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arXiv 0901.3099hep-phhep-th
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四费米算符的手征真空排列和自发CP破坏

Chiral Vacuum Alignment and Spontaneous CP Violation by Four-Fermi Operators

Tonguç Rador

备注：
Minor expansion of the manuscript to ameliorate exposition
发表信息：
Phys.Rev.D79:105008,2009
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摘要：

在存在自发破缺到其矢量子群的全局手征对称性的模型中，引入明确的对称性破缺微扰将定义理论的真正真空。这个真真空是通过最小化不同真空之间的微扰哈密顿量的期望值而得到的。寻找理论正确真空的过程可能导致CP对称性的自发破缺，即使一开始要求微扰的CP不变性。在这项工作中，我们详细研究模型的微扰是由四个费米运营商。我们提出了两种费米子味模型的精确处理方法，并对三种费米子味模型进行了深入的数值研究。我们表明，后Dashen程序应用的解决方案，真正的真空下降在三个不同的CP破坏模式类。临界过渡是可能的这些类之间的变化的参数的扰动。我们严格表明，在这些过渡的伪戈德斯通玻色子质量消失。我们还主张，并证实与各种类型的模型的数值统计分析，如果一个强加CP不变性的扰动之前解决真空对齐，由此产生的真空结构将有一个相当大的概率轻伪戈德斯通玻色子质量。这是Peccei-Quinn机制的统计变体，可以推测其起作用。

英文摘要：

In models where there is a global chiral symmetry which spontaneously breaks to its vectorial subgroup, the introduction of an explicit symmetry breaking perturbation will define the true vacuum of the theory. This true vacuum is found via the minimization of the expectation value of the perturbing hamiltonian between different vacua as prescribed by Dashen. The procedure of finding the correct vacuum of the theory may result in the spontaneous breaking of CP symmetry even if one initially demands CP invariance on the perturbation. In this work we study in detail models where the perturbation is provided by four-Fermi operators. We present exact treatment for models with two fermion flavors and study the three flavor case in depth numerically. We show that after Dashen procedure is applied the solutions for the true vacuum fall in three classes with different CP breaking patterns. Critical transitions is possible between these classes as one varies the parameters of the perturbation. We rigorously show that at these transitions a pseudo-Goldstone boson mass vanishes. We also advocate, and substantiate with numerical statistical analysis for various types of models, that if one imposes CP invariance on the perturbation before solving the vacuum alignment, the resulting vacuum structure will have a sizable probability for a light pseudo-Goldstone boson mass. That is a statistical variant of Peccei-Quinn mechanism can be speculated to operate.

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