QCD evolution equations from conformal symmetry

TL;DR

This paper presents a novel method to derive QCD evolution equations using conformal symmetry in a modified non-integer dimensional theory, enabling the calculation of two-loop evolution kernels for parton distributions.

Contribution

It introduces a technique leveraging conformal symmetry in non-integer dimensions to obtain complete evolution kernels in physical dimensions at higher perturbative orders.

Findings

Derived two-loop evolution equations for flavor-nonsinglet quark-antiquark operators.

Established a method to recover physical QCD evolution kernels from conformal symmetry considerations.

Enhanced the understanding of scale dependence in generalized parton distributions.

Abstract

QCD evolution equations in $\text{MS}$-like schemes can be recovered from the same equations in a modified theory, QCD in non-integer $d=4-2\epsilon$ dimensions, which enjoys exact scale and conformal invariance at the critical point. Restrictions imposed by the conformal symmetry of the modified theory allow one to obtain complete evolution kernels in integer (physical) dimensions at the given order of perturbation theory from the spectrum of anomalous dimensions added by the calculation of the special conformal anomaly at one order less. We use this technique to derive two-loop evolution equations for flavor-nonsinglet quark-antiquark light-ray operators that encode the scale dependence of generalized hadron parton distributions.