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I'm having a difficult time with this particular problem. I'm really hoping for some guidance.

A proton and an antiproton annihilate at rest (or in a $p\bar{p}$ atom in an $S$ state) into pions.

(a) Show that a $\pi^0\pi^0$ state cannot be produced by strong interactions.

I know that a way to do this is to show that the interaction is not symmetric under parity, but am not sure how to go about doing that.

(b) Show that the decay into a $\pi^+\pi^-$ final state is possible from a $^3S_1$ state, but not from a $^1S_0$ state. (Here we use the spectroscopic notation $^{2S+1}L_J$.) Consider $C$, $P$, and $CP$, where $C$ is the charge conjugation operator, and $P$ is the parity operator.

I don't even know what "spectroscopic notation" is.

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