Non divergent formula in the four body region of the Dalitz plot for the precise β energy spectrum in the semileptonic decay of hyperons

We have obtained analytical formulas and their corresponding numerical results for the contributions to the electron energy spectrum, due to the bremsstrahlung of semileptonic decays of charged and neutral baryons, in the region of the Dalitz plot that covers the four body-events. We show that the logarithmical singularity at the upper edge of the plot, contained in previous results disappears after performing an analytical integration. The new formulas contain terms of the order α times the momentum transfer. They are applicable to any beta decay process, and are suitable for a model-independent experimental analysis.