Radiative corrections to the semileptonic Dalitz plot with an angular correlation between polarized decaying and emitted hyperons: Effects of the four-body region

We obtain a model-independent expression for the complete Dalitz plot of semileptonic decays of polarized hyperons, which includes both the three-body and the four-body regions. We calculate radiative corrections to order α, neglecting terms of order αq/πM₁, where q is the four-momentum transfer and M₁ is the mass of the decaying hyperon. Our results exhibit explicitly the correlation between the emitted hyperon three-momentum and the spin of the decaying hyperon. This allows us to obtain the corresponding radiative corrections to the integrated emitted hyperon spin-asymmetry coefficient. Our formulas are valid for charged as well as for neutral decaying hyperons and are appropriate for model-independent experimental analysis whether or not the real photon is discriminated.