Three-flavor Nambu–Jona-Lasinio model at finite isospin chemical potential
Three-flavor Nambu–Jona-Lasinio model at finite isospin chemical potential
复制标题
DOI：
10.1103/physrevd.88.056013
复制
发表时间：
2013-07
影响因子：
5
通讯作者：
Tao Xia;Lianyi He;P. Zhuang
中科院分区：
文献类型：
--
作者：
Tao Xia;Lianyi He;P. Zhuang
有限同位旋化学势下的QCD具有正定的费米子行列式，可以成功地进行格点模拟。虽然双味有效模型可能足以描述π介子凝聚现象，但有趣的是研究奇异自由度和U${\rmA}（1）$反常的作用。本文系统地研究了具有Kobayashi-Maskawa-'tHooft（KMT）项的三味Nambu-Jona-Lasinio模型，该模型模拟了有限同位旋化学势下的U${\rmA}（1）$反常.在平均场近似下，该模型预测了从真空到π超流相的相变，这发生在$\mu_{\rm I}$等于π质量$m_\pi$。由于U${\rmA}（1）$反常，奇异自由度与轻夸克自由度耦合，奇异夸克有效质量依赖于π凝聚.而在π超流相中，奇异夸克凝聚体和奇异夸克有效质量变化不大，验证了双味模型的正确性。构造了在π介子凝聚存在下的Kobayashi-Maskawa-'tHooft项的有效四费米子相互作用。由于U${\rmA}（1）$反常，π介子凝聚通常会引起标量-赝标量相互作用。建立了介子激发的Bethe-Salpeter方程，并在有限的同位旋化学势和温度下得到了介子的质量谱。最后，导出了有限同位旋化学势下拓扑磁化率的一般表达式。与有限温度效应抑制$\chi$相反，同位旋密度效应导致$\chi$的增强。
QCD at finite isospin chemical potential $\mu_{\text I}$ possesses a positively definite fermion determinant and the lattice simulation can be successfully performed. While the two-flavor effective models may be sufficient to describe the phenomenon of pion condensation, it is interesting to study the roles of the strangeness degree of freedom and the U$_{\rm A}(1)$ anomaly. In this paper, we present a systematic study of the three-flavor Nambu--Jona-Lasinio model with a Kobayashi-Maskawa-'t Hooft (KMT) term that mimics the U$_{\rm A}(1)$ anomaly at finite isospin chemical potential. In the mean-field approximation, the model predicts a phase transition from the vacuum to the pion superfluid phase, which takes place at $\mu_{\rm I}$ equal to the pion mass $m_\pi$. Due to the U$_{\rm A}(1)$ anomaly, the strangeness degree of freedom couples to the light quark degrees of freedom and the strange quark effective mass depends on the pion condensate. However, the strange quark condensate and the strange quark effective mass change slightly in the pion superfluid phase, which verifies the validity of the two-flavor models. The effective four-fermion interaction of the Kobayashi-Maskawa-'t Hooft term in the presence of the pion condensation is constructed. Due to the U$_{\rm A}(1)$ anomaly, the pion condensation generally induces scalar-pseudoscalar interaction. The Bethe-Salpeter equation for the mesonic excitations is established and the meson mass spectra are obtained at finite isospin chemical potential and temperature. Finally, the general expression for the topological susceptibility $\chi$ at finite isospin chemical potential $\mu_{\rm I}$ is derived. In contrast to the finite temperature effect which suppresses $\chi$, the isospin density effect leads to an enhancement of $\chi$.