Pseudo-neutrino versus recoil formalism for 4-body phase space and applications to nuclear decay
It is well known that the traditional treatment of radiative corrections that utilizes the “true” neutrino momentum$\overrightarrow{p}_v$ in the differential decay rate formula could lead to a ~α/π systematic error in certain observables due to the mistreatment of 4-body kinematics. Here, I investigate the theory structure of one of the proposed solutions, the “v'-formalism”, in the nonrecoil limit appropriate for neutron and nuclear β decays. I derive an elegant master formula for the 4-body phase space and use it to reanalyze the spectrum-dependent “outer” radiative corrections to the β decay of a polarized spin-half nucleus; a complete set of analytic expressions is provided for readers to straightforwardly obtain the final numerical results. Furthermore, I compare it to the “recoil formalism” where the energy of the recoil nucleus is fixed.