BFKL, BK and the Infrared

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.