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

You-Chang Yang,Hong-Shi Zong,Jialun Ping,Zhi-Yun Tan

doi:10.1140/epjc/s10052-017-5137-6

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 Schrödinger 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 X(3872) and Z^0_b(10610), respectively. The dependence of the results on the model parameters is also discussed.

Highlights

It is unlikely for most X Y Z states that they can be interpreted as a conventional ccor bbmeson because of their unusual properties
Swanson [14] proposed the interpretation of X (3872) as a D0 D 0∗ molecular state with J PC = 1++ which is bound by both pion and quark exchange
No D0 D 0∗ molecular state was obtained in Ref. [14] if only taking into account of one-pion exchange between D0 and D 0∗

Summary

Introduction

It is unlikely for most X Y Z states that they can be interpreted as a conventional ccor bbmeson because of their unusual properties. Wong [13] applied a quark-based model, which is similar to adding a shortrange quark–gluon force, to study the molecular states composed of two heavy mesons. [17], the authors obtained a D0 D 0∗ bound state when they systematically studied possible D D , D D ∗ and D∗ D ∗ molecular states by considering vector, pseudoscalar and scalar meson exchanges. We would like to study the possible neutral molecular states D(∗) D (∗) and B(∗) B (∗) by two constituent quark models, which are extended by including the one-gluon annihilation interaction between uuor ddlight quark pairs.

The constituent quark model with s-channel one-gluon exchange

Wave function

Numerical results and discussion

Summary