\begin{document}$s\bar{s}g$\end{document} hybrids are investigated from lattice QCD in the quenched approximation. In the Coulomb gauge, spatially extended operators are constructed for \begin{document}$1^{--}$\end{document} and \begin{document}$(0,1,2)^{-+}$\end{document} states with the color octet \begin{document}$s\bar{s}$\end{document} component being separated from the chromomagnetic field strength by the spatial distance \begin{document}$r$\end{document}, whose matrix elements between the vacuum and the corresponding states are interpreted as Bethe-Salpeter (BS) wave functions. In each of the \begin{document}$(1,2)^{-+}$\end{document} channels, the masses and the BS wave functions are reliably derived. The \begin{document}$1^{-+}$\end{document} ground state mass is approximately 2.1-2.2 GeV, and that of \begin{document}$2^{-+}$\end{document} is approximately 2.3-2.4 GeV, whereas the mass of the first excited state is approximately 1.4 GeV higher. This mass splitting is much larger compared to that expected based on the phenomenological flux-tube model or constituent gluon model for hybrids, which is usually a few hundred MeV. The BS wave functions with respect to \begin{document}$r$\end{document}exhibit clear radial nodal structures of a non-relativistic two-body system, which imply that \begin{document}$r$\end{document} is a meaningful dynamical variable for these hybrids and motivate a color halo picture of hybrids, in which the color octet \begin{document}$s\bar{s}$\end{document} is surrounded by gluonic degrees of freedom. In the \begin{document}$1^{--}$\end{document} channel, the properties of the lowest two states are consistent with those of \begin{document}$\phi(1020)$\end{document} and \begin{document}$\phi(1680)$\end{document}. We did not obtain convincing information with respect to \begin{document}$\phi(2170)$\end{document}. However, we argue that regardless of whether \begin{document}$\phi(2170)$\end{document} is a conventional \begin{document}$s\bar{s}$\end{document} meson or a \begin{document}$s\bar{s}g$\end{document} hybrid in the color halo scenario, the ratio of partial decay widths \begin{document}$\Gamma(\phi \eta)$\end{document} and \begin{document}$\Gamma (\phi \eta')$\end{document} observed by BESIII can be understood based on the mechanism of hadronic transition of a strangeonium-like meson in addition to \begin{document}$\eta-\eta'$\end{document} mixing."> Strangeonium-like hybrids on the lattice -
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