Spin-parity of two photons

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I am trying to understand how charmonium states can be produced in electron-positron collisions, and which quantum numbers are possible for each process. I am having trouble understanding the quantum numbers that are possible for the two-photon process, e+e- → e+e- γγ → e+e- cc̅.

I have read in several places [1-3] that the C-parity for the final states from these reactions must be +1. This I get, since both photons have C-parity -1. However, JP seems to be restricted to 0±, 2±, 3+, 4±, 5+, ... This I don't get.

The spins of the two photons couple to 0 or 2, correct? I tried to come up with allowed quantum numbers by assuming different orbital angular momenta, starting from 0, and then trying to combine them (somewhat naively) with the 0/2 state. I tried to get the final state's parity using (-1)(-1)(-1)L. Obviously, this leads to completely different values, including, for example, JPC=1++.

What would be the right way to understand the allowed quantum numbers? Is it possible to calculate them in such a simplistic way?

[1] http://www-conf.kek.jp/qwg08/session3_3/uehara.pdf
[2] http://inspirehep.net/record/1257857/files/Beauty 2013_048.pdf
[3] http://arxiv.org/pdf/1311.0968v1
 
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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