Abstract
We consider the production of the and states recoiled with a photon up to at BESIII and B-factories within the frame of NRQCD factorization. With the corrections, we revisit the numerical calculations to the cross sections for the and the states. We argue that the search for states with even charge conjugation such as , , , and recoiled with a photon at BESIII may help clarify the nature of these states. For completeness, the production of charmonium with even charge conjugation recoiled with a photon at B factories is also discussed.
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