Decomposition of nonlocal light-cone operators into harmonic operators of definite twist

TL;DR

This paper develops a method to decompose nonlocal light-cone operators in QCD into harmonic operators of definite twist, aiding the analysis of their matrix elements and conformal properties.

Contribution

It introduces a group-theoretical approach to decompose bilocal light-ray operators into traceless harmonic tensor operators with fixed twist and spin.

Findings

Operators are expressed as harmonic tensor functions with definite twist.

The method clarifies the group theoretical structure of light-cone operators.

Applications include analysis of nonforward matrix elements and conformal generalizations.

Abstract

Bilocal light-ray operators which are Lorentz scalars, vectors or antisymmetric tensors, and which appear in various hard scattering QCD processes, are decomposed into operators of definite twist. These operators are harmonic tensor functions and their Taylor expansion consists of (traceless) local light-cone operators with span irreducible representations of the Lorentz group with definite spin j and common geometric twist (= dimension - spin). Some applications concerning the nonforward matrix elements of these operators and the generalization fo conformal light-cone operators of definite twist is considered. The group theoretical background of the method has been made clear.