Abstract
We investigate the role played by the three-body dynamics on the near-threshold resonance charmonium state, which is assumed to be formed by nonperturbative dynamics. It is demonstrated that, as compared to the naive static-pions approximation, the imaginary parts that originate from the inclusion of dynamical pions reduce substantially the width from the intermediate state. In particular, for a resonance peaked at 0.5 MeV below the threshold, this contribution to the width is reduced by about a factor of 2, and the effect of the pion dynamics on the width grows as long as the resonance is shifted towards the threshold. Although the physical width of the is dominated by inelastic channels, our finding should still be of importance for the line shapes in the channel below threshold. For example, in the scattering length approximation, the imaginary part of the scattering length includes effects of all the pion dynamics and does not only stem from the width. Meanwhile, we find that another important quantity for the phenomenology, the residue at the pole, is weakly sensitive to dynamical pions. In particular, we find that the binding energy dependence of this quantity from the full calculation is close to that found from a model with pointlike interactions only, consistent with earlier claims. Coupled-channel effects (inclusion of the charged channel) turn out to have a moderate impact on the results.
- Received 2 September 2011
DOI:https://doi.org/10.1103/PhysRevD.84.074029
© 2011 American Physical Society