Quark mass dependence of the X(3872) binding energy

TL;DR

This study investigates how the binding energy of the X(3872) state varies with quark mass using a three-body approach, highlighting the importance of short-range interaction dependence and providing insights for future lattice QCD studies.

Contribution

It introduces a nonrelativistic three-body framework to analyze the quark-mass dependence of the X(3872) and emphasizes the role of short-range interactions in its binding energy.

Findings

X(3872) trajectory depends strongly on quark-mass assumptions.

Provides a method to connect lattice QCD results with molecular models.

Offers insights into chiral extrapolation in the X channel.

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 $D^*$ 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.