Electromagnetic Correction Effects on theπ+→π0e+νDecay

Recently experiments have been done on the rare decay of the ${\pi }^{+}$ into the ${\pi }^0{e}^{+}\nu$ mode as a third and independent test of the conserved vector current hypothesis. This note reports briefly on a simple perturbation calculation of the radiative corrections. With a cutoff of around a nuclear mass, the radiative correction shortens the lifetime by ∼-1.1%.