$\eta$ and $\eta'$ production in $J/\psi$ radiative decays from quantum chromodynamics

TL;DR

This paper presents a pioneering lattice QCD calculation of $J/3$ radiative decays into $1$ and $1'$ mesons, providing detailed form factors and insights into meson production mechanisms.

Contribution

First lattice QCD calculation of $J/3$ radiative decays into $1$ and $1'$ with improved techniques and analysis of transition form factors across photon virtualities.

Findings

Enhanced $1'$ production observed over $1$.

Reliable extraction of transition form factors at multiple kinematic points.

Demonstration of lattice technology suitability for light meson resonance processes.

Abstract

We present a first principles calculation within quantum chromodynamics (QCD) of the radiative decays of the $J/\psi$ into the light pseudoscalar mesons $\eta$ and $\eta'$. Within a lattice computation we obtain the transition form-factors as a function of photon virtuality from the timelike region, accessible experimentally via the 'Dalitz' decay $J/\psi \to e^+ e^-\, \eta^{(\prime)} $, through to the real photon point corresponding to $J/\psi \to \gamma\, \eta^{(\prime)} $. This is the first calculation in lattice QCD with two (heavier than physical) degenerate flavors of light quark and a heavier strange quark, in which the $\eta'$ appears as the first-excited state with pseudoscalar isoscalar quantum numbers. We access it reliably by using variationally optimized operators, use of which also improves the purity of the $J/\psi$ and $\eta$ signals, reducing systematic uncertainties. High quality results at a large number of kinematic points are obtained in a typically noisy disconnected process by using a novel correlator averaging procedure. Our results show the expected enhanced production of the $\eta'$ over the $\eta$ in this process, and suggest that the demonstrated lattice technology is suitable for future calculations considering processes in which light meson resonances are produced.