Is $Z_b(10610)$ a Molecular State?

TL;DR

This paper investigates whether the $Z_b(10610)$ resonance is a molecular state or a tetraquark, using a Bethe-Salpeter approach to analyze heavy meson interactions mediated by light meson exchange.

Contribution

It provides a theoretical analysis indicating that $Z_b(10610)$ is unlikely to be a molecular state, suggesting it is more consistent with a tetraquark structure.

Findings

Heavy mesons can form isospin singlet bound states via light meson exchange.

The $Z_b(10610)$ is unlikely to be a molecular state based on the model.

The $Z_b(10610)$ is more likely a tetraquark than a molecular state.

Abstract

Whether molecular states indeed exist in nature has been disputed for a long time. Several new resonances have been observed in the recent experiments and they seem to be of exotic structures and some of them have been proposed to be molecular states. The very recent observation of $Z_b(10610)[(10608.4\pm 2.0)$ MeV] and $Z_b(10650)[(10653.2\pm 1.5)$ MeV] encourages the interpretation of multi-quark states. In the Beter-Salpeter (BS) approach, we study the possibility if two heavy mesons can form a molecular state by exchanging light mesons. Our results indicate that two heavy mesons can form an isospin singlet (I=0) bound state but cannot form an isospin triplet (I=1) when the contribution of $\sigma-$ exchange is reasonably small, i.e. as the coupling of $\sigma$ with mesons $g_{\sigma}$ takes the value given in previous literatures. Thus we conclude that the newly observed $Z_b(10610)$ should not be a molecular state, but a tetraquark state instead, at most, the fraction of the molecular state in the physical resonance $Z_b(10610)$ is tiny.