Numerical precision radiative corrections to the Dalitz plot of baryon semileptonic decays including the spin-momentum correlation of the decaying and emitted baryons

We calculate the radiative corrections to the angular correlation between the polarization of the decaying and the direction of the emitted spin one-half baryons in the semileptonic decay mode. The final results are presented, first, with the triple integration of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. A third presentation of our results in the form of numerical arrays of coefficients to be multiplied by the quadratic products of form factors is discussed. This latter may be the most practical one to use in Monte Carlo simulations. A series of crosschecks is performed. Previous results to order (alpha/pi)(q/M_1) for the decays of unpolarized baryons are reviewed, too, where q is the momentum transfer and M_1 is the mass of the decaying baryon. This paper is self-contained and organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments involving heavy quarks and is not compromised to fixing the form factors at predetermined values. It is assumed that the real photons are kinematically discriminated. Otherwise, our results have a general model-independent applicability.