Separating entanglement at emission from femtoscopic correlations

We investigate how femtoscopic correlations modify the relation between the spin entanglement of emitted particle pairs and that of pairs selected at a given relative momentum. For two spin-$\frac{1}{2}$ particles, we show that the momentum-selected spin state can be entangled even when the corresponding state at emission is separable. We derive a momentum-dependent separability criterion that determines whether the observed spin correlations require entanglement at emission. As an application, we consider a pair of identical $\mathrm{\Lambda }$ hyperons, for which quantum statistics and final-state interactions affect the singlet and triplet spin channels differently at low relative momentum. Our results provide a framework for using experimentally accessible spin correlations to investigate entanglement at emission.