Interactions of Reggeized Gluons in the Möbius Representation
J. Bartels, L. N. Lipatov, G. P. Vacca
TL;DR
This work shows that Möbius invariance of the BFKL Hamiltonian and the triple Pomeron vertex constrains reggeized-gluon interactions such that, in the large $N_c$ limit within the Möbius function space, the triple Pomeron vertex reduces to the BK kernel. Consequently, the BK equation for dipole density is recovered as a special case of the nonlinear fan-diagram evolution of BFKL Green's functions, providing a bridge between reggeon calculus and the dipole picture. The authors also compute $O(1/(N_c^2-1))$ corrections to the triple Pomeron vertex and outline a generalized BK-type evolution including next-to-leading $1/N_c$ effects, and propose a coupled system incorporating four-gluon states. This Möbius framework thus enables a systematic extension beyond leading order and beyond large-$N_c$ while preserving unitarity properties at high energy.
Abstract
We investigate consequences of the Möbius invariance of the BFKL Hamiltonian and of the triple Pomeron vertex. In particular, we show that the triple Pomeron vertex in QCD, when restricted to the large $N_c$ limit and to the space of Möbius functions, simplifies and reduces to the vertex used in the Balitsky-Kovchegov (BK) equation. As a result, the BK equation for the dipole density appears as a special case of the nonlinear evolution equation which sums the fan diagrams for BFKL Green's functions in the Möbius representation. We also calculate the corrections $O(1/(N_c^2-1)$ to the triple Pomeron vertex in the space of Möbius functions, and we present a generalization of the BK-equation in the next-to-leading order approximation in the $1/N_c$ expansion.