Baryon Operators of Higher Twist in QCD and Nucleon Distribution Amplitudes

TL;DR

This paper develops a conformal symmetry-based framework for higher-twist baryon operators in QCD, analyzes their renormalization, and applies the results to nucleon distribution amplitudes relevant for exclusive reactions.

Contribution

It introduces a comprehensive conformal operator basis for all twists and provides the first complete one-loop renormalization analysis of twist-4 operators in QCD.

Findings

The evolution equation for certain three-quark operators is integrable.

The spectrum of anomalous dimensions matches the energy spectrum of a specific spin chain.

Provides an all-order expression for twist-3 contributions to twist-4 nucleon distribution amplitudes.

Abstract

We develop a general theoretical framework for the description of higher-twist baryon operators which makes maximal use of the conformal symmetry of the QCD Lagrangian. The conformal operator basis is constructed for all twists. The complete analysis of the one-loop renormalization of twist-4 operators is given. The evolution equation for three-quark operators of the same chirality turns out to be completely integrable. The spectrum of anomalous dimensions coincides in this case with the energy spectrum of the twist-4 subsector of the SU(2,2) Heisenberg spin chain. The results are applied to give a general classification and calculate the scale dependence of subleading twist-4 nucleon distribution amplitudes that are relevant for hard exclusive reactions involving a helicity flip. In particular we find an all-order expression (in conformal spin) for the contributions of geometric twist-3 operators to the (light-cone) twist-4 nucleon distribution amplitudes, which are usually referred to as Wandzura-Wilczek terms.