Radiative correction to the νe(νe) spectrum in β decay

We derive an analytic expression for the O(α) radiative correction to the νe(νe) spectrum in allowed β decay. The m→0 limit is convergent and leads to a very simple result (m is the electron mass). This is in sharp contrast to the correction to the e-(e+) spectrum, that diverges as m→0, an important difference that we explain on theoretical grounds. After discussing some of their general properties, we use the corrections to the νe and e- spectra to derive the corresponding correction to the conversion from the e- spectrum to the νe spectrum, a relation that is of considerable interest for reactor studies of neutrino oscillations.