Helicity suppression

A spin-zero parent decaying through a chiral weak charged current to a charged lepton and a massless neutrino cannot supply the helicities selected by a massless interaction. A charged-lepton mass insertion makes the amplitude proportional to $m_{\ell }$ and the decay width proportional to $m_{\ell }^2$. A spin-one W boson does not suffer this suppression.

A spin-zero parent at rest decaying to two particles requires their helicities to be equal. Choosing particle 1 along $+z$ and particle 2 along $-z$ gives total projection $J_z=h_1-h_2=0$. In negative-pion decay, the massless antineutrino has positive helicity, so the negative charged lepton must also have positive helicity. This is the suppressed component for a left-chiral weak charged current.

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.