One gluon, two gluon: multigluon production via high energy evolution

TL;DR

This work develops a generating-functional framework to compute inclusive multigluon production within the JIMWLK/KLWMIJ high-energy evolution, bridging from single to arbitrary gluon multiplicities. In the general theory, gluon emission is encoded by an operator ${ m O}_g$ and a higher-level evolution Hamiltonian $H_3$ that couples projectile and target degrees of freedom; the authors show that AGK cutting rules are violated for multigluon production due to multipole (beyond dipole) exchanges. In the physically tractable dipole limit, the problem reduces to a diagrammatic expansion with propagators for dipoles, quadrupoles, and their mixtures, allowing explicit recovery of the known single- and double-gluon results and clarifying where AGK rules hold or fail. To make progress beyond double gluons, the paper proposes a physically motivated ansatz for the unknown four-point fluctuation propagator $t$, enabling approximate numerical studies and guiding future refinements of multigluon observables in saturation physics.

Abstract

We develop an approach for calculating the inclusive multigluon production within the JIMWLK high energy evolution. We give a formal expression of multigluon cross section in terms of a generating functional for arbitrary number of gluons $n$. In the dipole limit the expression simplifies dramatically. We recover the previously known results for single and double gluon inclusive cross section and generalize those for arbitrary multigluon amplitude in terms of Feynman diagramms of Pomeron - like objects coupled to external rapidity dependent field $s(η)$. We confirm the conclusion that the AGK cutting rules in general are violated in multigluon production. However we present an argument to the effect that for doubly inclusive cross section the AGK diagramms give the leading contribution at high energy, while genuine violation only occurs for triple and higher inclusive gluon production. We discuss some general properties of our expressions and suggest a line of argument to simplify the approach further.

Figures (5)

• Figure 1: The propagator and the vertex $\lambda$
• Figure 2: Single inclusive gluon production
• Figure 3: Double inclusive gluon production
• Figure 4: Three- gluon production
• Figure 5: The "source" term $J$ in the gluon emission vertex.