Radiative corrections to the muon polarization in the semileptonic decay of a neutral kaon

A model-independent expression for the Dalitz plot of the semileptonic decays of a neutral kaon $K_{\mu 3}^0$ \( {K}_{\mu 3}^0 \) , including radiative corrections to order $\mathcal{O}$ \( \mathcal{O} \) [(α/π)(q/M₁)], where q is the four-momentum transfer and M₁ is the mass of the decaying kaon, is presented. In this paper the emitted muon is considered to be polarized so the analysis is centered on numerically evaluating the radiative corrections to the longitudinal, transverse, and normal polarization muon components. The model dependence of radiative corrections is kept in general form within this approximation, which is useful for model-independent experimental analyses. The final expressions, with the triple integration of the bremsstrahlung photon variables are ready to be evaluated numerically, they are free of the infrared divergence or ultraviolet cutoff. The radiative corrections to the components of the muon polarization are found to be very small compared to their respective uncorrected values.