Finiteness of radiative corrections to πβ-decay

Abstract

We show that the radiative corrections to π-β-decay are finite if a sum rule involving weak and e.m. transitions for π's is satisfied. The sum rule is evaluated in the vector meson dominance hypothesis and found to predict Γ(ω→πγ) and Γ(−πO→γγ) in good agreement with the experimental data. Some comments are made on the possible general cancellation of the divergences in the radiative corrections to β-decay.