# Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics

## TL;DR

This paper computes the three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics using conformal symmetry, providing explicit kernels and anomalous dimensions relevant for QCD distributions.

## Contribution

It presents the first three-loop (NNLO) calculation of the evolution kernel for flavor-nonsinglet operators in off-forward kinematics, including explicit expressions and anomalous dimensions.

## Key findings

- Derived the three-loop evolution kernel in coordinate space.
- Provided explicit anomalous dimensions for operators up to seven derivatives.
- Applicable to renormalization of pion distribution amplitudes and generalized parton distributions.

## Abstract

Using the approach based on conformal symmetry we calculate the three-loop (NNLO) contribution to the evolution equation for flavor-nonsinglet leading twist operators in the $\overline{\text{MS}}$ scheme. The explicit expression for the three-loop kernel is derived for the corresponding light-ray operator in coordinate space. The expansion in local operators is performed and explicit results are given for the matrix of the anomalous dimensions for the operators up to seven covariant derivatives. The results are directly applicable to the renormalization of the pion light-cone distribution amplitude and flavor-nonsinglet generalized parton distributions.