<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>η</mml:mi> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>η

We present a first principles calculation within quantum chromodynamics (QCD) of the radiative decays of the J/ψ into the light pseudoscalar mesons η and η^{'}. 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/ψ→e^{+}e^{-}η^{(')}, through to the real photon point corresponding to J/ψ→γη^{(')}. 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 η^{'} appears as the first excited state with pseudoscalar isoscalar quantum numbers. We access it reliably by using variationally optimized operators, the use of which also improves the purity of the J/ψ and η 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 η^{'} over the η in this process, and suggest that the demonstrated lattice technology is suitable for future calculations considering processes in which light meson resonances are produced.