Dalitz decays of a hyperon resonance to a ground-state hyperon and an electron-positron pair can give access to some information about the composite structure of hyperons. We present expressions for the multi-differential decay rates in terms of general transition form factors for spin-parity combinations J^P = 1/2^+/-, 3/2^+/- of the hyperon resonance. Even if the spin of the initial hyperon resonance is not measured, the self-analyzing weak decay of the final ground-state hyperon contains information about the relative phase between combinations of transition form factors. This relative phase is non-vanishing because of the unstable nature of the hyperon resonance. If all form factor combinations in the differential decay formulae are replaced by their respective values at the photon point, one obtains a QED type approximation, which might be interpreted as characterizing hypothetical hyperons with point-like structure. We compare the QED type approximation to a more realistic form factor scenario for the lowest-lying singly-strange hyperon resonances. In this way we explore which accuracy in the measurements of the differential Dalitz decay rates is required in order to distinguish the composite-structure case from the pointlike case. Based on the QED type approximation we obtain as a by-product a rough prediction for the ratio between the Dalitz decay width and the corresponding photon decay width.
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