标题： 来自 spurion 分析的最广义 EFTs：希尔伯特级数与最小轻子味破坏 显示英文标题

标题： Most general EFTs from spurion analysis: Hilbert series and Minimal Lepton Flavor Violation

摘要： 我们推导了一般有效场论（EFT）的饱和定理，这些EFT使用 spurion 分析构建。 设$S$是一组 spurion 场，用于组织全局对称性$G_f$的破缺，设$H_S$是$G_f$在任意真空期望值$\langle S\rangle$下未破缺的子群；我们证明了由 spurion 分析构造的EFT拉格朗日量$saturates$等价于没有 spurion 但限制在$H_S$对称性的EFT拉格朗日量，前提是允许 spurion 场的任意幂次。 作为例子，我们研究了几种极小轻子味破坏（MLFV）原理的实现，对应于中微子质量的各种起源。 在每种情况下，我们计算Hilbert级数以获得出现在相应EFT中质量维数为6的独立轻子味协变量的数量。 这些数字与不含 spurion 的 EFT 中的$H_S$不变量数量一致，证明了饱和定理。 受唯象学联系的启发，我们为选定的轻子味协变量提供了线性独立的 spurion 多项式。 附带的文件可在 https://github.com/HilbertSeries/Group_Invariants_and_Covariants 获取，这是一份 Mathematica 笔记本，提供了用于计算紧致经典群不变量和协变量的通用 Hilbert 系列函数。 它展示了使用代码的示例，包括我们 MLFV 场景的 Hilbert 系列。 显示英文摘要

摘要： We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let $S$ be a set of spurion fields introduced to organize the breaking of a global symmetry $G_f$, and $H_S$ be the subgroup of $G_f$ that remains unbroken under a generic vacuum expectation value $\langle S\rangle$; we show that the EFT Lagrangian constructed from the spurion analysis $saturates$ the EFT Lagrangian without the spurions but restricted to $H_S$ invariance, provided that arbitrary powers of the spurion fields are allowed. As examples, we study several implementations of the Minimal Lepton Flavor Violation (MLFV) principle, corresponding to various origins of the neutrino masses. In each scenario, we compute the Hilbert series to obtain the numbers of independent lepton flavor covariants that appear in the corresponding EFT at mass dimension 6. These numbers agree with the number of $H_S$ invariants in the EFT without the spurions, demonstrating the saturation theorem. Motivated by phenomenological connections, we provide linearly independent spurion polynomials for selected lepton flavor covariants. An ancillary file is supplied at https://github.com/HilbertSeries/Group_Invariants_and_Covariants , which is a Mathematica notebook that provides functions for computing general Hilbert series of invariants and covariants of compact classical groups. It presents examples demonstrating the use of the code, including the Hilbert series for our MLFV scenarios.