Radiative Correction toβDecays

The ultraviolet divergent part of the radiative correction to the pion $\beta$ decay is evaluated generally, including the term induced by the radiative correction to the axial current. Although the divergence remains for the quark model, there exists a case when the divergences canal, and this corresponds to a model where the $\beta$ decay is due to the $\beta$ decay of a fermion of unit negative charge. The model is applied to the general hadronic $\beta$ decays, and it is shown that the correction to the vector current is always finite, although no definite conclusion can be drawn for the axial current.