Evolution equations for leading-twist operators in high orders of perturbation theory can be restored from the spectrum of anomalous dimensions and the calculation of the special conformal anomaly at one order less using conformal symmetry of QCD at the Wilson-Fisher critical point at noninteger $d=4-2ϵ$ space-time dimensions. In this work, we generalize this technique to axial-vector operators. We calculate the corresponding three-loop evolution kernels in Larin’s scheme and derive explicit expressions for the finite renormalization kernel that describes the difference to the vector case to restore the conventional modified minimal subtraction scheme. The results are directly applicable to deeply virtual Compton scattering and the transition form factor ${\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}}^{*}\mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}\to \mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}$.

• Received 7 January 2021
• Accepted 22 April 2021

DOI:https://doi.org/10.1103/PhysRevD.103.094018

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society