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I've been reading on conservation laws in particle decays, specifically total angular momentum. I stumbled on two other questions about the decay of a pion to two photons and why it's allowed. In one, they describe why the orbital angular momentum must be 1 to conserve parity, however one describes that "the spins of the two photon can combine to give total spin $S=1$".

This is what confuses me, from what I understood the helicities of the photon can only be $1$ or $-1$ as they are massless, would this not mean that the two photon system can only have total spin $2$ or $0?$ Or am I misinterpreting something?

https://physics.stackexchange.com/a/450460/365109
https://physics.stackexchange.com/a/638818/365109

Blazeboy01
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This has stumped me before, but my Clebsch-Gordan table says for $s_1=s_2=1$:

$$|S=1, S_z=0\rangle = \sqrt{\frac 1 2}\Big( |+-\rangle - |-+\rangle \Big) $$

($+-$ refers to helicity, $S, s_i$ are total and individual spins, respectively).

Not sure why I was confused before...

Combing $S=1$ and $L=1$ ($|S_z, M\rangle$) in to $|J, J_z\rangle = |0, 0\rangle$ proceeds as:

$$|J=0, J_z=0\rangle= \sqrt{\frac 1 3} \Big( |1, -1\rangle - |0, 0\rangle + |-1, 1\rangle \Big) $$

JEB
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