Inclusive gluon production in the dipole approach: AGK cutting rules

TL;DR

This paper extends the dipole model to include single gluon production, deriving non-linear evolution equations, confirming the dipole structure at all orders, and analyzing AGK cutting rules with new violations in gluon emission.

Contribution

It introduces a formalism that confirms the dipole structure for gluon production at all orders and derives modified AGK cutting rules, revealing violations in gluon emission cases.

Findings

Validates the adjoint dipole structure to all orders.

Derives non-linear evolution equations for non-diagonal cross sections.

Reveals violations of AGK rules in gluon production for single emissions.

Abstract

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 deriving and solving the non-linear evolution for the non-diagonal cross section of a dipole scattering off the target. The form of the solution to this equation restores the dipole interpretation for non-diagonal cross sections, that appear in gluon production. Using this formalism, we analyse 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.