Decay properties of light $1^{-+}$ hybrids from $N_f=2$ lattice QCD

We explore the decay properties of the isovector and isoscalar $1^{-+}$ light hybrids, $\pi_1$ and $\eta_1$, in $N_f=2$ lattice QCD at a pion mass $m_\pi \approx 417~\mathrm{MeV}$. 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 $\pi_1(1600)$ and $\eta_1(1855)$ by assuming SU(3) symmetry. The partial decay widths of $\pi_1(1600)$ are predicted to be $(\Gamma_{b_1\pi}, \Gamma_{f_1(1285)\pi}, \Gamma_{\rho\pi}, \Gamma_{K^*\bar{K}}) = (323 \pm 72, \mathcal{O}(10), 48 \pm 7, 7.9 \pm 1.3)~\mathrm{MeV}$, and the total width is estimated to be $390 \pm 88~\mathrm{MeV}$, considering only statistical errors. If $\eta_1(1855)$ and the $4.4\sigma$ signal observed by BESIII (labeled as $\eta_1(2200)$) are taken as the two mass eigenstates of the isoscalar $1^{-+}$ light hybrids in SU(3), then the dominant decay channel(s) of $\eta_1(1855)$ ($\eta_1(2200)$) 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 $\eta_1$ states. Using the mixing angle $\alpha \approx 22.7^\circ$ obtained from lattice QCD for the two $\eta_1$ states, the total widths are estimated to be $\Gamma_{\eta_1(1855)}=268(91)~\mathrm{MeV}$ and $\Gamma_{\eta_1(2200)}=435(154)~\mathrm{MeV}$. The former is compatible with the experimental width of $\eta_1(1855)$. Although many systematic uncertainties are not well controlled, these results are qualitatively informative for the experimental search for light hybrids.