Inclusive gluon production in the dipole approach: Abramovskii-Gribov- Kancheli (AGK) cutting rules

We consider single gluon production in the dipole model and reproduce the result of Kovchegov and Tuchin for the adjoint (gluonic) dipole structure of the inclusive cross section. We show the validity of the adjoint dipole structure to any order of evolution by deriving and solving the nonlinear evolution for the nondiagonal cross section of a dipole scattering off the target. The form of the solution to this equation restores the dipole interpretation for nondiagonal cross sections that appear in gluon production. Using this formalism, we analyze the single inclusive production cross section in terms of the contributions of different multiplicities, and we derive the Abramovskii-Gribov-Kancheli (AGK) cutting rules for two-Pomeron exchange. The cutting rules, which were found in this formalism, fully reproduce the original AGK rules for the total cross section. However, for the case of gluon production, the AGK rules are violated already for one-gluon emission from the vertex.