Prediction of new states from $D^{(*)}B^{(*)}\bar{B}^{(*)}$ three-body interactions

TL;DR

This paper investigates three-body interactions involving $D^{(*)}$, $B^{(*)}$, and $ar{B}^{(*)}$ particles, predicting bound states and resonances using a fixed center approach to the Faddeev equations.

Contribution

It introduces a novel application of the fixed center approach to three-body systems with heavy mesons, predicting new bound states and resonances.

Findings

Identified bound states with binding energies of a few tens of MeV.

Predicted broad resonant states about ten MeV above thresholds.

Found clear bound state peaks in specific three-body systems.

Abstract

We study three-body systems composed of $D^{(*)}$, $B^{(*)}$ and $\bar{B}^{(*)}$ in order to look for possible bound states or resonances. In order to solve the three-body problem, we use the fixed center approach for the Faddeev equations considering that the $B^*\bar{B}^*(B\bar{B})$ are clusterized systems, generated dynamically, which interact with a third particle $D(D^*)$ whose mass is much smaller than the two-body bound states forming the cluster. In the $DB^*\bar{B}^*$, $D^*B^*\bar{B}^*$, $DB\bar{B}$ and $D^*B\bar{B}$ systems with $I=1/2$, we found clear bound state peaks with binding energies typically a few tens MeV and more uncertain broad resonant states about ten MeV above the threshold with widths of a few tens MeV.