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We argue that the recent BESIII data on the cross section for the process in the center of mass energy range 4.21 - 4.42 GeV can be described by the contribution of the known charmonium-like resonance with the mass of about 4190,MeV. The value of the coupling in the transition needed for this mechanism is comparable to that in another known similar transition $\chi_{c0}(2P) \to J/\psi , \omega$. The suggested mechanism also naturally explains the reported relative small value of the cross section for the final states $\chi_{c1} , \omega\chi_{c2} , \omega$ above their respective thresholds.

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