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arXiv 1306.5647hep-phhep-th
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戈德斯通定理保护自发破缺的SO的自然性和不存在Brout-Englert-Higgs微调（2）

The Goldstone theorem protects naturalness, and the absence of Brout-Englert-Higgs fine-tuning, in spontaneously broken SO(2)

Bryan W. Lynn, Glenn D. Starkman

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摘要：

Gell-Mann-Levy（GML）、Schwinger和标准模型之前被证明缺乏Brout-Englert-Higgs（BEH）的微调问题，因为所有O（Λ^2）贡献都遵守对称性，所以具有有限的欧几里得截断Λ。我们将这些结果推广到SO（2）版本GML和Schwinger中某些M_{Heavy} ^2>> m_{BEH} ^2粒子的有限贡献。我们证明了两个SO（2）单态例子：一个重的实标量S和一个右手1型跷跷板Majorana中微子的明确的1-循环物理自然性。我们证明，对于低|Q^2|在最坏的情况下，大的自由度在自发破缺的SO（2）Schwinger中贡献了边际算子。GML从这些例子中得到的关键教训是，伪南武-戈德斯通玻色子（NGB）的质量平方必须被适当地重整化。一个真正的NGB值m_3^2 = 0，则由戈德斯通定理保护。对于Schwinger模型，出现了两个关键的观察结果：全局Ward-Takahashi恒等式（WTI）强制所有相关算子进入伪NGB质量平方; WTI通过禁止所有相关算子在自发破缺Goldstone模中的贡献来强制Goldstone定理，π_3在那里是无质量的NGB。Goldstone模，具有弱尺度m_{BEH} ^2 \&amp;<H>^2，即使作为具有某些高质量尺度扩展的低能有效理论，也不能被微调。它的“戈德斯通异常自然性（GEN）”，即所有相关算子都消失，是对微调的有力抑制，只是WTI、自发对称性破缺和戈德斯通定理的另一个（尽管不熟悉）结果。如果GEN可以以某种方式扩展到标准模型（SM），就不应该期望LHC会发现任何与中微子混合无关的超越SM的物理学，即标准模型加上广义相对论范式的唯一已知的实验必要修改。

英文摘要：

The Gell-Mann-Levy (GML), Schwinger and Standard Models were previously shown to lack a Brout-Englert-Higgs (BEH) fine-tuning problem due to quadratic divergences, with finite Euclidean cut-off Λ, because of the symmetries obeyed by all O(Λ^2) contributions. We extend those results to finite contributions from certain M_{Heavy}^2>> m_{BEH}^2 particles in SO(2) versions of GML and Schwinger. We demonstrate explicit 1-loop physical naturalness for two SO(2) singlet examples: a heavy real scalar S and a right-handed Type 1 see-saw Majorana neutrino. We prove that for low |q^2| the heavy degrees of freedom contribute, at worst, marginal operators in spontaneously broken SO(2) Schwinger. The key GML lesson from these examples is that the pseudo Nambu-Goldstone boson (NGB) mass-squared must be properly renormalized. A true NGB value, m_3^2 = 0, is then protected by the Goldstone theorem. For the Schwinger model, two crucial observations emerge: global Ward-Takahashi identities (WTI) force all relevant operators into the pseudo-NGB mass-squared; and WTI enforce the Goldstone theorem by forbidding all relevant operator contributions in the spontaneously broken Goldstone mode, π_3 is a massless NGB there. Goldstone mode, with weak-scale m_{BEH}^2 \& <H>^2, is not-fine-tuned even as a low-energy effective theory with certain high-mass-scale extensions. Its "Goldstone Exceptional Naturalness (GEN)," where all relevant operators vanish, a powerful suppression of fine-tuning, is simply another (albeit un-familiar) consequence of WTI, spontaneous symmetry breaking and the Goldstone theorem. If GEN can somehow be extended to the Standard Model (SM), there should be no expectation that LHC will discover any Beyond the SM physics unrelated to neutrino mixing, i.e. the only known experimentally necessary modification of the Standard Model plus General Relativity paradigm.

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