Model-independent determination of the parity of $Ξ$ hyperons

Based on reflection symmetry in the reaction plane, it is shown that measuring the transverse spin-transfer coefficient $K_{yy}$ in the $\bar{K}N \to KΞ$ reaction directly determines the parity of the produced cascade hyperon in a model-independent way as $π_Ξ=K_{yy}$, where $π_Ξ=\pm 1$ is the parity. This result based on Bohr's theorem provides a completely general, universal relationship that applies to the entire hyperon spectrum. A similar expression is obtained for the photoreaction $γN \to K K Ξ$ by measuring both the double-polarization observable $K_{yy}$ and the photon-beam asymmetry $Σ$. Regarding the feasibility of such experiments, it is pointed out that the self-analyzing property of the $Ξ$'s can be invoked, thus requiring only a polarized nucleon target.

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