Double heavy tri-hadron bound state with strange flavor

Li Ma,A Bondar,S Eidelman

doi:10.1051/epjconf/201920206007

Abstract

Through the Born-Oppenheimer Approximation, we have performed a comprehensive investigation of the DD∗K, D$ \overline D $*K, BB∗$ \overline K $ and B$ \overline B $*$ \overline K $ molecular states. In the framework of One-Pion Exchange model as well as the treatments of the coupled-channel eﬀects and S-D wave mixing, we find a loosely bound tri-meson molecular state these systems with the isospin configuration |0,$ {1 \over 2} $, ±$ {1 \over 2} $> and quantum number I(JP) = 1/2(1−), where the, $ {1 \over 2} $ is the total isospin of the three-body system, the 0 is the isospin of the D∗K, $ \overline D $*K, B∗$ \overline K $ and $ \overline B $∗$ \overline K $. With the estimated error, the mass of the DD∗K or D$ \overline D $∗K molecule is $ 4317.92_{ - 4.32}^{ + 3.66} $ MeV or $ 4317.92_{ - 6.55}^{ + 6.13} $MeV. We also extend our calculations to the bottom sector and find tri-meson bound states for the BB∗$ \overline K $ and B$ \overline B $*$ \overline K $ with the mass $ 11013.65_{ - 8.84}^{ + 8.49} $ MeV and $ 11013.65_{ - 9.02}^{ + 8.68} $MeV respectively.

Highlights

The investigations on the three body systems have been an important issue in recent years
The explorations on the few-body systems were first proposed to focus on the few nucleon systems or nucleons and hyperons [1,2,3,4]
After solving the Schrödinger equation for the three-body system, we find out the loosely bound system states for the DD∗ DD∗K and DD ∗K, K if and with the isospin configuration

Summary

Introduction

The investigations on the three body systems have been an important issue in recent years. Systematical calculations on the resonances containing three mesons were studied [5,6,7]. The theoretical calculations on the BDDand BDD systems were performed, and the hints of a bound state in the energy region 8935-8985 MeV with the quantum numbers I(JP) = 1/2(0−) for the BDDsystem was claimed [18]. The one pion exchange model (OPE) has been widely used to study the di-meson or dibaryon molecular systems. The Born-Oppenheimer Approximation has been employed to study the fewbody systems containing several heavy particles and several light particles [22]. To a very good extent, it is a pion shared by the two constitutes providing an attraction which makes them bound It can be regarded as a σ bond similar to the σ bond in hydrogen molecules. Whether there exist hadronic π bond in the tri-meson systems like DD∗K, DD ∗K, BB∗Kand BB∗K

One-pion-exchange model and the two-body sector

Three-body sector and Born-Oppenheimer Approximation

Summary and Discussion