Abstract
We analyze the D{bar{D}} mass distribution from a recent Belle experiment on the e^+e^- rightarrow 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.
Highlights
In Ref. [18] it is shown that the use of the unquenched quark model, where, in addition to the quark components, the meson-meson components are taken into account via loops with these intermediate states [19,20,21,22,23], provides an answer to the problems posed to the χc0(2P) hypothesis in Refs. [11,12], in particular the puzzle of the charmonium masses and the decay widths discussed above
In order to investigate the potential information of the present data, we use a dynamical model with coupled channels and unitarity, including the D+ D−, D0 D 0, Ds Ds channels, plus the ηη channel as a means to account for the contribution of light channels to this process
The amplitudes that our model produces have a limited range of validity and should not be used much above the Ds Ds threshold
Summary
X (3915), and possible inconsistencies in the mass compared to other charmonium states. Some quark models get a reduced width to D Dof the radially excited χc0(2P) state because of the node in the wave function [15], and the enhancement of the OZI suppressed width into J/ψω can find an explanation in a generalized screened potential model [16]. The χc0(2P) hypothesis for the X (3915) has been reinforced by new studies in Refs. [17] assuming that the X (3915) and X (3930) are the χc0(2P) In Ref. [17] assuming that the X (3915) and X (3930) are the χc0(2P)
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