发表机构
Fermi National Accelerator Laboratory（费米国家加速器实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出理论-操作模型（TOM）框架，通过类型化分解前向预测，给出参数鲁棒性与简并性的局部判据，并应用于μ子-电子转换实验，揭示归一化简并及部分参数等价效应。
AI 中文摘要
复杂实验通过物理模型与数据缩减的耦合链来推断理论参数。我们将理论-操作模型（TOM）形式化为这种前向预测的类型化分解，并研究制备、现象建模、读出、本底和分析的变化如何投影到由物理参数生成的局部流形上。对于平滑预测和局部可辨识的加权最小二乘估计，所得响应图将每个模型形变分解为参数等价分量和无法通过改变拟合物理参数吸收的残差分量。这为参数推断的鲁棒性、完全简并性和部分简并性提供了局部判据。该构造应用于铝中带电轻子味破坏的μ子-电子转换。单箱转换率模型表现出精确的归一化简并性。在弹性-非弹性谱的双模板模型中，共同的信号归一化被拟合转换率吸收而不改变算符敏感的核响应比，而相对的弹性-非弹性效率变化在一阶上精确等价于该比率的变化。基于已发表的Mu2e谱的数值Run-I示例表明，100 keV/c的动量尺度失配仅为部分参数等价：其投影到由弹性归一化R0和对数非弹性-弹性响应比ρ生成的局部切空间上的投影比为η=0.331，而大部分加权谱形变仍作为残差形状保留。因此，TOM在粒子/核现象学与实验实现的界面处提供了参数鲁棒性和简并性的局部理论描述。
英文摘要
Complex experiments infer theory parameters through a coupled chain of physical models and data reduction. We formulate the theoretical--operational model (TOM) as a typed factorization of this forward prediction and study how changes of preparation, phenomenon modelling, readout, backgrounds, and analysis project onto the local manifold generated by the physics parameters. For a smooth prediction and a locally identifiable weighted least-squares estimate, the resulting response map separates each model deformation into a parameter-equivalent component and a residual component that cannot be absorbed by a change of the fitted physics parameters. This gives local criteria for robustness, exact degeneracy, and partial degeneracy of parameter inference. The construction is applied to charged-lepton-flavour-violating muon--electron conversion in aluminium. A one-bin conversion-rate model exhibits an exact normalization degeneracy. In a two-template model of the elastic--inelastic spectrum, a common signal normalization is absorbed by the fitted conversion rate without changing an operator-sensitive nuclear-response ratio, whereas a relative elastic--inelastic efficiency change is exactly parameter-equivalent to a change of that ratio at first order. A numerical Run-I example based on published Mu2e spectra shows that a \(100\,\mathrm{keV}/c\) momentum-scale mismatch is only partially parameter-equivalent: its projection ratio onto the local tangent space generated by the elastic normalization \(R_0\) and the logarithmic inelastic-to-elastic response ratio \(ρ\) is \(η=0.331\), while most of the weighted spectral deformation remains as a residual shape. TOM thereby provides a local theoretical description of parameter robustness and degeneracy at the interface of particle/nuclear phenomenology and experimental realization.
