Search for $C=+$ charmonium states in $e^+e^-\to γ+~X$ at BEPCII/BESIII

We extend our original study in Ref. [1] on the production of $C=+$ charmonium states $X=η_c(1S/2S)$ and $χ_{cJ}(1P/2P)$ in $e^+e^-\toγ~+~X$ at B factories to the BEPCII/BESIII energy region with $\sqrt{s}=4.0\mbox{-}5.0$ GeV. In the framework of nonrelativistic QCD factorization, the cross sections are estimated to be as large as $0.1\mbox{-}0.9$ pb. The results could be used to search for the missing $2P$ charmonium states or to estimate the continuum backgrounds in the resonance region.

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