I型跷跷板作为相对论费米子邻近效应：谱矩、EFT一致性与惰性区重建
The Type-I Seesaw as a Relativistic Fermionic Proximity Effect: Spectral Moments, EFT Consistency, and Sterile-Sector Reconstruction
- National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究将I型跷跷板表述为相对论费米子邻近效应，推导了其谱矩、EFT一致性条件及惰性区重建方法，区分了静态舒尔补核与物理Takagi极点质量。
AI中文摘要：
我们将I型跷跷板表述为精确活性区两点核中的相对论费米子邻近效应。活性中微子无重整化可重整化规范不变马约拉纳质量，通过轻子数守恒的汤川杂交耦合至惰性马约拉纳配对核。积分惰性场得到非局域的Nambu-Gorkov嵌入自能。在惰性Takagi基下，其反常和正常味响应分别为$\boldsymbol{\textit{A}}(Q^2)=\boldsymbol{\textit{\textSigma}}_i M_i y_i y_i^T/(Q^2+M_i^2)$和$\boldsymbol{\textit{B}}(Q^2)=\boldsymbol{\textit{\textSigma}}_i y_i y_i^\boldsymbol{\textdag}/(Q^2+M_i^2)$。它们的低能展开产生关联的轻子数破坏和轻子数守恒矩塔，领头矩重现Weinberg系数和六维动力学算子。两个矩塔共享同一惰性质量集，其正的正常支撑提供共同湮灭子，尽管反常留数可在精确简并时抵消。我们证明正常块汉克尔正性及量纲缩放的混合Nambu-Hankel序列的正性，后者给出轻子数守恒与轻子数破坏数据间的矩阵柯西-施瓦茨不等式，可揭示被简并正常留数隐藏的配对方向。孤立非简并极点留数满足额外的非线性相容性恒等式。这些结果给出树级EFT一致性检验及可见极点与总留数数据的矩阵铅笔重建；选择唯一的紫外拉格朗日量需要关于惰性基多重性的额外信息。单代精确例子区分静态舒尔补核与物理Takagi极点质量。该邻近结构无需费米面或凝聚态即可应用，且Nambu加倍不引入新的物理自由度。
英文摘要：
We formulate the type-I seesaw as a relativistic fermionic proximity effect in the exact active-sector two-point kernel. Active neutrinos have no renormalizable gauge-invariant Majorana mass and couple by lepton-number-conserving Yukawa hybridization to a sterile Majorana pairing kernel. Integrating out the sterile fields gives a nonlocal Nambu-Gorkov embedding self-energy. In a sterile Takagi basis its anomalous and normal flavor responses are $\mathcal{A}(Q^2)=\sum_i M_i y_i y_i^T/(Q^2+M_i^2)$ and $\mathcal{B}(Q^2)=\sum_i y_i y_i^\dagger/(Q^2+M_i^2)$, respectively. Their low-energy expansions generate correlated lepton-number-violating and lepton-number-conserving moment towers. The leading moments reproduce the Weinberg coefficient and the dimension-six kinetic operator. Both towers share one sterile mass set; its positive normal support supplies a common annihilator, although anomalous residues can cancel at exact degeneracy. We prove normal block-Hankel positivity and positivity of a dimensionally rescaled mixed Nambu-Hankel sequence. The latter gives matrix Cauchy-Schwarz inequalities between lepton-number-conserving and lepton-number-violating data and can reveal paired directions hidden by a degenerate normal residue. Isolated nondegenerate pole residues satisfy an additional nonlinear compatibility identity. These results yield tree-level EFT consistency tests and a matrix-pencil reconstruction of visible pole and aggregate-residue data; selecting a unique ultraviolet Lagrangian requires additional information about sterile-basis multiplicities. An exact one-generation example distinguishes the static Schur-complement kernel from the physical Takagi pole mass. The proximity structure applies without a Fermi surface or condensate, and Nambu doubling introduces no new physical degrees of freedom.
