Radiative Decay Width of $J/\psi\to \gamma \eta_{(2)}$ from $N_f=2$ Lattice QCD

The large radiative production rate for pseudoscalar mesons in the $J/\psi$ radiative decay remains elusive. We present the first lattice QCD calculation of partial decay width of $J/\psi$ radiatively decaying into $\eta_{(2)}$, the $\mathrm{SU(2)}$ flavor singlet pseudoscalar meson, which confirms QCD $\mathrm{U_A(1)}$ anomaly enhancement to the coupling of gluons with flavor singlet pseudoscalar mesons. The lattice simulation is carried out using $N_f=2$ lattice QCD gauge configurations at the pion mass $m_{\pi} \approx 350$ MeV. In particular, the distillation method has been utilized to calculate light quark loops. The results are reported here with the mass $m_{\eta_{(2)}}= 718(8)$ MeV and the decay width $\Gamma(J/\psi\to\gamma \eta_{(2)})=0.385(45)$ keV. By assuming the dominance of $\mathrm{U_A(1)}$ anomaly and flavor singlet-octet mixing angle $\theta=-24.5^\circ$, the production rates for the physical $\eta$ and $\eta'$ in $J/\psi$ radiative decay are predicted to be $1.15(14)\times 10^{-3}$ and $4.49(53)\times 10^{-3}$, respectively, which agree well with the experimental measurement data. Our study manifests the potential of lattice QCD studies on the light hadron production in $J/\psi$ radiative decays.