Decay properties of light $1^{-+}$ hybrids
We explore the decay properties of the isovector and isoscalar $1^{-+}$ light hybrids, $π_1$ and $η_1$, in $N_f=2$ lattice QCD at a pion mass $m_π\approx 417~\mathrm{MeV}$. The McNeile and Michael method is adopted to extract the effective couplings for individual decay modes, which are used to estimate the partial decay widths of $π_1(1600)$ and $η_1(1855)$ by assuming SU(3) symmetry. The partial decay widths of $π_1(1600)$ are predicted to be $(Γ_{b_1π}, Γ_{f_1(1285)π}, Γ_{ρπ}, Γ_{K^*\bar{K}}) = (325 \pm 75, \mathcal{O}(10), 52 \pm 7, 8.6 \pm 1.3)~\mathrm{MeV}$, and the total width is estimated to be $396 \pm 90~\mathrm{MeV}$, considering only statistical errors. If $η_1(1855)$ and the $4.4σ$ signal observed by BESIII (labeled as $η_1(2200)$) are taken as the two mass eigenstates of the isoscalar $1^{-+}$ light hybrids in SU(3), then the dominant decay channel(s) of $η_1(1855)$ ($η_1(2200)$) is $K_1(1270)\bar{K}$ ($K_1(1270)\bar{K}$ and $K_1(1400)\bar{K}$) through the $1^{+(-)}0^{-(+)}$ mode. The vector-vector decay modes are also significant for the two $η_1$ states. Using the mixing angle $α\approx 22.7^\circ$ obtained from lattice QCD for the two $η_1$ states, the total widths are estimated to be $Γ_{η_1(1855)}=282(85)~\mathrm{MeV}$ and $Γ_{η_1(2200)}=455(143)~\mathrm{MeV}$. The former is compatible with the experimental width of $η_1(1855)$. Although many systematic uncertainties are not well controlled, these results are qualitatively informative for the experimental search for light hybrids.