Abstract
In this paper we apply the method of characteristic identities to calculate the color factors of Feynman diagrams obtained by consecutive glueing identical pieces in non-Abelian gauge theories. The color factors of several ladder diagrams with an arbitrary number of loops are obtained for \(SU(N)\) and \(SO(N)\) gauge theories. These diagrams describe the scattering (via exchange of gluons) of two quarks, and the scattering of a quark and an antiquark, where the quarks and antiquarks transform, respectively, under the defining and contragredient to defining representations of the gauge groups mentioned. Universal expressions (based on the Vogel parametrisation) for the color factors of ladder diagrams in gluodynamics are obtained. These expressions are valid for all simple gauge Lie groups. Based on the universal formulas obtained, the idea of a universal analogue of the ’t Hooft’s \({1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-0em} N}\) expansion for all simple gauge Lie groups is formulated.
