BFKL, BK and the infrared

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 ∼ 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 ∼ < 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 Λ −1 QCD . The latter issue is also commented below.

Color screening, absorption, and σ tot pp at LHC

“…At superhigh energies, E Lab > 10 4 − 10 5 GeV, the perturbative component starts taking over and its unitarization becomes a central issue. In [8,9,10] it was demonstrated that the non-linear, i.e., unitarity effects are very sensitive to the IR regularization which defines a transition between the nonperturbative and perturbative domains. Empirically, the bulk of the total cross section at E Lab ∼ 10 4 −10 5 GeV comes from the nonperturbative domain and our analysis suggests rather small, infrared cutoff for the perturbative contribution, R c = 0.26 fm.…”

“…absorption corrections to the BFKL evolution are described by the non-linear BK equation [6,7]. The strength of non-linear effects depends crucially on the IR cutoff R c [8,9,10]. Hence, one more issue we address in this communication is the role of the absorption corrections to σ pp tot and the non-linear dynamics of the perturbative component of pp-interactions at the LHC energies.…”