arXiv 1301.40132013-01-23hep-phhep-latnucl-th

三味QCD的禁闭和Z_3对称性

Confinement and Z_3 symmetry in three-flavor QCD

Hiroaki Kouno, Takahiro Makiyama, Takahiro Sasaki, Yuji Sakai, Masanobu Yahiro

备注：: 21 pages, 22 figures. Typos have been revised. Six references are added
DOI：: 10.1088/0954-3899/40/9/095003

摘要：

利用Polyakov圈扩展的Nambu-Jona-Lasinio（PNJL）模型研究了具有虚同位旋化学势$(μ_u,μ_d,μ_s)=(iθT,-iθT,0)$的三味QCD的禁闭机制，其中$T$为温度.对于三种简并味，系统在$θ=2π/3$处具有$\mathbb{Z}_{3}$对称性，因此对于小的$T$，Polyakov环$Φ$在那里消失。对于2+1风味，对于任何$θ$都不保持对称性，但是对于小的$T$，$Φ$在$θ=θ_{\rm conf} < 2π/3$处变为零。即使系统不完全具有$\mathbb{Z}_{3}$对称性，也能实现由$Φ=0$定义的约束相。在$θ$ - $T$平面上，存在一个临界的去禁闭转变终点。在零化学势下的解禁闭交叉是在$θ=θ_{\rm conf}$的一级解禁闭跃迁的残余。研究了夸克数磁化率非对角元$χ_{us}$与退禁闭跃迁之间的关系。由于格点QCD模拟不涉及任何$θ$的符号问题，因此本文的结果可以直接用格点QCD模拟来检验。

英文摘要：

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 $θ$.

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英文摘要：

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