NNLO anomalous dimension matrix for twist-two flavor-singlet operators

TL;DR

This paper calculates the next-to-next-to-leading order (NNLO) anomalous dimension matrix for flavor-singlet twist-two operators in QCD, utilizing conformal symmetry at the Wilson-Fisher critical point to simplify computations.

Contribution

It introduces a method to derive off-diagonal anomalous dimensions from two-point functions using conformal symmetry, providing explicit NNLO results for spin N ≤ 8.

Findings

Computed NNLO anomalous dimension matrix for flavor-singlet operators.

Demonstrated the use of conformal symmetry to simplify calculations.

Provided explicit results for spins up to N=8.

Abstract

Conformal symmetry of QCD is restored at the Wilson-Fisher critical point in noninteger $4-2\epsilon$ space-time dimensions. Correlation functions of multiplicatively renormalizable operators with different anomalous dimensions at the critical point vanish identically. We show that this property allows one to calculate off-diagonal parts of the anomalous dimension matrices for leading-twist operators from a set of two-point correlation functions of gauge-invariant operators which can be evaluated using standard computer algebra techniques. As an illustration, we present the results for the NNLO anomalous dimension matrix for flavor-singlet QCD operators for spin $N\le 8$.