The 13th International Workshop on e+e- collisions from Phi to Psi

We present the first theoretical prediction of the production rate of $1^{-+}$ light hybrid meson $\eta_1$ in $J/\psi$ radiative decays. In the $N_f = 2$ lattice QCD formalism with the pion mass $m_\pi\approx 350$ MeV, the related electromagnetic multipole form factors are extracted from the three-point functions that involve necessarily quark annihilation diagrams, which are calculated through the distillation method. The partial width of $J/\psi \to \gamma \eta_1$ is determined to be $2.29(77)~\mathrm{eV}$ at the $\eta_1$ mass $m_{\eta_1} = 2.23(4)~\rm GeV$. If $\eta_1$ corresponds to the recently observed $\eta_1 (1855)$ in the process $J/\psi \to \gamma \eta_1 (1855) \to \gamma \eta \eta^\prime$ by BESIII, then the branching fraction $\mathrm{Br}(J/\psi \to \gamma \eta_1(1855))$ is estimated to be $6.2(2.2) \times 10^{-5}$, which implies $\mathrm{Br}(\eta_1(1855)\to \eta\eta^\prime)\sim 4.3\%$.