Three-body D(D)over-barπ dynamics for the X(3872)

We investigate the role played by the three-body DD pi dynamics on the near-threshold resonance X(3872) charmonium state, which is assumed to be formed by nonperturbative DD* 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 DD pi intermediate state. In particular, for a resonance peaked at 0.5 MeV below the (DD)-D-0*(0) 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 (DD0)-D-0 pi(0) threshold. Although the physical width of the X is dominated by inelastic channels, our finding should still be of importance for the X line shapes in the DD pi channel below DD* 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 D* width. Meanwhile, we find that another important quantity for the X phenomenology, the residue at the X 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 DD* interactions only, consistent with earlier claims. Coupled-channel effects (inclusion of the charged DD* channel) turn out to have a moderate impact on the results.