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

Abstract

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 ${\mathrm{U}}_{\mathrm{A}}(1)$ 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 ${\mathrm{U}}_{\mathrm{A}}(1)$ anomaly and flavor singlet-octet mixing angle $\theta =-24.5^{\circ }$, the production rates for the physical $\eta$ and ${\eta }^{\prime }$ 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.

Comments: 6 pages, 4 figures, 2 tables