Neutral-pseudoscalar vector-pion charge-conjugation selection

A neutral self-conjugate pseudoscalar with $C=+1$ cannot decay through charge-conjugation-conserving interactions into a neutral $C=-1$ vector and a neutral $C=+1$ pion. The two final particles are distinct and each maps to itself under charge conjugation, so their total C eigenvalue is the product, without an exchange factor $(-1{)}^L$. Their relative orbital angular momentum still enters their total parity. For $0^{-}\to 0^{-}{1}^{-}$, $L=1$ gives a CP-violating transition if a weak amplitude is retained.