Composite nature of $Z_b$ states from data analysis

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 $B^{(\ast )}{\bar{B}}^{\ast }$ 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 $B^{(\ast )}{\bar{B}}^{\ast }$ 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 $B{\bar{B}}^{\ast }$ ($B^{\ast }{\bar{B}}^{\ast }$) component in the resonance $Z_b(10610)$ ($Z_b(10650)$).

15 pages, 2 figures, 2 tables, more discussions clarified, accepted for publication in EPJC

References in corpus (10)

• Multiquark Resonances
• Hadro-Charmonium
• On the Strangeness -1 S-wave Meson-Baryon Scattering
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• The electromagnetic form factors of the proton in the timelike region
• Interplay of quark and meson degrees of freedom in a near-threshold resonance
• Study of $B{\bar{B}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ interactions in $I=1$ and relationship to the $Z_b(10610)$, $Z_b(10650)$ states
• A comprehensive study on the semileptonic decay of heavy flavor mesons
• $Z_b(10610)$ and $Z_b^{\prime }(10650)$ decays in a covariant quark model
• Bound states on the lattice with partially twisted boundary conditions

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• Effective $\Lambda$CDM model emerging from $f(Q,T)$ under a special EOS limit in symmetric cosmology with Bayesian and ANN observational constraints