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(adsbygoogle = window.adsbygoogle || []).push({}); ^{+}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, J^{P}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, J^{PC}=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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# Spin-parity of two photons

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