The $\bar B \bar B$ strong interaction with chiral perturbation theory

Zhan-Wei Liu,Ning Li,Shi-Lin Zhu

doi:10.1142/s2010194514602257

Abstract

We study the strong interaction potentials of [Formula: see text] up to order [Formula: see text] with the heavy meson chiral perturbation theory. Besides the leading contributions from the contact terms we also consider the one-loop corrections to the contact diagrams and the contributions from the 2ϕ-exchange diagrams. Hopefully, the analytical structures of our result will be helpful in the extrapolation of the relevant heavy meson interaction in the lattice QCD simulation.

Highlights

The hadronic molecule might be the most popular one since many of the exotic states appear near the threshold of two heavy mesons
To judge whether two heavy mesons can form a hadronic molecule, one should first investigate whether there exists the attractive force between the two mesons
We expand the potentials in terms of a small parameter = p/Λχ, where p represents the small momentum of light pseudoscalar. This is an Open Access article published by World Scientific Publishing Company

Summary

Introduction

More and more charmonium-like or bottomonium-like particles have been observed experimentally, their structures are still not very clear.[1,2,3] Many interpretations have been proposed, such as hadronic molecules, hybrid, glueball, et al.[4,5,6,7] The hadronic molecule might be the most popular one since many of the exotic states appear near the threshold of two heavy mesons. We will study the interaction potentials of BBup to order O( 2) with the heavy meson chiral perturbation theory. We expand the potentials in terms of a small parameter = p/Λχ, where p represents the small momentum of light pseudoscalar. This is an Open Access article published by World Scientific Publishing Company. Weinberg first pointed out that the double pole in the 2-particle-reducible(2PR) Feynman diagrams breaks the power counting in the study of the few-hadron system with the chiral perturbation theory.[8, 9] It is easier to study the interaction potentials of the heavy hadronic systems, which do not have the contribution of the double pole and can be calculated perturbatively.

Lagrangians

Interaction Potentials

Results and Discussions