# Possible $D^{(*)}\bar{D}^{(*)}$ and $B^{(*)}\bar{B}^{(*)}$ molecular states in the extended constituent quark models

## TL;DR

This paper investigates potential molecular states formed by heavy meson pairs within extended constituent quark models, predicting specific bound states that could correspond to known exotic particles like X(3872) and Z_b(10610).

## Contribution

It introduces an extended quark model including s-channel gluon exchange and solves the four-body Schrödinger equation to identify possible molecular states.

## Key findings

- Bound states of D*D̄ and B*B̄ with specific quantum numbers are predicted.
- D*D̄ with J^{PC}=1^{++} may correspond to X(3872).
- B*B̄ with J^{PC}=1^{+-} may correspond to Z_b(10610).

## Abstract

The possible neutral $D^{(*)}\bar{D}^{(*)}$ and $B^{(*)}\bar{B}^{(*)}$ molecular states are studied in the framework of the constituent quark models, which is extended by including the $s$-channel one gluon exchange. Using different types of quark-quark potentials, we solve the four-body Schr\"{o}dinger equation by means of the Gaussian expansion method. The bound states of $D^{(*)}\bar{D}^{(*)}$ with $J^{PC}=1^{++},2^{++}$ and $B^{(*)}\bar{B}^{(*)}$ with $J^{PC}=0^{++},1^{+-},1^{++},2^{++}$ are obtained. The molecular states $D^{*}\bar{D}$ with $J^{PC}=1^{++}$ and $B^{*}\bar{B}$ with $J^{PC}=1^{+-}$ are good candidates for the $X(3872)$ and $Z^0_b(10610)$, respectively.