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We investigate the role played by the three-body $D\bar{D}\pi$ dynamics onthe near-threshold resonance X(3872) charmonium state, which is assumed to beformed by nonperturbative $D\bar D^*$ dynamics. It is demonstrated that, ascompared to the naive static-pions approximation, the imaginary parts thatoriginate from the inclusion of dynamical pions reduce substantially the widthfrom the $D\bar{D}\pi$ intermediate state. In particular, for a resonancepeaked at 0.5 MeV below the $D^0\bar D^{*0}$ threshold, this contribution tothe width is reduced by about a factor of 2, and the effect of the piondynamics on the width grows as long as the resonance is shifted towards the$D^0\bar{D^0}\pi^0$ threshold. Although the physical width of the $X$ isdominated by inelastic channels, our finding should still be of importance forthe $X$ line shapes in the $D\bar{D}\pi$ channel below $D{\bar D}^*$ threshold.For example, in the scattering length approximation, the imaginary part of thescattering length includes effects of all the pion dynamics and does not onlystem from the $D^*$ width. Meanwhile, we find that another important quantityfor the $X$ phenomenology, the residue at the $X$ pole, is weakly sensitive todynamical pions. In particular, we find that the binding energy dependence ofthis quantity from the full calculation is close to that found from a modelwith pointlike $D\bar D^*$ interactions only, consistent with earlier claims.Coupled-channel effects (inclusion of the charged $D\bar{D}^*$ channel) turnout to have a moderate impact on the results.

Three-body $D\bar{D}\pi$ dynamics for the X(3872)