Towards a symmetric approach to high energy evolution: generating functional with Pomeron loops

TL;DR

This paper develops a symmetric, probabilistic description of high-energy QCD evolution by reformulating dipole dynamics through a generating functional that includes both dipole emission and recombination. The authors introduce explicit dipole vertices for 1\rightarrow2, 2\rightarrow1, and 2\rightarrow3 transitions, building a kernel chi that acts like a Hamiltonian for a two-dimensional dipole field theory and summing BFKL Pomeron loops within a Balitsky-type framework. A key result is the demonstration that Pomeron interactions can be incorporated in a controlled way, with 1/N_c^2 corrections captured by the new vertices and a discussion of dynamical dipole correlations that lead to a BLV-like modification of the BK equation. The framework provides a probabilistic Reggeon-calculus perspective on high-energy scattering, potentially enabling more accurate descriptions of saturation effects and nucleus–nucleus collisions while clarifying the role of Pomeron loops beyond JIMWLK/BK phenomenology.

Abstract

We derive an evolution equation for the generating functional which accounts for processes for both gluon emission and recombination. In terms of color dipoles, the kernel of this equation describes evolution as a classical branching process with conserved probabilities. The introduction of dipole recombination allows one to obtained closed loops during the evolution, which should be interpreted as Pomeron loops of the BFKL Pomerons. In comparison with the emission, the dipole recombination is formally $1/N_c^2$ suppressed. This suppression, nevertheless, is compensated at very high energies when the scattering amplitude tends to its unitarity bound.

Figures (5)

• Figure 1: The lowest order diagrams for $\Gamma(2\,\rightarrow\, 1)$ (Fig. \ref{['v12ba']}-a) and for $\Gamma(1\,\rightarrow\, 2)$ (Fig. \ref{['v12ba']}-b) .
• Figure 2: The first enhanced diagram and the vertex of annihilation of two dipoles into one dipole.
• Figure 3: The process $x_{12} + x_{34} \,\rightarrow\, x_{14} + x_{35} + x_{45}$.
• Figure 4: Pomeron interactions described by Eq. (\ref{['C2']}).
• Figure 5: The typical Pomeron diagrams for interactions described by Eq. (\ref{['C2']}). Fig. \ref{['pomint']}-a describes the GLR approach GLR which for Eq. (\ref{['C2']}) coincide with the Balitsky-JIMWLK approach JIMWLKB; Fig. \ref{['pomint']}-b corresponds to Iancu-Mueller approachIM which suggests the way out of the JIMWLK approach and can be justified in limited region of energy. Fig. \ref{['pomint']}-c shows the general type of the diagrams that can be summed in the framework of the approach based on Eq. (\ref{['C2']}). Fig. \ref{['pomint']}-d are diagrams that we need to sum for nucleus-nucleus interaction at high energy.