标准模型有效场论中的九维算子完备集
Complete Set of Dimension-9 Operators in the Standard Model Effective Field Theory
摘要：
利用振幅算符对应的自动算法，给出了标准模型有效场论中9维算符基的一个完整而独立的列表。首先通过列举辅助$SU(N)$群和规范群的Young表来构造一个完整的基（y基），其中运动方程和分部积分的冗余都被去除。在存在重复域的情况下，从y基导出另一个具有显式味对称性的基（p基），其通过称为去对称化的系统过程进一步导出独立单项式算子的基。我们的运营商的形式具有优势，在传统的方式呈现运营商的风味关系的约束下，在简单的消除风味冗余和识别独立的风味指定的运营商。我们列出了90456（560）个三（一）代费米子的算符，它们都违反了重子数或轻子数守恒，其中我们发现了新的违反模式，如$ΔB = 2$和$ΔL = 3$，它们只出现在$d \ge 9$维。
英文摘要：
We present a complete and independent list of the dimension 9 operator basis in the Standard Model effective field theory by an automatic algorithm based on the amplitude-operator correspondence. A complete basis (y-basis) is first constructed by enumerating Young tableau of an auxiliary $SU(N)$ group and the gauge groups, with the equation-of-motion and integration-by-part redundancies all removed. In the presence of repeated fields, another basis (p-basis) with explicit flavor symmetries among them is derived from the y-basis, which further induces a basis of independent monomial operators through a systematic process called de-symmetrization. Our form of operators have advantages over the traditional way of presenting operators constrained by flavor relations, in the simplicity of both eliminating flavor redundancies and identifying independent flavor-specified operators. We list the 90456 (560) operators for three (one) generations of fermions, all of which violate baryon number or lepton number conservation; among them we find new violation patterns as $ΔB = 2$ and $ΔL = 3$, which only appear at the dimensions $d \ge 9$.
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