AI 中文总结
研究提出符号轨道技术，系统分类GOOFy变换对多希格斯模型二次部分的影响，明确其兼容二次结构的存在条件及SU(2)的特殊代数性质对重整化群稳定性的作用。
AI 中文摘要
除了常规的希格斯家族变换和一般CP变换外，还可考虑更广泛的非标准“GOOFy”变换，其中标量场及其共轭被赋予相关但不等价的变换。尽管这些变换在常规意义上并非整个拉格朗日量的对称性，但部分变换仍能稳定标量势。它们对二次部分的影响尚未得到系统分类。我们开发了符号轨道技术，以确定与这些变换兼容的双线性结构。该技术应用于三希格斯二重态模型（three-Higgs-doublet models, 3HDMs），并被设计为可扩展至更大的多希格斯 sector。研究表明，仅当满足两个独立条件时，才存在非零的GOOFy兼容二次部分： underlying群具有非平凡的符号特征，且该特征在标量表示与其共轭的张量积中实现。作为关键结论，我们证明，孤立的$r_0 \to -r_0$流形的重整化群稳定性并非多希格斯势的通用特征，而是SU(2)特殊代数性质的直接结果。这些结果对可允许的GOOFy二次结构及其不变双线性子空间进行了分类，凸显了其重整化群稳定性的代数障碍。
英文摘要
Beyond conventional Higgs-family and general CP transformations, one may also consider a broader class of non-standard "GOOFy" transformations, in which the scalar fields and their conjugates are assigned related but inequivalent transformations. Although these transformations are not symmetries of a full Lagrangian in the conventional sense, some nevertheless stabilise the scalar potential. Their impact on the quadratic sector has not yet been systematically classified. We develop a sign-orbit technique to determine the bilinear structures compatible with these transformations. Applied to three-Higgs-doublet models, and formulated so as to extend to larger multi-Higgs sectors, the method shows that a non-vanishing GOOFy-compatible quadratic sector exists only when two independent conditions are met: the underlying group admits a non-trivial sign character, and that character is realised within the tensor product of the scalar representation and its conjugate. As a key consequence, we demonstrate that the renormalisation-group stability of the $r_0 \to -r_0$ manifold in isolation is not a generic feature of multi-Higgs potentials, but rather a direct consequence of special algebraic properties of $SU(2)$. These results provide a classification of the admissible GOOFy quadratic structures and their invariant bilinear subspaces, highlighting the algebraic obstructions to their renormalisation-group stability.
Comments41 pages
