Twist decomposition of nonlocal light-cone operators II: General tensors of 2nd rank

TL;DR

This paper extends a group theoretical method to decompose nonlocal light-cone operators of arbitrary rank into definite twist components, crucial for understanding higher twist effects in quantum chromodynamics.

Contribution

It applies the twist decomposition procedure to second rank tensors and extends the results to trilocal operators, advancing the analysis of higher twist distribution amplitudes.

Findings

Decomposition of bilocal gluon operators into twists 2 to 6.

Extension of twist decomposition to trilocal operators like three-gluon and four-quark operators.

Development of harmonic tensor polynomials for second rank tensors in arbitrary dimensions.

Abstract

A group theoretical procedure, introduced earlier (hep-th/9901090), to decompose bilocal light-ray operators into (harmonic) operators of definite twist is applied to the case of arbitrary 2nd rank tensors. As a generic example the bilocal gluon operator is considered which gets contributions of twist-2 up to twist-6 from four different symmetry classes characterized by conrresponding Young tableaus; also the twist decomposition of the related vector and scalar operators is considered. In addition, we extend these reselts to various trilocal light-ray operators, like the Shuryak-Vainshtein, the three-gluon and the four-quark operators, which are required for the consideration of higher twist distribution amplitudes. The present results rely on the knowledge of harmonic tensor polynomials of any order n which habe been determined up to the case of 2nd rank symmetric tensors for arbitrary space-time dimension.