${\alpha }_s{v}^2$ corrections to ${\eta }_c$ and ${\chi }_{cJ}$ production recoiled with a photon at $e^{+}{e}^{-}$ colliders

Abstract

We consider the production of the ${\eta }_c$ and ${\chi }_{cJ}$ states recoiled with a photon up to $\mathcal{O}({\alpha }_s{v}^2)$ 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 ${\eta }_c(nS)$ and the ${\chi }_{cJ}(mP)$ states. We argue that the search for $XYZ$ states with even charge conjugation such as $X(3872)$, $X(3940)$, $X(4160)$, and $X(4350)$ 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.

Comments and suggestions are welcome

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• Relativistic corrections to exclusive ${\chi }_{cJ}+\gamma$ production from $e^{+}{e}^{-}$ annihilation
• Observation of $e^{+}{e}^{-}\to \gamma {\chi }_{c1}$ and search for $e^{+}{e}^{-}\to \gamma {\chi }_{c0},\gamma {\chi }_{c2},$ and $\gamma {\eta }_c$ at $\sqrt{s}$ near 10.6 GeV at Belle
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