Conditioning-Induced Invariants in Λ–Hyperon Pair Spin Correlations

Recent proceedings by Vanek et al. (STAR Collaboration) introduce a novel measurement of ΛΛ, ΛΛ̄, and Λ̄Λ̄ spin–spin correlations in high-energy p̄+p collisions, motivated by the observation that standard factorized event generators predict vanishing pair polarization in the presence of flat single-particle marginals. In this work, I present a complementary, conditioning-aware analysis of the same observable. I show that any nonzero Λ–pair spin correlation with vanishing single-Λ polarization cannot arise from factorizable (local) conditioning, acceptance, or fragmentation effects. This result is established at the level of conditioned probability distributions and is independent of detector modeling or microscopic dynamics. I further introduce a scalar acceptance-derived invariant constructed solely from measured pair yields and demonstrate how it provides a model-independent diagnostic for organizing correlation strength across kinematic bins. The framework distinguishes global (non-factorizable) conditioning effects from local mechanisms without invoking modifications to quantum mechanics or QCD, and complements the original experimental motivation of the STAR measurement.