On the behaviour of single scale hard small $x$ processes in QCD near the black disc limit

Abstract

We argue that at sufficiently small Bjorken $x$ where pQCD amplitude rapidly increases with energy and violates probability conservation the shadowing effects in the single-scale small $x$ hard QCD processes can be described by an effective quantum field theory of interacting quasiparticles. The quasiparticles are the perturbative QCD ladders. We find, within the WKB approximation, that the smallness of the QCD coupling constant ensures the hierarchy among many-quasiparticle interactions evaluated within physical vacuum and in particular, the dominance in the Lagrangian of the triple quasiparticle interaction. It is explained that the effective field theory considered near the perturbative QCD vacuum contains a tachyon relevant for the divergency of the perturbative QCD series at sufficiently small $x$. We solve the equations of motion of the effective field theory within the WKB approximation and find the physical vacuum and the transitions between the false (perturbative) and physical vacua. Classical solutions which dominate transitions between the false and physical vacua are kinks that cannot be decomposed into perturbative series over the powers of $α_s$. These kinks lead to color inflation and the Bose-Einstein condensation of quasiparticles. The account of the quantum fluctuations around the WKB solution reveals the appearance of the "massless" particles-- "phonons". It is explained that "phonons" are relevant for the black disc behaviour of small $x$ processes, leading to a Froissart rise of the cross-section. The condensation of the ladders produces a color network occupying a "macroscopic" longitudinal volume. We discuss briefly the possible detection of new QCD effects.