Interactions of Reggeized Gluons in the Möbius Representation

Details Interactions of Reggeized Gluons in the Möbius Representation Interactions of Reggeized Gluons in the Möbius Representation

2004-04-13

arxiv.org/abs/hep-ph/0404110v1

Nucl.Phys.B706:391-410,2005

Physics

High Energy Physics

High Energy Physics - Phenomenology

19 pages, 1 figure

Scientific paper

10.1016/j.nuclphysb.2004.10.008

We investigate consequences of the M\"obius 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 M\"obius 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 M\"obius representation. We also calculate the corrections $O(1/(N_c^2-1)$ to the triple Pomeron vertex in the space of M\"obius functions, and we present a generalization of the BK-equation in the next-to-leading order approximation in the $1/N_c$ expansion.

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