<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>γ</mml:mi> <mml:mo>*</mml:mo> </mml:msup> <mml:mo stretchy="false">→</mml:mo> <mml:mi>η</mml:mi> <mml:mi>γ</mml:mi> </mml:math> and <mml:math xmlns:mml="htt

We use conformal symmetry to calculate the next to next to leading order (NNLO) anomalous dimension matrix (three loops) for flavor-singlet axial-vector QCD operators for spin <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>N</a:mi> <a:mo>≤</a:mo> <a:mn>8</a:mn> </a:math> from a set of gauge-invariant two-point correlation functions. Combining this result with the recent calculation of the two-loop coefficient functions, we carry out the calculation of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>γ</c:mi> <c:msup> <c:mi>γ</c:mi> <c:mo>*</c:mo> </c:msup> <c:mo stretchy="false">→</c:mo> <c:mi>η</c:mi> </c:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi>γ</f:mi> <f:msup> <f:mi>γ</f:mi> <f:mo>*</f:mo> </f:msup> <f:mo stretchy="false">→</f:mo> <f:msup> <f:mi>η</f:mi> <f:mo>′</f:mo> </f:msup> </f:math> form factors at large momentum transfers to the NNLO accuracy in perturbative QCD.