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arXiv 1504.07585hep-phhep-latnucl-th
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从类Z3-symmetric QCD理论理解高密度下的QCD

Understanding of QCD at high density from Z3-symmetric QCD-like theory

Hiroaki Kouno, Kouji Kashiwa, Junichi Takahashi, Tatsuhiro Misumi, Masanobu Yahiro

备注：
8 pages, 8 figures
发表信息：
Phys. Rev. D 93, 056009 (2016)
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摘要：

本文用Z_3对称SU（3）规范理论研究了大μ/T下的QCD，其中μ为夸克数化学势，T为温度。我们在QCD中对夸克施加了与味道相关的扭曲边界条件。这个类QCD理论以扭曲角θ为参数，当θ =0时与QCD一致，当θ =2π/3时成为对称。对于QCD和Z_3对称SU（3）规范理论，用Polyakov圈扩展的Nambu-Jona-Lasinio模型在μ-T平面上画出了相图。在Z_3对称SU（3）规范理论中，在T \lsim 200 MeV处出现的受限相中，Polyakov圈varphi为零。由于色超导相中的有限双夸克凝聚破坏了Z_3对称性，使varphi有限，因此完全受限相与色超导相永远不会共存。当μ \gsim为300 MeV时，CSC相比T \lsim 100 MeV时的完全受限相更稳定。同时，由于手征凝聚体是Z_3不变量的，在完全受限相中，手征对称性可以被破缺。因此，完全受限相被划分为μ \lsim 300 MeV和T \lsim 200 MeV的区域中没有手征对称性恢复的完全受限相和μ \gsim 300 MeV和100 \lsim T \lsim 200 MeV的区域中具有手征对称性恢复的完全受限相。在QCD中保留了Z_3对称类QCD理论的基本相结构。利用重夸克理论，我们证明了在完全受限相中，由于φ=0，符号问题变得不那么严重。我们讨论了一个格点量子色动力学框架来计算θ=0和θ=2π/3的观测值。

英文摘要：

We investigate QCD at large mu/T by using Z_3-symmetric SU(3) gauge theory, where mu is the quark-number chemical potential and T is temperature. We impose the flavor-dependent twist boundary condition on quarks in QCD. This QCD-like theory has the twist angle theta as a parameter, and agrees with QCD when theta=0 and becomes symmetric when theta=2π/3. For both QCD and the Z_3-symmetric SU(3) gauge theory, the phase diagram is drawn in mu--T plane with the Polyakov-loop extended Nambu--Jona-Lasinio model. In the Z_3-symmetric SU(3) gauge theory, the Polyakov loop varphi is zero in the confined phase appearing at T \lsim 200 MeV. The perfectly confined phase never coexists with the color superconducting (CSC) phase, since finite diquark condensate in the CSC phase breaks Z_3 symmetry and then makes varphi finite. When mu \gsim 300 MeV, the CSC phase is more stable than the perfectly confined phase at T \lsim 100 MeV. Meanwhile, the chiral symmetry can be broken in the perfectly confined phase, since the chiral condensate is Z_3 invariant. Consequently, the perfectly confined phase is divided into the perfectly confined phase without chiral symmetry restoration in a region of mu \lsim 300 MeV and T \lsim 200 MeV and the perfectly confined phase with chiral symmetry restoration in a region of μ\gsim 300 MeV and 100 \lsim T \lsim 200 MeV. The basic phase structure of Z_3-symmetric QCD-like theory remains in QCD. We show that in the perfectly confined phase the sign problem becomes less serious because of φ=0, using the heavy quark theory. We discuss a lattice QCD framework to evaluate observables at θ=0 from those at θ=2π/3.

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