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

Abstract

A group theoretical procedure, introduced earlier in 20, 21, 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 corresponding Young tableaux; also the twist decomposition of the related vector and scalar operators is considered. In addition, we extend these results 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 have been determined up to the case of 2nd rank symmetric tensor for arbitrary space-time dimension.