Uncovering the triple pomeron vertex from Wilson line formalism

TL;DR

The paper addresses the computation of the triple $\mathbb{P}$omeron vertex, including planar and non-planar parts, within the Wilson line framework of high-energy QCD. It combines diffractive (Keldysh) and fan-diagram (BK/JIMWLK) approaches, performing a $2g$-order linearization and projecting onto BFKL Green functions and conformal blocks to construct the vertex $V^{1\mathbb{P}\to 2\mathbb{P}}$. The resulting expression, formulated in the Moebius representation and using conformal eigenfunctions $E_{h\bar h}$, matches the Extended Generalized Leading Log Approximation (EGLLA) results from reggeon calculus up to normalization, validating the Wilson line method for multi-Pomeron unitarization. The work paves the way for deriving higher-order vertices and other exchanges (e.g., Odderons) within the same formalism, with potential applications to unitarization schemes in high-energy scattering.

Abstract

We compute the triple pomeron vertex from the Wilson line formalism, including both planar and non-planar contributions, and get perfect agreement with the result obtained in the Extended Generalized Logarithmic Approximation based on reggeon calculus.

Figures (2)

• Figure 1: A typical diagram contributing to the triple $\mathbb{P}$omeron vertex $V,$ with three 4-gluon Green functions (denoted as $\tilde{\Psi}$ and $\tilde{\Psi}'$ in the Moebius representation) at $g^2$ order. This exhibits explicitly the amputation of the above Green function from below.
• Figure 2: a) Configuration of planar diagrams. b) Configuration of non-planar diagrams.