Standard calculations by Fermi's golden rule involve approximations. These approximations could lead to deviations from the predictions of the standard model, as discussed in another paper. In this paper we propose experimental searches for such deviations in the two-photon spectra from the decay of the neutral pion in the process ? ? ? + ? ? ?0 and in the annihilation of the positron from nuclear ? decay. © The Author(s) 2019. Published by Oxford University Press on behalf of the Physical Society of Japan.