$1^{-+}$ Hybrid in $J/\psi$ Radiative Decays from Lattice QCD

Abstract

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 $m_{\eta_1}=2.23(4)$ GeV. If $\eta_1$ corresponds to the recently observed $\eta_1(1855)$ in the process $J/\psi\to \gamma\eta_1(1855)\to \gamma \eta\eta'$ 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 $\mathrm{Br}(\eta_1(1855)\to \eta\eta')\sim 4.3\%$.