泡利求和规则隐含着BSM物理学
The Pauli sum rules imply BSM physics
摘要：
大约67年前（1951年），沃尔夫冈·泡利提出了三个求和规则：\[ \sum_n (-1)^{2S_n} g_n = 0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^2 =0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^4=0. \]这三个求和规则与洛伦兹不变性和零点应力能量张量的有限性密切相关。更远的地方，这三个限制也密切相关的有限QFT的存在，最终基于费米-玻色取消。（超对称性对于这些有限量子场论的存在既不是必要的，也不是充分的;尽管轻微但明确的破缺超对称性或错位超对称性可以被用作簿记设备，以保持计算的可管理性。在本文中，我将把这三个泡利求和规则当作给定的，假设它们是精确的非微扰有效性，将它们与观测到的标准模型粒子物理谱进行对比，并使用它们来提取尽可能多的关于超越标准模型（BSM）物理的与模型无关的信息。
英文摘要：
Some 67 years ago (1951) Wolfgang Pauli mooted the three sum rules: \[ \sum_n (-1)^{2S_n} g_n = 0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^2 =0; \qquad \sum_n (-1)^{2S_n} g_n \; m_n^4=0. \] These three sum rules are intimately related to both the Lorentz invariance and the finiteness of the zero-point stress-energy tensor. Further afield, these three constraints are also intimately related to the existence of finite QFTs ultimately based on fermi--bose cancellations. (Supersymmetry is neither necessary nor sufficient for the existence of these finite QFTs; though softly but explicitly broken supersymmetry or mis-aligned supersymmetry can be used as a book-keeping device to keep the calculations manageable.) In the current article I shall instead take these three Pauli sum rules as given, assume their exact non-perturbative validity, contrast them with the observed standard model particle physics spectrum, and use them to extract as much model-independent information as possible regarding beyond standard model (BSM) physics.
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