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

We report on the computation of amplitudes describing the radiative decay processes $J\mathrm{/}\psi \to \gamma \eta$ and $J\mathrm{/}\psi \to \gamma {\eta }^{\mathrm{\prime }}$ 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 ${\eta }^{\mathrm{\prime }}$, 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 $J\mathrm{/}\psi \to e^{+}{e}^{-}{\eta }^{(\mathrm{\prime })}$. Significantly lower magnitudes of transition form-factor for both the $\eta$ and ${\eta }^{\mathrm{\prime }}$ are found than those extracted from experimental data, and possible explanations for this observation are presented.