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I have to determine whether the neutral rho meson could decay into a neutral pion and eta.
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I have checked the quantum numbers and all of them seem to be conserved adding an orbital angular momentum to the pion-eta system.
Nevertheless, this reaction seems not to be allowed and I was wondering if this could be because the rho meson doesn't have enough energy to provide angular momentum to the system. Looks like this decay via the strong interaction is not allowed due to violation of G-parity, as @Cosmas Zachos hinted in a comment, but it is probably allowed via the electromagnetic interaction, but such decay may be difficult to observe as rho decays very fast via the strong interaction.