 One-photon spin-zero transition prohibition

A spin-zero particle cannot decay into a spin-zero particle and one on-shell real photon. In the parent rest frame the two final helicities must be equal for total angular momentum zero, whereas the photon has helicity $\pm 1$ and the scalar has helicity zero. The prohibition is rotational and independent of charge-conjugation conservation. An off-shell photon producing additional particles is a different process.