Triple pomeron vertex in the limit Nc to infinity

TL;DR

In the $N_c\to\infty$ limit, the hard pomeron diffractive amplitude is shown to be dominated by a single BFKL pomeron, with subleading contributions decomposing into double pomeron exchange (DPE) and triple pomeron interaction (TPI). A key result is that the DPE can be replaced by an equivalent TPI term, causing the triple-pomeron vertex to align with the finite-$N_c$ and Mueller–dipole formulations; both the vertex $G(1,2,3)$ and the derived three-pomeron vertex $Z$ are conformal invariant. By projecting onto the conformal basis, the TPI term matches the Mueller dipole double-dipole density up to normalization, while higher-order dipole densities reduce to fan diagrams with only triple-pomeron coupling, predicting the absence of higher $1\to k$ couplings in this regime. The work unifies different approaches to high-energy diffractive scattering, clarifies the role of the triple-pomeron vertex, and highlights a notable gap between the s-channel unitarity framework and the dipole picture that merits further investigation.

Abstract

In the hard pomeron theory with the number of colours Nc in the infinity limit the diffractive amplitude obtained in [3] is compared with the results found for Nc=3 in [1] and in the dipole approach in [5]. It is shown that the double pomeron exchange contribution can be substituted by an equivalent triple pomeron interaction term. After such a substitution the triple pomeron vertices in [1,3,5] essentially coincide. It is demonstrated that, in any form, the triple pomeron vertex is conformal invariant. It is also shown that higher order densities in the dipole approach do not involve 1 to k pomeron verteces with k>2 but are rather given by a set of pomeron fan diagrams with only a triple pomeron coupling.