The $Z_b(10610{)}^{\pm }$ and $Z_b(10650{)}^{\pm }$ are two bottomoniumlike structures discovered in the $\pi h_b(mP)$, $\pi \mathrm{\Upsilon }(nS)$ and $B^{*}{\overline{B}}^{(*)}+\mathrm{H}.\mathrm{c}.$ invariant mass spectra, where $m=\{1,2\}$ and $n=\{1,2,3\}$. Their nature is puzzling due to their charge, which forces its minimal quark content to be $b\overline{b}u\overline{d}$ ($b\overline{b}d\overline{u}$). Thus, it is necessary to explore four-quark systems in order to understand their inner structure. Additionally, their strong coupling to channels such as $\pi \mathrm{\Upsilon }$ and the closeness of their mass to $B^{*}{\overline{B}}^{(*)}$ thresholds stimulates a molecular interpretation. Within the framework of a constituent quark model which satisfactorily describes a wide range of properties of (non)conventional hadrons containing heavy quarks, we perform a coupled-channels calculation of the $I^G(J^{PC})=1^{+}(1^{+-})$ hidden-bottom sector including $B^{(*)}{\overline{B}}^{*}+\mathrm{H}.\mathrm{c}.$, $\pi h_b$, $\pi \mathrm{\Upsilon }$, and $\rho {\eta }_b$ channels. We analyze the line shapes in the different channels, describing the $\mathrm{\Upsilon }(5S)\to \pi B^{(*)}{\overline{B}}^{(*)}$ by means of the ${}^3{P}_0$ model. Since our description of the line shapes is promising, we perform the same coupled-channels calculation for the $Z_b$’s with $J^{--}$, where $J=\{0,1,2\}$. This allows us to obtain a fair description of the corresponding line shapes. The study of the analytic structure of the $S$-matrix suggests that the experimental $Z_b$ structures arise as a combination of several poles with $J^{PC}=0^{--}$, $1^{\pm -}$ and $2^{--}$ quantum numbers nearby the $B{\overline{B}}^{*}$ and $B^{*}{\overline{B}}^{*}$ thresholds.

• Received 14 July 2021
• Accepted 27 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.094004

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Published by the American Physical Society