Evolution kernels of skewed parton distributions: method and two-loop results

TL;DR

This paper introduces a new formalism for calculating two-loop evolution kernels of skewed parton distributions in QCD, leveraging conformal symmetry and supersymmetry constraints to simplify complex computations.

Contribution

It provides explicit two-loop flavor singlet evolution kernels using a novel approach that avoids direct multiloop calculations by exploiting symmetry principles.

Findings

Derived the conformal symmetry breaking part of the kernels.

Reconstructed the symmetric part from known splitting functions.

Validated the approach with explicit two-loop results.

Abstract

We present a formalism and explicit results for two-loop flavor singlet evolution kernels of skewed parton distributions in the minimal subtraction scheme. This approach avoids explicit multiloop calculations in QCD and is based on the known pattern of conformal symmetry breaking in this scheme as well as constraints arising from the graded algebra of the $\cN = 1$ super Yang-Mills theory. The conformal symmetry breaking part of the kernels is deduced from commutator relations between scale and special conformal anomalies while the symmetric piece is recovered from the next-to-leading order splitting functions and $\cN = 1$ supersymmetry relations.