# $G$-parity in an electromagnetic decay

I am looking at the decay $\eta\rightarrow\pi^+\pi^-\gamma$ and I would assume that the decay itself (ignoring the $\pi\pi$ final state interaction that is obviously strong) is electromagnetic since there is a photon involved. In a paper by Stollenwerk et al. on this decay they write that the partial wave of the pion pair is dominated by $1^{--}$. I assume this means that only odd partial waves contribute and that the F wave is already suppressed enough to be neglected. I can only explain this via $G$-parity conservation, which would yield a photon isospin of $1$ and consequently $I_{\pi\pi}=1$, but for an apparently electromagnetic process I cannot see why that should apply.

So my actual questions:

a) Is there any way a process involving a photon can be strong?

b) Are there types of electromagnetic processes for which $G$-parity is conserved?

I sure hope I could get into details but I will be straightforward.

a) Is there any way a process involving a photon can be strong?

I suppose you mean "strong" in a phenomenological description of the processes involved. In a loose way of speaking they could be similar if you restrict yourself to discussing conservation of certain quantities e.g. total Isospin, parity, etc, however it is the fact that these can be considered somehow "accidental" what makes them different in a general playground. The process you describe is an example of this.

b) Are there types of electromagnetic processes for which G-parity is conserved?

Of course, behind this there are two important facts. The first is:

Non-conservation of a property doesn't mean violation under all circumstances.

while the second is:

G-parity relates a rotation in Isospin space ($R_T$) and charge conjugation ($C$).

Electromagnetic interaction is already $C$-invariant so what you could ask, for G-parity to be conserved in the end, is if the process you're studying is invariant under the Isospin rotation involved. I happened to find your question while looking for something related to a problem in Fayyazuddin's "A modern introduction to particle physics". There you can check that: $$|\pi^{\pm}\rangle \xrightarrow{R_T} |\pi^{\mp}\rangle$$ $$|\pi^{0}\rangle \xrightarrow{R_T} |\pi^{0}\rangle$$

since $\eta$ (interaction eigenstate) is a singlet you should have similarly $|\eta\rangle \xrightarrow{R_T} |\eta\rangle$. The photon part may seem trivial but remember that in general a photon may be considered to be a superposition of a $I=0$ and a $I=1$ contribution (do not confuse with EW Isospin). If however you could justify $|\gamma\rangle \xrightarrow{R_T} |\gamma\rangle$ the exercise would be over (this is part of my homework) and G-parity conservation would be a reasonable tool to use.