AI 中文总结
针对丢失中微子导致的对撞机自旋层析成像问题，提出仅用可见数据的自洽不动点展开方法，可准确重建可识别自旋系数与微分产生率，解决运动学模糊偏差问题。
AI 中文摘要
丢失的中微子不一定会破坏对撞机自旋层析成像。我们将不可见粒子引起的运动学模糊下的可见测量，表述为对产生自旋密度矩阵的粗粒化正算子值测度。研究表明，信息损失由所得可见数据映射的零空间决定，而非运动学解的数量。在$e^+e^-\to\tau^+\tau^-\to pi^+\bar{\nu}\nu$过程中，双重模糊仅使反对称自旋关联组合$C_{nr}-C_{rn}$无法识别，而微分产生率及其余14个自旋系数均可识别。为解决运动学模糊下的实际重建问题，我们开发了一种仅使用可见数据的自洽不动点展开方法，无需假设理论产生模板。在标准模型和反常tau偶极基准的闭合测试中，该方法可复现真实水平的微分产生率及所有可识别自旋系数，而通常对运动学折叠的平均会产生显著偏差的重建结果。当存在非平凡零空间时，重建的可识别子空间结合正性，可得到纠缠度和CHSH参数的可控范围。
英文摘要
Missing neutrinos need not destroy collider spin tomography. We formulate the visible measurement under kinematic ambiguities arising from invisible particles as a coarse-grained positive-operator-valued measure on the production spin density matrix. We show that information loss is governed by the null space of the resulting visible-data map, not by the number of kinematic solutions. In $e^+e^-\toτ^+τ^-\toπ^+π^-+ν\barν$, the twofold ambiguity leaves only the antisymmetric spin-correlation combination $C_{nr}-C_{rn}$ unidentifiable, while the differential production rate and the remaining fourteen spin coefficients are identifiable. For practical reconstruction under kinematic ambiguities, we develop a self-consistent fixed-point unfolding method using only visible data, without assuming a theoretical production template. Closure tests in Standard Model and anomalous tau-dipole benchmarks show that the method reproduces the truth-level differential production rate and all identifiable spin coefficients, whereas the usual flat average over kinematic folds gives significantly biased reconstructions. When a nontrivial null space is present, the reconstructed identifiable subspace together with positivity yields controlled ranges for concurrence and the CHSH parameter.
Comments45 pages, 1 table, 10 figures
