Radiative Corrections to the Muon Polarization inKμ30Decays

Radiative corrections to the muon polarization vector in $K_{\mu 3}^0$ decays have been calculated, based on a phenomenological weak $K-\pi$ vertex and perturbation theory. All terms which contribute to order $\alpha$ have been retained, with no approximations concerning the smallness of the muon mass or the "real" inner bremsstrahlung. The results depend logarithmically on a cutoff, but are not particularly sensitive to variations between one and two proton masses. The radiative corrections to the three components of the polarization vector (longitudinal, transverse, and perpendicular) have been evaluated numerically at 10-MeV intervals throughout the Dalitz plot, for various complex values of $\xi$. In addition, the integrated radiative correction to the degree of polarization as a function of muon energy has also been computed. It is found that these corrections are generally small, less than 1% degree of polarization in magnitude.