$\eta$ and ${\eta }^{\prime }$ meson production in $J/\psi$ radiative decays from lattice QCD

Abstract

We report on the computation of amplitudes describing the radiative decay processes $J/\psi \to \gamma \eta$ and $J/\psi \to \gamma {\eta }^{\prime }$ from first principles via lattice QCD. Using lattices with two degenerate flavors of light quark and a heavier strange quark where $m_{\pi }\sim 391$ MeV, we compute three-point correlation functions using optimized meson operators with a range of momenta. The use of optimized operators allows access to the ${\eta }^{\prime }$, even though it appears as an excited state, lying above the ground-state $\eta$ in the isoscalar pseudoscalar channel. Statistically precise signals are obtained in this disconnected process by averaging over large numbers of kinematically equivalent correlators. We determine transition form-factors as a function of photon virtuality across the timelike region, which describe also the 'Dalitz' processes $J/\psi \to e^{+}{e}^{-}{\eta }^{(\prime )}$. Significantly lower magnitudes of transition form-factor for both the $\eta$ and ${\eta }^{\prime }$ are found than those extracted from experimental data, and possible explanations for this observation are presented.