On factorisation at small x

TL;DR

The paper investigates whether factorisation survives small-x diffusion by extending collinear-model insights to the full BFKL equation with running coupling. It introduces a two-pronged approach: analytical extension via a higher-pole collinear model and a numerical method to extract effective anomalous dimensions in the full LL BFKL framework. The key finding is that factorisation can persist even when higher-twist terms grow at small x, because the mechanism tying the Pomeron to G_omega does not induce non-factorisable singularities in the anomalous dimension. This supports the use of factorisation-based predictions at small x and provides a practical method to quantify effective anomalous dimensions in the presence of non-perturbative effects.

Abstract

We investigate factorisation at small x using a variety of analytical and numerical techniques. Previous results on factorisation in collinear models are generalised to the case of the full BFKL equation, and illustrated in the example of a collinear model which includes higher twist terms. Unlike the simplest collinear model, the BFKL equation leads to effective anomalous dimensions containing higher-twist pieces which grow as a (non-perturbative) power at small x. While these pieces dominate the effective splitting function at very small x they do not lead to a break-down of factorisation insofar as their effect on the predicted scaling violations remains strongly suppressed.