A Compact Representation of the Three-Gluon Vertex

Abstract

The three-gluon vertex is a basic object of interest in nonabelian gauge theory. It contains important structural information, in particular on infrared divergences, and also figures prominently in the Schwinger-Dyson equations. At the one-loop level, it has been calculated and analyzed by a number of authors. Here we use the worldline formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation. The SUSY - related sum rule found by Binger and Brodsky follows from an off-shell extension of the Bern-Kosower replacement rules. We explain the relation of the structure of our representation to the low-energy effective action.

Comments: 6 pages, 1 figure. Talk given by N. Ahmadiniaz at the 3rd Young Researchers Workshop "Physics Challenges in the LHC Era", Frascati, May 7 and 10, 2012