Towards the establishment of the light $J^{P(C)}=1^{-(+)}$ hybrid nonet

The observation of the light hybrid candidate $\eta_1(1855)$ by the BESIII Collaboration brings great opportunities for advancing our knowledges about exotic hadrons in the light flavor sector. We show that this observation provides a crucial clue for establishing the $J^{P(C)}=1^{-(+)}$ hybrid nonet. Based on the flux tube model picture, the production and decay mechanisms for the $J^{P(C)}=1^{-(+)}$ hybrid nonet in the $J/\psi$ radiative decays into two pseudoscalar mesons are investigated. In the $I=0$ sector, we find that the SU(3) flavor octet and singlet mixing is non-negligible and apparently deviates from the flavor ideal mixing. Since only signals for one isoscalar $\eta_1(1855)$ are observed in the $\eta\eta'$ channel, we investigate two schemes of the nonet structure in which $\eta_1(1855)$ can be either the higher or lower mass state that strongly couples to $\eta\eta'$. Possible channels for detecting the multiplets are suggested. In particular, a combined analysis of the hybrid production in $J/\psi\to VH$, where $V$ and $H$ stand for the light vector mesons and $1^{-(+)}$ hybrid states, may provide further evidence for this nonet structure and finally establish these mysterious exotic species in experiment.