Collider Spin Tomography with Missing Neutrinos

Abstract

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 $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}\to {\pi }^{+}{\pi }^{-}+\nu \bar{\nu }$, 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.

45 pages, 1 table, 10 figures

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