Radiative corrections to the semileptonic Dalitz plot with angular correlation between polarized decaying hyperons and emitted charged leptons

We obtain a model-independent expression for the Dalitz plot of semileptonic decays of polarized hyperons including radiative corrections to order $\alpha$ and neglecting terms of order $\alpha q/\pi M_1,$ where q is the four-momentum transfer and $M_1$ is the mass of the decaying hyperon. We specialize our results to exhibit the correlation between the charged-lepton momentum and the spin of the decaying hyperon. We present results for the three-body region of the Dalitz plot and for the complete Dalitz plot (which includes the four-body region). From these results we also obtain the corresponding radiative corrections to the integrated lepton spin-asymmetry coefficient. Our formulas are valid for charged as well as for neutral decaying hyperons and are appropriate for model-independent experimental analyses whether the real photon is discriminated or not.