General considerations on the nature of $Z_b(10610)$ and $Z_b(10650)$ from their pole positions

Abstract

The nature of the bottomonium-like states $Z_b(10610)$ and $Z_b(10650)$ is studied by calculating the $B^{(\ast )}{\overline{B}}^{\ast }$ compositeness ($X$) in those resonances. We first consider uncoupled isovector $S$-wave scattering of $B^{(\ast )}{\overline{B}}^{\ast }$ within the framework of effective-range expansion (ERE). Expressions for the scattering length ($a$) and effective range ($r$) are derived exclusively in terms of the masses and widths of the two $Z_b$ states. We then develop compositeness within ERE for the resonance case and deduce the expression $X=1/\sqrt{2r/a-1}$, which is then applied to the systems of interest. Finally, the actual compositeness parameters are calculated in terms of resonance pole positions and their experimental branching ratios into $B^{(\ast )}{\overline{B}}^{\ast }$ by using the method of Ref.[1]. We find the values $X=0.66\pm 0.11$ and $0.51\pm 0.10$ for the $Z_b(10610)$ and $Z_b(10650)$, respectively. We also compare the ERE with Breit-Wigner and Flatté parameterizations to discuss the applicability of the last two ones for near-threshold resonances with explicit examples.

15 pages, 1 figure

References in corpus (19)

• Big-Bang Nucleosynthesis
• Constituent quark model study of the meson spectra
• Hadro-Charmonium
• Pion Interactions in the X(3872)
• On the Strangeness -1 S-wave Meson-Baryon Scattering
• $Z_b$ and $Z_c$ Exotic States as Coupled Channel Cusps
• Could the near-threshold $XYZ$ states be simply kinematic effects?
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• Confirming the molecular nature of the $Z_b(10610)$ and the $Z_b(10650)$
• A New Hadron Spectroscopy
• The electromagnetic form factors of the proton in the timelike region
• Amplitude analysis of e+e- => Y(nS)pi+pi- at sqrt(s)=10.865 GeV
• Decays of Zb(+) and Zb'(+) as hadronic molecules
• Hidden-Beauty Charged Tetraquarks and Heavy Quark Spin Conservation
• 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
• On the near-threshold $\bar{p}p$ invariant mass spectrum measured in $J/\psi$ and ${\psi }^{\prime }$ decays
• Is $Z_b(10610)$ a Molecular State?
• Resolving the puzzling decay patterns of charged $Z_c$ and $Z_b$ states
• Bound states on the lattice with partially twisted boundary conditions

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