$1^{-+}$ 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 $J/\psi \to \gamma {\eta }_1(1855)\to \gamma \eta {\eta }^{\prime }$ 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 $\mathrm{Br}({\eta }_1(1855)\to \eta {\eta }^{\prime })\sim 4.3\%$.

Comments: v2: Published in prd