential μ. When θ=2π/3, meanwhile, the PNJL model with the μ_f has the Z_{Nc} symmetry exactly for any real μ, so that the quarkyonic phase exists at small T and large μ. Once θvaries from 2π/3, the quarkyonic phase exists only on a line of T=0 and μlarger than the dynamical quark mass, and the region at small T and large μis dominated by the quarkyonic-like phase in which the Polyakov loop is small but finite.

Figures (4)

• Figure 1: Location of $\exp[i\theta_f]$ in the complex plane; here, $(\theta_f)=(0,\theta,-\theta)$.
• Figure 2: (a) The Polyakov loop $\Phi$ and (b) the chiral condensate $\sigma_1$ in the $\theta$-$T$ plane at $\mu=0$MeV.
• Figure 3: Phase diagram in the $T$-$\mu$ plane. Panels (a)-(c) correspond to three cases of $\theta=0$, $8\pi/15$ and $2\pi/3$, respectively. The thick (thin) solid curve means the first-order deconfinement (chiral) phase transition line, while the thick (thin) dashed curve does the deconfinement (chiral) crossover line. The closed circles stand for the endpoints of the first-order deconfinement and chiral phase transition lines. In panels (a) and (b), the thick-solid line at $T=0$ and $\mu \gtrsim M_f=323$ MeV represents the quarkyonic phase.
• Figure 4: $T$ dependence of $\Phi$ for $\mu=0.1,~0.3$ GeV in the lowest order approximation. Panel (a) corresponds to the case of $\theta =0$ and panel (b) does to the case of $\theta =2\pi /3$.