QCD evolution equations from conformal symmetry

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.

8 pages, contribution to the proceedings of the conferences "Loops and Legs in Quantum Field Theory", April 27 - May 02, 2014, Weimar, Germany, and "QCD Evolution Workshop", May 12-16, 2014, Santa Fe, USA

References in corpus (11)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• The Uses of Conformal Symmetry in QCD
• Baryon Distribution Amplitudes in QCD
• Predictions from conformal algebra for the deeply virtual Compton scattering
• Evolution kernels of skewed parton distributions: method and two-loop results
• The equivalence of the SU(N) Yang Mills Theory with a Purely Fermionic Model
• Evolution equations beyond one loop from conformal symmetry
• Determination of the anomalous dimension of gluonic operators in deep inelastic scattering at O(1/N_f)
• Quark mass anomalous dimension at O(1/N_f^2) in QCD
• Two-loop evolution equations for light-ray operators