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We analyze the    $$D{\bar{D}}$$  D D ¯ mass distribution from a recent Belle experiment on the    $$e^+e^- \rightarrow J/\psi D{\bar{D}}$$  e + e - → J / ψ D D ¯ reaction, and show that the mass distribution divided by phase space does not have a clear peak above the    $$D{\bar{D}}$$  D D ¯ threshold that justifies the experimental claim of a    $$\chi _{c0}(2P)$$  χ c 0 ( 2 P ) state from those data. Then we use a unitary formalism with coupled channels    $$D^+D^-$$  D + D - ,    $$D^0{\bar{D}}^0$$  D 0 D ¯ 0 ,    $$D_s{\bar{D}}_s$$  D s D ¯ s , and    $$\eta \eta $$  η η , with some of the interactions taken from a theoretical model, and use the data to fix other parameters. We then show that, given the poor quality of the data, we can get different fits leading to very different    $$D{\bar{D}}$$  D D ¯ amplitudes, some of them supporting a    $$D{\bar{D}}$$  D D ¯ bound state and others not. The main conclusion is that the claim for the    $$\chi _{c0}(2P)$$  χ c 0 ( 2 P ) state, already included in the PDG, is premature, but refined data can provide very valuable information on the    $$D{\bar{D}}$$  D D ¯ scattering amplitude. As side effects, we warn about the use of a Breit-Wigner amplitude parameterization close to threshold, and show that the    $$D_s{\bar{D}}_s$$  D s D ¯ s channel plays an important role in this reaction.

Analysis of the $$ \varvec{e^+ e^- \rightarrow J/\psi D{\bar{D}}}$$ reaction close to the threshold concerning claims of a $$\chi _{c0}(2P)$$ state