Quark mass dependence of the X(3872) binding energy

Abstract

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 $D^{\ast }$ 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 $D{\bar{D}}^{\ast }$ 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.

Comments: LaTeX2e, 14 pages, 5 figures, references updated and extended, to appear in Phys.Lett.B