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

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.

Dispersive analysis of the $γγ\to D \bar{D}$ data and the confirmation of the $D \bar{D}$ bound state

“…only a few available experimental points in the near-threshold region, the data from [11] alone is not constraining enough to provide a unique and meaningful solution without introducing additional assumptions. The same observation has been made in [13]. Therefore, we only check the consistency with the γγ → D D results by taking the best set of conformal expansion parameters given by Fit II and adjusting only the normalisation constant N in Eq.…”

“…Second, the proper resonance analysis should account for the S-matrix constraints, unlike simple Breit-Wigner parametrizations. In [13] a unitary approach based on the Bethe-Salpeter equation was used to describe the Belle data. No peak structure that justifies the claim for the X(3860) state was found.…”

Role of the newly measured $B\to KD\bar{D}$ process to establish $χ_{c0}(2P)$ state

“…Except for the results from the Lanzhou group, in the Ref. [13], the authors studied the D D mass distribution in e + e − → J/ψD D reaction [9]. With the unitary formalism, they found that it was premature to claim the X(3860) as a χ c0 (2P) state.…”

Revisit the $Z_c(4025)$ structure observed by BESIII in the $e^+e^- \to (D^*\bar{D}^*)^{\pm,0}π^{\mp,0}$ reactions at $\sqrt{s}=4.26$ GeV

“…It is interesting to notice that many charmonium-like states have been observed around the thresholds of a pair of heavy hadrons, such as X(3872) and Z c (3900) around D D * threshold, Z cs (3985)/Z cs (4000) around the D s D * /D * s D threshold, and X(3930) around D s Ds threshold. Recently, we have shown that the existence of the D D bound state is supported by the measurements of the e + e − → J/ψD D and γγ → D D [36,37], and suggested to search for it in the Λ b → ΛD D reaction [38]. As discussed in Ref.…”