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

Abstract

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

arXiv comment9 figures, 11 pages, the version to be published in EPJA

References in corpus (20)

• Hadronic molecules
• Higher Charmonia
• Dynamically Generated Open and Hidden Charm Meson Systems
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• Bethe-Salpeter Approach for Unitarized Chiral Perturbation Theory
• Meson production in nucleon--nucleon collisions close to the threshold
• Coupled-channel model for charmonium levels and an option for X(3872)
• Light Flavour and Heavy Quark Spin Symmetry in Heavy Meson Molecules
• Near threshold enhancement of the ppbar mass spectrum in J/Psi decay
• Coupled-Channel and Screening Effects in Charmonium Spectrum
• Decay channels and charmonium mass-shifts
• X(3915) and X(4350) as new members in P-wave charmonium family
• Where is the χ_{c0}(2P)?
• Observation of a near-threshold enhancement in the ωϕmass spectrum from the doubly OZI suppressed decay J/ψ\to γωϕ
• On the treatment of $NN$ interaction effects in meson production in $NN$ collisions
• Could the $X(3915)$ and the $X(3930)$ Be the Same Tensor State?
• The radiative decay of $\psi (3770)$ into the predicted scalar state X(3700)
• Are the $X$(4160) and $X$(3915) charmonium states?
• Hidden-charm decays of $X(3915)$ and $Z(3930)$ as the P-wave charmonia
• Amplitude Analysis for Mesons and Baryons: Tools and Technology