Composite nature of $Z_b$ states from data analysis

TL;DR

This paper analyzes the $Z_b$ states near threshold using a generalized parameterization including Castillejo-Dalitz-Dyson poles, fitting experimental data to support their molecular nature and extracting physical quantities like scattering lengths and compositeness.

Contribution

It introduces a more general near-threshold parameterization with CDD poles to analyze $Z_b$ states, providing detailed physical insights and supporting their molecular interpretation.

Findings

Data fits support the molecular interpretation of $Z_b$ states.

Physical quantities like scattering length and residue are extracted.

Compositeness ranges indicate significant molecular components.

Abstract

We use a near-threshold parameterization with explicit inclusion of the Castillejo-Dalitz-Dyson poles, which is more general than the effective range expansion, to study the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$. In terms of the partial-wave amplitude, we fit the event number distribution of $B^{(*)}\bar B^*$ system to the experimental data for these resonances from Belle Collaboration. The data could be described very well in our method, which supports the molecular interpretation. Then the relevant physical quantities are obtained, including the $B^{(*)}\bar{B}^*$ scattering length ($a$), effective range ($r$), and residue squared ($\gamma_s^2$) of the pole in the complex plane. In particular, we find the compositeness can range from about 0.4 up to 1 for the $B\bar B^*$ ($B^*\bar B^*$) component in the resonance $Z_b(10610)$ ($Z_b(10650)$).