Two-loop evolution equations for flavor-singlet light-ray operators

Abstract

QCD in non-integer $d=4-2\epsilon$ space-time dimensions enjoys conformal invariance at the special fine-tuned value of the coupling. Counterterms for composite operators in minimal subtraction schemes do not depend on $\epsilon$ by construction, and therefore the renormalization group equations for composite operators in physical (integer) dimensions inherit conformal symmetry. This observation can be used to restore the complete evolution kernels that take into account mixing with the operators containing total derivatives from their eigenvalues (anomalous dimensions). Using this approach we calculate the two-loop (NLO) evolution kernels for the leading twist flavor-singlet operators in the position space (light-ray operator) representation. As the main result of phenomenological relevance, in this way we are able to confirm the evolution equations of flavor-singlet generalized hadron parton distributions derived earlier by Belitsky and Müller using a different approach.

27 pages, 4 figures

References in corpus (18)

• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Parton Physics on Euclidean Lattice
• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Exclusive processes in position space and the pion distribution amplitude
• Anomalous dimensions of high-spin operators beyond the leading order
• Broken conformal invariance and spectrum of anomalous dimensions in QCD
• A Critical Appraisal and Evaluation of Modern PDFs
• Scale dependence of twist-three contributions to single spin asymmetries
• Evolution kernels of skewed parton distributions: method and two-loop results
• Operator product expansion in QCD in off-forward kinematics: Separation of kinematic and dynamical contributions
• Restricted conformal invariance in QCD and its predictive power for virtual two-photon processes
• A detailed next-to-leading order QCD analysis of deeply virtual Compton scattering observables
• Next-to-leading order evolution of twist-two conformal operators: The abelian case
• Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics
• A next-to-leading order QCD analysis of deeply virtual Compton scattering amplitudes
• Evolution equations beyond one loop from conformal symmetry
• Two-loop conformal generators for leading-twist operators in QCD
• Two-loop evolution equations for light-ray operators

Cited by in corpus (7)

• Complete Matching for Quasi-distribution Functions in Large Momentum Effective Theory
• Two-loop evolution equation for the B-meson distribution amplitude
• Two-loop coefficient function for DVCS: Vector contributions
• An introductory lecture on Generalised Parton Distributions
• Heavy quark expansion for heavy-light light-cone operators
• Three-loop off-forward evolution kernel for axial-vector operators in Larin's scheme
• Revisiting evolution equations for generalised parton distributions