X(3872) and the bound state problem of $D^0\bar{D}^{\ast0}$ ($\bar{D}^0{D}^{\ast0}$) in a chiral quark model

TL;DR

This study investigates whether the X(3872) can be described as a molecular bound state of D mesons using a chiral quark model, finding that certain meson exchanges influence binding but no definitive conclusion can be drawn.

Contribution

The paper applies a chiral quark model with the resonating group method to analyze the bound state problem of D meson pairs, exploring the effects of meson exchanges on molecular formation.

Findings

D^0ar{D}^{*0} system is unbound with S-wave nd  interactions.

Inclusion of nd xchanges aids molecule formation.

A bound Bar{B}^* state is possible in the bottom sector.

Abstract

The bound state problem of $D^0\bar{D}^{\ast0}$ ($\bar{D}^0{D}^{\ast0}$) is relevant to the molecular interpretation of the X(3872). We investigated this problem in a chiral quark model by solving the resonating group method equation. We found the system is unbound through S-wave $\pi$ and $\sigma$ interactions. The inclusion of $\rho$ and $\omega$ meson exchanges is helpful to the formation of a molecule. Because the binding energy relies on the coupling constants, we cannot draw a definite conclusion whether a molecular state exists in $D^0\bar{D}^{\ast0}$ ($\bar{D}^0{D}^{\ast0}$) system. When moving on to the bottom counterpart, we obtained an S-wave $B\bar{B}^\ast$ state.