$\eta$ and $\eta'$ meson production in $J/\psi$ radiative decays from lattice QCD

TL;DR

This paper uses lattice QCD to compute the amplitudes of radiative decays of $J/ar{psi}$ into $ar{ ext{eta}}$ and $ar{ ext{eta}}'$ mesons, providing first-principles theoretical insights into these processes.

Contribution

First lattice QCD calculation of $J/ar{psi}$ radiative decay amplitudes to $ar{ ext{eta}}$ and $ar{ ext{eta}}'$ mesons, including transition form-factors across the timelike region.

Findings

Transition form-factors are lower than experimental values.

Optimized operators enable access to the $ar{ ext{eta}}'$ state.

Discrepancies suggest possible missing effects or systematic uncertainties.

Abstract

We report on the computation of amplitudes describing the radiative decay processes $J/\psi \to \gamma \, \eta$ and $J/\psi \to \gamma \, \eta'$ 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 $\eta'$, 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 $\eta'$ are found than those extracted from experimental data, and possible explanations for this observation are presented.