从壳上残量出发的特征锥跑动：物理有效场论（EFT）商上的可识别性
Characteristic-cone running from on-shell residues: Identifiability on the physical EFT quotient
浏览论文内容
中文总结 AI 辅助
本研究针对平直空间壳上残量，提出数据完备性测试，在四维宇称守恒的爱因斯坦-标量-麦克斯韦EFT中推导残量相关系数，验证响应可识别性，明确算子不完备性及标量-光子接触项的混合特性。
中文摘要 AI 辅助
我们提出一种数据完备性测试，用于从平直空间的壳上重整化群残量中提取低能特征锥跑动。在四维、宇称守恒的爱因斯坦-标量-麦克斯韦有效场论（EFT）中，该理论包含四阶导数与四个外场，威尔逊方向首先被置于物理EFT商上，背景传播由全无质量根扇区上的无迹响应表示。当振幅核恰好位于响应核中时，该响应可通过选定的振幅坐标识别。对于已发表的异螺旋度矢量-标量残量，我们得到β_μ C_{γφ}^{(2)}=-55/(96π²)；经阶约化的框架变换后，贡献为β_μ(r_T - r_γ)=-55/(48π²M_P⁴)。有限算子登记给出明确的二阶不完备性测试：独立的F⁴方向在磁背景下分裂光子极化，而CFF在彼得罗夫型I的爱因斯坦-标量背景上沿主外尔轴产生解析分裂。对于孤立的标量-光子接触，通过直接舒尔约化得到非零的原始混合，但根据麦克斯韦沃德恒等式，不存在一阶物理非对角项。因此，该残量确定了一个对角锥贡献，但无法确定所声明的容许系数域上的完整项特征响应。
英文摘要
We formulate a data-completeness test for extracting low-energy characteristic-cone running from flat-space on-shell renormalization-group residues. In four-dimensional, parity-even Einstein--scalar--Maxwell effective field theory through four derivatives and four external fields, Wilson directions are first placed on the physical EFT quotient and background propagation is represented by a traceless response on the full massless root sector. The response is identifiable from chosen amplitude coordinates precisely when the amplitude kernel lies in the response kernel. For the published opposite-helicity vector--scalar residue we find $β_μC_{γϕ}^{(2)}=-55/(96π^2)$ and, after an order-reduced frame translation, the contribution $β_μ(r_T-r_γ)=-55/(48π^2M_{\rm P}^4)$. A finite operator registry gives explicit rank-two incompleteness tests: independent $F^4$ directions split photon polarizations on a magnetic background, while $\mathcal CFF$ produces an analytic splitting along a principal Weyl axis on a Petrov-I Einstein--scalar background. For the isolated scalar--photon contact, direct Schur reduction finds nonzero raw mixing but no first-order physical off-diagonal entry, by the Maxwell Ward identity. Thus the residue fixes one diagonal cone contribution but does not determine the term-complete characteristic response over the declared admissible coefficient domain.
