Quark mass dependence of the X(3872) binding energy

V. Baru, E. Epelbaum, A. A. Filin, C. Hanhart, U. -G. Meißner, A. V. Nefediev

Published 2013-06-18, updated 2013-09-03Version 2

We explore the quark-mass dependence of the pole position of the X(3872) state within the molecular picture. The calculations are performed within the framework of a nonrelativistic Faddeev-type three-body equation for the $D\bar{D}\pi$ system in the $J^{PC}=1^{++}$ channel. The $\pi D$ interaction is parametrised via a $D^*$ pole, and a three-body force is included to render the equations well defined. Its strength is adjusted such that the X(3872) appears as a $D\bar{D}^*$ bound state 0.5 MeV below the neutral threshold. 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 future lattice QCD calculations. At the same time we are able to provide nontrivial information on the chiral extrapolation in the $X$ channel.