$η$ and $η'$ meson production in $J/ψ$ radiative decays from lattice QCD

Abstract

We report on the computation of amplitudes describing the radiative decay processes $J/ψ\to γ\, η$ and $J/ψ\to γ\, η'$ from first principles via lattice QCD. Using lattices with two degenerate flavors of light quark and a heavier strange quark where $m_π\sim 391$ 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 $η'$, even though it appears as an excited state, lying above the ground-state $η$ 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 $J/ψ\to e^+ e^- \, η^{(\prime)}$. Significantly lower magnitudes of transition form-factor for both the $η$ and $η'$ are found than those extracted from experimental data, and possible explanations for this observation are presented.