BFKL, BK and the Infrared

TL;DR

This paper investigates the impact of infrared regularization on small-x gluon density evolution, finding that non-linear effects are weak with a perturbative IR cutoff but more significant with softer IR cutoffs.

Contribution

It clarifies how different IR regularizations influence non-linear effects in small-x gluon evolution, highlighting the relative weakness of these effects with perturbative IR scales.

Findings

Weak non-linear effects (~10%) with perturbative IR cutoff R_c=0.26 fm.

More pronounced non-linear effects with softer IR regularization.

BFKL description remains effective over a wide range of x and Q^2.

Abstract

The perturbative non-linear (NL) effects in the small-$x$ evolution of the gluon densities depend crucially on the infrared (IR) regularization. The IR regulator, $R_c$, is determined by the scale of the non-perturbative fluctuations of QCD vacuum. From the instanton models and from the lattice $R_c\sim 0.3$ fm. For perturbative gluons with the propagation length $R_c= 0.26$ fm the linear BFKL gives a good description of the proton structure function $F_2(x,Q^2)$ in a wide range of $x$ and $Q^2$. The NL effects turn out to be rather weak and amount to the 10% correction to $F_2(x,Q^2)$ for $x\lsim 10^{-5}$. Much more pronounced NL effects were found in the non-linear model, described in the literature, with a very soft IR regularization corresponding to the IR cutoff at $\simeq \Lambda^{-1}_{QCD}$. The latter issue is also commented below.