Polyakov-loop拓展的夸克介子模型中的Roberge-Weiss相变研究

${\mathbb{Z}}_3$-QCD是具有严格中心对称性的类QCD理论，研究其在特殊条件下的性质有助于理解QCD退禁闭相变。本文应用三种味道的Polyakov-loop拓展的夸克介子模型作为${\mathbb{Z}}_3$-QCD的低能有效理论，研究了不同中心对称性破缺模式下的Roberge-Weiss(RW)相变。为保证RW周期性，本文采用味道依赖的虚化学势$(\mu_{\rm{u}},\mu_{\rm{d}},\mu_{\rm{s}})={\rm{i}}T(\theta-2C\pi/3,\theta,\theta+2C\pi/3)$，其中${\mathbb{Z}}_3$-QCD是具有严格中心对称性的类QCD理论，研究其在特殊条件下的性质有助于理解QCD退禁闭相变。本文应用三种味道的Polyakov-loop拓展的夸克介子模型作为${\mathbb{Z}}_3$-QCD的低能有效理论，研究了不同中心对称性破缺模式下的Roberge-Weiss(RW)相变。为保证RW周期性，本文采用味道依赖的虚化学势$(\mu_{\rm{u}},\mu_{\rm{d}},\mu_{\rm{s}})={\rm{i}}T(\theta-2C\pi/3,\theta,\theta+2C\pi/3)$，其中$0\!\leqslant\!{C}\!\leqslant1$。传统的和夸克反馈效应改进的两种不同Polyakov-loop势被分别用于相应的计算。研究表明，当$N_{\rm{f}}\!=\!3$，$C\!\ne\!1$时，RW相变出现在$\theta=\pi/3$(mod $2\pi/3$)处，其强度随$C$值的减小而加强；当$C\!=\!1$，$N_{\rm{f}}\!=\!2\!+\!1$时，RW相变位置出现反常，变为$\theta=2\pi/3$(mod $2\pi/3$)；而当$C\!=\!1$，$N_{\rm{f}}\!=\!1\!+\!2$时，RW相变点又返回$\theta\!=\!\pi/3$(mod $2\pi/3$)。上述几种情形的RW相变端点均为三相点。研究发现，夸克反馈效应使得RW相变强度减弱，退禁闭相变温度变低，但并未改变前述的定性结论。

Roberge-Weiss Transition in the Polyakov-loop Extended Quark-meson Model

${\mathbb{Z}}_3$-QCD is a QCD-like theory with strict center symmetry. We use the Polyakov-loop extended quark meson model (PQM) as a low-energy effective theory of ${\mathbb{Z}}_3$-QCD to study the RW transitions in different center symmetry breaking patterns. The flavor-dependent imaginary chemical potentials, namely $(\mu_{\rm{u}},\,\mu_{\rm{d}},\,\mu_{\rm{s}})= {\rm{i}}T(\theta-2C\pi/3,\theta,\theta+2C\pi/3)$ are adopted, which guarantees the RW periodicity. The traditional and quark improved Polyakov-loop potentials are used, respectively. For $N_{\rm{f}}\!=\!3$ with $C\!\ne\!1$, the RW transition occurs at $\theta\!=\!\pi/3$ (mod $2\pi/3$), which gets stronger when $C$ declines from one to zero. When $C\!=\!1$, the RW transition happens at $\theta\!=\!2\pi/3$ (mod $2\pi/3$) for $N_{\rm{f}}\!=\!2+1$, but $\theta\!=\!\pi/3$ (mod $2\pi/3$) for $N_{\rm{f}}\!=\!1+2$. We find that all RW transition endpoints are triple points when $C\!=\!1$. We confirm that the RW transition becomes weaker and the deconfinement temperature gets lower when taking into account the quark back-reaction effect. However, the modification of the gluon sector due to the quark effect does not change the main conclusions mentioned above.