Three-loop off-forward evolution kernel for axial-vector operators in Larin's scheme

TL;DR

This paper derives three-loop evolution kernels for axial-vector operators in QCD using conformal symmetry techniques, providing explicit expressions relevant for high-precision predictions in processes like deeply-virtual Compton scattering.

Contribution

It extends the conformal symmetry approach to axial-vector operators and calculates the three-loop kernels in Larin's scheme, including the finite renormalization to the bcb5bcm scheme.

Findings

Derived explicit three-loop evolution kernels for axial-vector operators.

Provided finite renormalization kernel for scheme conversion.

Results applicable to high-precision QCD processes like DVCS.

Abstract

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 non-integer $d=4-2\epsilon$ 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 ${\overline{\mathrm{MS}}}$-scheme. The results are directly applicable to deeply-virtual Compton scattering and the transition form factor $\gamma^*\gamma\to\pi$.