Study of $B\bar{B}^*$ and $B^*\bar{B}^*$ interactions in $I=1$ and relationship to the $Z_b(10610)$, $Z_b(10650)$ states

TL;DR

This study investigates the interactions of B meson pairs using a gauge approach, revealing a bound state near the Zb(10610) and a cusp at 10650 MeV, shedding light on exotic hadron states.

Contribution

It introduces a comprehensive analysis of B meson interactions considering multiple meson exchange mechanisms and predicts states related to the Zb resonances.

Findings

Identifies a loosely bound B B* state near 10600 MeV.

Finds a cusp at 10650 MeV across all spin states.

Supports the molecular interpretation of Zb states.

Abstract

We use the local hidden gauge approach in order to study the $B\bar{B}^*$ and $B^*\bar{B}^*$ interactions for isospin I=1. We show that both interactions via one light meson exchange are not allowed by OZI rule and, for that reason, we calculate the contributions due to the exchange of two pions, interacting and noninteracting among themselves, and also due to the heavy vector mesons. Then, to compare all these contributions, we use the potential related to the heavy vector exchange as an effective potential corrected by a factor which takes into account the contribution of the others light mesons exchange. In order to look for poles, this effective potential is used as the kernel of the Bethe-Salpeter equation. As a result, for the $B\bar{B}^*$ interaction we find a loosely bound state with mass in the range $10587-10601$ MeV, very close to the experimental value of the $Z_b(10610)$ reported by Belle Collaboration. For the $B^*\bar{B}^*$ case, we find a cusp at $10650$ MeV for all spin $J=0,\,1,\,2$ cases.