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

Abstract

AbstractWe 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.