Constructing the $J^{P(C)}=1^{-(+)}$ light flavor hybrid nonet with the newly observed $\eta_1(1855)$

Abstract

The recently discovered $\eta_1(1855)$ and the previously observed $\pi_1(1600)$ state present a valuable opportunity for the investigation of the $J^{P(C)}=1^{-(+)}$ light hybrid nonet. In this study, we employ a semirelativistic quark potential model to examine the masses of the $J^{P(C)}=1^{-(+)}$ light hybrid states. The static potential, which portrays the confinement force between the quark-antiquark pair in a hybrid system, is borrowed from the SU$(3)$ lattice gauge theory. Additionally, we utilize a constituent gluon model to analyze the strong decay characteristics of these light $1^{-+}$ hybrids. Our findings suggest that the $\pi_1(1600)$ and $\eta_1(1855)$ states could be potential candidates for $1^{-+}$ $(u\bar{u}-d\bar{d})g/\sqrt{2}$ and $s\bar{s}g$ hybrids, respectively. To ensure comprehensiveness, we also investigate the isospin partners of the $\pi_1(1600)$ and $\eta_1(1855)$ states within the $1^{-(+)}$ nonet$-$specifically, the $(u\bar{u}+d\bar{d})g/\sqrt{2}$ and $s\bar{q}g$ ($q=u$ and $d$ quarks) states. We propose some potential decay channels which could be explored in experimental settings to detect these undiscovered states.