Summing Pomeron loops in the dipole approach

TL;DR

This paper demonstrates that within a specific kinematic range, Pomeron loop summation simplifies to non-interacting Pomerons with renormalized interactions, leading to a geometrical scaling solution using an improved approximation.

Contribution

It introduces a method to sum Pomeron loops in the dipole approach by reducing the problem to non-interacting Pomerons with renormalized target interactions, providing a new analytical solution.

Findings

Derivation of a geometrical scaling solution for the simplified BFKL kernel.

Identification of overlapping singularities in the Pomeron calculus.

Proposed method to handle singularities in Pomeron loop summation.

Abstract

In this paper we argue that in the kinematic range given by $ 1 \ll \ln(1/\as^2) \ll \as Y \ll \frac{1}{\as}$, we can reduce the Pomeron calculus to the exchange of non-interacting Pomerons with the renormalized amplitude of their interaction with the target. Therefore, the summation of the Pomeron loops can be performed using the improved Mueller, Patel, Salam and Iancu approximation and this leads to the geometrical scaling solution. This solution is found for the simplified BFKL kernel. We reproduce the findings of Hatta and Mueller that there are overlapping singularities. We suggest a way of dealing with these singularities.