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

We report on the computation of amplitudes describing the radiative decay processes <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>J</a:mi><a:mo>/</a:mo><a:mi>ψ</a:mi><a:mo stretchy="false">→</a:mo><a:mi>γ</a:mi><a:mi>η</a:mi></a:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>J</d:mi><d:mo>/</d:mo><d:mi>ψ</d:mi><d:mo stretchy="false">→</d:mo><d:mi>γ</d:mi><d:msup><d:mi>η</d:mi><d:mo>′</d:mo></d:msup></d:math> from first principles via lattice quantum chromodynamics (QCD). Using lattices with two heavier than physical degenerate flavors of light quark where <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>m</g:mi><g:mi>π</g:mi></g:msub><g:mo>∼</g:mo><g:mn>391</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>MeV</g:mi></g:math>, and a strange quark tuned to approximately the physical value, we compute three-point correlation functions using optimized meson operators with a range of momenta. The use of optimized operators allows access to the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>η</i:mi><i:mo>′</i:mo></i:msup></i:math>, even though it appears as an excited state, lying above the ground-state <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>η</k:mi></k:math> 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>J</m:mi><m:mo>/</m:mo><m:mi>ψ</m:mi><m:mo stretchy="false">→</m:mo><m:msup><m:mi>e</m:mi><m:mo>+</m:mo></m:msup><m:msup><m:mi>e</m:mi><m:mo>−</m:mo></m:msup><m:msup><m:mi>η</m:mi><m:mrow><m:mo stretchy="false">(</m:mo><m:mo>′</m:mo><m:mo stretchy="false">)</m:mo></m:mrow></m:msup></m:math>. Significantly lower magnitudes of transition form factor for both the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>η</r:mi></r:math> and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msup><t:mi>η</t:mi><t:mo>′</t:mo></t:msup></t:math> are found than those extracted from experimental data, and possible explanations for this observation are presented.