We discuss the role of the non-perturbative pion dynamics on the near-threshold resonance X(3872) charmonium state, which is assumed to be an S-wave $D\bar D^$ bound system [1,2]. The calculations are performed within the framework of coupled-channels Faddeev-type three-body equations for the $D\bar{D}\pi$ system in the $J^{PC}=1^{++}$ channel. The $\pi D$ interaction is parameterised via a $D^$ pole, and a three-body contact interaction is included to render the equations well defined. The strength of the contact term is adjusted such that the $X(3872)$ appears as a $D\bar{D}^*$ bound state 0.5 MeV below the neutral threshold. We discuss the contribution to the width of the $X(3872)$ from the $D\bar{D}\pi$ intermediate state treated non-perturbatively and compare it with different approximate treatments. Moreover, we explore the quark-mass dependence of the pole position of the $X(3872)$ state. We find that the trajectory of the $X(3872)$ depends strongly on the assumed quark-mass dependence of the short-range interactions which can be determined in lattice QCD calculations, see e.g. [3] for the first results.

[1] V. Baru, E. Epelbaum, A. A. Filin, C. Hanhart, U.-G.Meissner and A. V. Nefediev, Phys. Rev. D 84, 074029 (2011) [2] V. Baru, E. Epelbaum, A. A. Filin, C. Hanhart, U.-G. Meissner and A. V. Nefediev, Phys. Lett. B 726, 537 (2013) [3] S. Prelovsek and L. Leskovec, Phys. Rev. Lett. 111, 192001 (2013).