The $Z_b$ structures in a constituent quark model coupled-channels calculation

Abstract

The $Z_b(10610{)}^{\pm }$ and $Z_b(10650{)}^{\pm }$ are two bottomonium-like structures discovered in the $\pi h_b(mP)$, $\pi {\rm Y}(nS)$ and $B^{\ast }{\bar{B}}^{(\ast )}+h.c.$ 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 $b\bar{b}u\bar{d}$ ($b\bar{b}d\bar{u}$). Thus, it is necessary to explore four-quark systems in order to understand their inner structure. Additionally, their strong coupling to channels such as $\pi {\rm Y}$ and the closeness of their mass to $B^{\ast }{\bar{B}}^{(\ast )}$-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 $B^{(\ast )}{\bar{B}}^{\ast }+h.c.$, $\pi h_b$, $\pi {\rm Y}$ and $\rho {\eta }_b$ channels. We analyze the line shapes in the different channels, describing the ${\rm Y}(5S)\to \pi B^{(\ast )}{\bar{B}}^{(\ast )}$ by means of the ${}^3{P}_0$ model. Since our description of the line shapes 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 $B{\bar{B}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ thresholds.

Comments: 10 pages, 5 figures. arXiv admin note: text overlap with arXiv:1808.00914