标准模型有效场论中的八维算子完备集
Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory
摘要：
我们提出了一个完整的列表中的标准模型有效场论使用群论技术在一个系统的和自动化的方式8维算子的基础。根据洛伦兹群的不可约表示，我们采用了一种新的算符形式，并将洛伦兹结构识别为$SU(N)$群中的态。在这种方式中，冗余的运动方程是不存在的，从积分的一部分被视为使用的事实，即独立的洛伦兹基形成不变的子空间的$SU(N)$组。我们还将算子分解为具有确定的味道指数之间的置换对称性的算子，以处理重复域的微妙之处。第一次，我们提供了显式形式的独立风味指定的运营商在一个系统的方式。我们的算法可以很容易地应用到高维标准模型有效场论和其他有效场论中，使这些研究更接近实际。
英文摘要：
We present a complete list of the dimension 8 operator basis in the standard model effective field theory using group theoretic techniques in a systematic and automated way. We adopt a new form of operators in terms of the irreducible representations of the Lorentz group, and identify the Lorentz structures as states in a $SU(N)$ group. In this way, redundancy from equations of motion is absent and that from integration-by-part is treated using the fact that the independent Lorentz basis forms an invariant subspace of the $SU(N)$ group. We also decompose operators into the ones with definite permutation symmetries among flavor indices to deal with subtlety from repeated fields. For the first time, we provide the explicit form of independent flavor-specified operators in a systematic way. Our algorithm can be easily applied to higher dimensional standard model effective field theory and other effective field theories, making these studies more approachable.
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